git: drawterm

Info  •  Files  •  Log  •  Branches

sync with 9front libsec and devtls, c2name() -> chanpath()

--- a/include/libsec.h

+++ b/include/libsec.h

@@ -23,7 +23,7 @@

 	ulong	ekey[4*(AESmaxrounds + 1)];	/* encryption key */

 	ulong	dkey[4*(AESmaxrounds + 1)];	/* decryption key */

 	uchar	ivec[AESbsize];			/* initialization vector */

-	uchar	mackey[3 * AESbsize];		/* 3 XCBC mac 96 keys */

+	uchar	mackey[3 * AESbsize];	/* 3 XCBC mac 96 keys */

 };

 /* block ciphers */

@@ -36,6 +36,20 @@

 void	setupAESXCBCstate(AESstate *s);

 uchar*	aesXCBCmac(uchar *p, int len, AESstate *s);

+

+typedef struct AESGCMstate AESGCMstate;

+struct AESGCMstate

+{

+	AESstate a;

+

+	ulong	H[4];

+	ulong	M[16][256][4];

+};

+

+void	setupAESGCMstate(AESGCMstate *s, uchar *key, int keylen, uchar *iv, int ivlen);

+void	aesgcm_setiv(AESGCMstate *s, uchar *iv, int ivlen);

+void	aesgcm_encrypt(uchar *dat, ulong ndat, uchar *aad, ulong naad, uchar tag[16], AESGCMstate *s);

+int	aesgcm_decrypt(uchar *dat, ulong ndat, uchar *aad, ulong naad, uchar tag[16], AESGCMstate *s);

 /*

  * Blowfish Definitions

--- a/kern/chan.c

+++ b/kern/chan.c

@@ -48,7 +48,7 @@

 char*

-c2name(Chan *c)		/* DEBUGGING */

+chanpath(Chan *c)

 {

 	if(c == nil)

 		return "<nil chan>";

--- a/kern/devfs-posix.c

+++ b/kern/devfs-posix.c

@@ -65,7 +65,7 @@

 	c->aux = uif;

 	c->dev = devno++;

 	c->qid.type = QTDIR;

-/*print("fsattach %s\n", c2name(c));*/

+/*print("fsattach %s\n", chanpath(c));*/

 	return c;

 }

@@ -169,7 +169,7 @@

 	int m, isdir;

 	Ufsinfo *uif;

-/*print("fsopen %s\n", c2name(c));*/

+/*print("fsopen %s\n", chanpath(c));*/

 	m = mode & (OTRUNC|3);

 	switch(m) {

 	case 0:

@@ -299,7 +299,7 @@

 	int fd, r;

 	Ufsinfo *uif;

-/*print("fsread %s\n", c2name(c));*/

+/*print("fsread %s\n", chanpath(c));*/

 	if(c->qid.type & QTDIR)

 		return fsdirread(c, va, n, offset);

@@ -503,7 +503,7 @@

 	struct stat stbuf;

 	Ufsinfo *uif;

-/*print("fsdirread %s\n", c2name(c));*/

+/*print("fsdirread %s\n", chanpath(c));*/

 	i = 0;

 	uif = c->aux;

--- a/kern/devfs-win32.c

+++ b/kern/devfs-win32.c

@@ -155,7 +155,7 @@

 {

 	char *s, *t;

-	s = c2name(c);

+	s = chanpath(c);

 	if((t = strrchr(s, '/')) == nil)

 		return s;

 	if(t[1] == 0)

--- a/kern/devip.c

+++ b/kern/devip.c

@@ -396,7 +396,7 @@

 	uchar ip[IPaddrlen];

 	char buf[128], *p;

-/*print("ipread %s %lux\n", c2name(ch), (long)ch->qid.path);*/

+/*print("ipread %s %lux\n", chanpath(ch), (long)ch->qid.path);*/

 	p = a;

 	switch(TYPE(ch->qid)) {

 	default:

--- a/kern/devmnt.c

+++ b/kern/devmnt.c

@@ -1152,12 +1152,12 @@

 	/* This routine is mostly vestiges of prior lives; now it's just sanity checking */

 	if(c->mchan == nil)

-		panic("mntchk 1: nil mchan c %s\n", c2name(c));

+		panic("mntchk 1: nil mchan c %s\n", chanpath(c));

 	m = c->mchan->mux;

 	if(m == nil)

-		print("mntchk 2: nil mux c %s c->mchan %s \n", c2name(c), c2name(c->mchan));

+		print("mntchk 2: nil mux c %s c->mchan %s \n", chanpath(c), chanpath(c->mchan));

 	/*

 	 * Was it closed and reused (was error(Eshutdown); now, it can't happen)

--- a/kern/devtls.c

+++ b/kern/devtls.c

@@ -1,5 +1,5 @@

 /*

- *  devtls - record layer for transport layer security 1.0 and secure sockets layer 3.0

+ *  devtls - record layer for transport layer security 1.2 and secure sockets layer 3.0

  */

 #include	"u.h"

 #include	"lib.h"

@@ -8,7 +8,7 @@

 #include	"error.h"

 #include	"libsec.h"

- 

+

 typedef struct OneWay	OneWay;

 typedef struct Secret	Secret;

 typedef struct TlsRec	TlsRec;

@@ -82,16 +82,18 @@

 {

 	char		*encalg;	/* name of encryption alg */

 	char		*hashalg;	/* name of hash alg */

+

+	int		(*aead_enc)(Secret*, uchar*, int, uchar*, uchar*, int);

+	int		(*aead_dec)(Secret*, uchar*, int, uchar*, uchar*, int);

+

 	int		(*enc)(Secret*, uchar*, int);

 	int		(*dec)(Secret*, uchar*, int);

 	int		(*unpad)(uchar*, int, int);

-	DigestState	*(*mac)(uchar*, ulong, uchar*, ulong, uchar*, DigestState*);

+	DigestState*	(*mac)(uchar*, ulong, uchar*, ulong, uchar*, DigestState*);

-	int		(*aead_enc)(Secret*, uchar*, int, uchar*, int);

-	int		(*aead_dec)(Secret*, uchar*, int, uchar*, int);

-

 	int		block;		/* encryption block len, 0 if none */

-	int		maclen;

+	int		maclen;		/* # bytes of record mac / authentication tag */

+	int		recivlen;	/* # bytes of record iv for AEAD ciphers */

 	void		*enckey;

 	uchar		mackey[MaxMacLen];

 };

@@ -245,8 +247,10 @@

 static int	des3dec(Secret *sec, uchar *buf, int n);

 static int	aesenc(Secret *sec, uchar *buf, int n);

 static int	aesdec(Secret *sec, uchar *buf, int n);

-static int	ccpoly_aead_enc(Secret *sec, uchar *aad, int aadlen, uchar *data, int len);

-static int	ccpoly_aead_dec(Secret *sec, uchar *aad, int aadlen, uchar *data, int len);

+static int	ccpoly_aead_enc(Secret *sec, uchar *aad, int aadlen, uchar *reciv, uchar *data, int len);

+static int	ccpoly_aead_dec(Secret *sec, uchar *aad, int aadlen, uchar *reciv, uchar *data, int len);

+static int	aesgcm_aead_enc(Secret *sec, uchar *aad, int aadlen, uchar *reciv, uchar *data, int len);

+static int	aesgcm_aead_dec(Secret *sec, uchar *aad, int aadlen, uchar *reciv, uchar *data, int len);

 static int	noenc(Secret *sec, uchar *buf, int n);

 static int	sslunpad(uchar *buf, int n, int block);

 static int	tlsunpad(uchar *buf, int n, int block);

@@ -818,14 +822,16 @@

 if(tr->debug) pdump(unpad_len, p, "decrypted:");

 		}

+		ivlen = sec->recivlen;

 		if(tr->version >= TLS11Version){

-			ivlen = sec->block;

-			len -= ivlen;

-			if(len < 0)

-				rcvError(tr, EDecodeError, "runt record message");

-			unpad_len -= ivlen;

-			p += ivlen;

+			if(ivlen == 0)

+				ivlen = sec->block;

 		}

+		len -= ivlen;

+		if(len < 0)

+			rcvError(tr, EDecodeError, "runt record message");

+		unpad_len -= ivlen;

+		p += ivlen;

 		if(unpad_len >= sec->maclen)

 			len = unpad_len - sec->maclen;

@@ -834,7 +840,7 @@

 		put16(header+3, len);

 		aadlen = (*tr->packAAD)(in->seq++, header, aad);

 		if(sec->aead_dec != nil) {

-			len = (*sec->aead_dec)(sec, aad, aadlen, p, unpad_len);

+			len = (*sec->aead_dec)(sec, aad, aadlen, p - ivlen, p, unpad_len);

 			if(len < 0)

 				rcvError(tr, EBadRecordMac, "record mac mismatch");

 		} else {

@@ -1188,7 +1194,9 @@

 		if(tr->out.sec != nil)

 			s = seprint(s, e, "EncOut: %s\nHashOut: %s\n", tr->out.sec->encalg, tr->out.sec->hashalg);

 		if(tr->out.new != nil)

-			seprint(s, e, "NewEncOut: %s\nNewHashOut: %s\n", tr->out.new->encalg, tr->out.new->hashalg);

+			s = seprint(s, e, "NewEncOut: %s\nNewHashOut: %s\n", tr->out.new->encalg, tr->out.new->hashalg);

+		if(tr->c != nil)

+			seprint(s, e, "Chan: %s\n", chanpath(tr->c));

 		qunlock(&tr->in.seclock);

 		qunlock(&tr->out.seclock);

 		n = readstr(offset, a, n, buf);

@@ -1296,8 +1304,11 @@

 		if(sec != nil){

 			maclen = sec->maclen;

 			pad = maclen + sec->block;

-			if(tr->version >= TLS11Version)

-				ivlen = sec->block;

+			ivlen = sec->recivlen;

+			if(tr->version >= TLS11Version){

+				if(ivlen == 0)

+					ivlen = sec->block;

+			}

 		}

 		n = BLEN(bb);

 		if(n > MaxRecLen){

@@ -1323,12 +1334,12 @@

 		put16(p+3, n);

 		if(sec != nil){

-			if(ivlen > 0)

-				randfill(p + RecHdrLen, ivlen);

 			aadlen = (*tr->packAAD)(out->seq++, p, aad);

 			if(sec->aead_enc != nil)

-				n = (*sec->aead_enc)(sec, aad, aadlen, p + RecHdrLen + ivlen, n) + ivlen;

+				n = (*sec->aead_enc)(sec, aad, aadlen, p + RecHdrLen, p + RecHdrLen + ivlen, n) + ivlen;

 			else {

+				if(ivlen > 0)

+					randfill(p + RecHdrLen, ivlen);

 				packMac(sec, aad, aadlen, p + RecHdrLen + ivlen, n, p + RecHdrLen + ivlen + n);

 				n = (*sec->enc)(sec, p + RecHdrLen, ivlen + n + maclen);

 			}

@@ -1417,7 +1428,6 @@

 static void

 initclearmac(Hashalg *ha, int version, Secret *s, uchar *p)

 {

-	s->maclen = 0;

 	s->mac = nomac;

 }

@@ -1478,7 +1488,6 @@

 	s->enckey = smalloc(sizeof(RC4state));

 	s->enc = rc4enc;

 	s->dec = rc4enc;

-	s->block = 0;

 	setupRC4state(s->enckey, p, ea->keylen);

 }

@@ -1506,12 +1515,8 @@

 initccpolykey(Encalg *ea, Secret *s, uchar *p, uchar *iv)

 {

 	s->enckey = smalloc(sizeof(Chachastate));

-	s->enc = noenc;

-	s->dec = noenc;

-	s->mac = nomac;

 	s->aead_enc = ccpoly_aead_enc;

 	s->aead_dec = ccpoly_aead_dec;

-	s->block = 0;

 	s->maclen = Poly1305dlen;

 	if(ea->ivlen == 0) {

 		/* older draft version, iv is 64-bit sequence number */

@@ -1524,11 +1529,23 @@

 }

 static void

+initaesgcmkey(Encalg *ea, Secret *s, uchar *p, uchar *iv)

+{

+	s->enckey = smalloc(sizeof(AESGCMstate));

+	s->aead_enc = aesgcm_aead_enc;

+	s->aead_dec = aesgcm_aead_dec;

+	s->maclen = 16;

+	s->recivlen = 8;

+	memmove(s->mackey, iv, ea->ivlen);

+	randfill(s->mackey + ea->ivlen, s->recivlen);

+	setupAESGCMstate(s->enckey, p, ea->keylen, nil, 0);

+}

+

+static void

 initclearenc(Encalg *ea, Secret *s, uchar *key, uchar *iv)

 {

 	s->enc = noenc;

 	s->dec = noenc;

-	s->block = 0;

 }

 static Encalg encrypttab[] =

@@ -1540,6 +1557,8 @@

 	{ "aes_256_cbc", 256/8, 16, initAESkey },

 	{ "ccpoly64_aead", 256/8, 0, initccpolykey },

 	{ "ccpoly96_aead", 256/8, 96/8, initccpolykey },

+	{ "aes_128_gcm_aead", 128/8, 4, initaesgcmkey },

+	{ "aes_256_gcm_aead", 256/8, 4, initaesgcmkey },

 	{ 0 }

 };

@@ -1670,8 +1689,8 @@

 		p = cb->f[4];

 		m = (strlen(p)*3)/2;

 		x = smalloc(m);

-		tos = nil;

-		toc = nil;

+		tos = smalloc(sizeof(Secret));

+		toc = smalloc(sizeof(Secret));

 		if(waserror()){

 			freeSec(tos);

 			freeSec(toc);

@@ -1678,22 +1697,23 @@

 			free(x);

 			nexterror();

 		}

+

 		m = dec64(x, m, p, strlen(p));

 		if(m < 2 * ha->maclen + 2 * ea->keylen + 2 * ea->ivlen)

 			error("not enough secret data provided");

-		tos = smalloc(sizeof(Secret));

-		toc = smalloc(sizeof(Secret));

 		if(!ha->initkey || !ea->initkey)

 			error("misimplemented secret algorithm");

+

 		(*ha->initkey)(ha, tr->version, tos, &x[0]);

 		(*ha->initkey)(ha, tr->version, toc, &x[ha->maclen]);

 		(*ea->initkey)(ea, tos, &x[2 * ha->maclen], &x[2 * ha->maclen + 2 * ea->keylen]);

 		(*ea->initkey)(ea, toc, &x[2 * ha->maclen + ea->keylen], &x[2 * ha->maclen + 2 * ea->keylen + ea->ivlen]);

-		if(!tos->mac || !tos->enc || !tos->dec

-		|| !toc->mac || !toc->enc || !toc->dec)

-			error("missing algorithm implementations");

+		if(!tos->aead_enc || !tos->aead_dec || !toc->aead_enc || !toc->aead_dec)

+			if(!tos->mac || !tos->enc || !tos->dec || !toc->mac || !toc->enc || !toc->dec)

+				error("missing algorithm implementations");

+

 		if(strtol(cb->f[3], nil, 0) == 0){

 			tr->in.new = tos;

 			tr->out.new = toc;

@@ -2042,10 +2062,15 @@

 static void

 freeSec(Secret *s)

 {

-	if(s != nil){

-		free(s->enckey);

-		free(s);

-	}

+	void *k;

+

+	if(s == nil)

+		return;

+	k = s->enckey;

+	if(k != nil)

+		free(k);

+	memset(s, 0, sizeof(*s));

+	free(s);

 }

 static int

@@ -2152,8 +2177,9 @@

 }

 static int

-ccpoly_aead_enc(Secret *sec, uchar *aad, int aadlen, uchar *data, int len)

+ccpoly_aead_enc(Secret *sec, uchar *aad, int aadlen, uchar *reciv, uchar *data, int len)

 {

+	USED(reciv);

 	ccpoly_aead_setiv(sec, aad);

 	ccpoly_encrypt(data, len, aad, aadlen, data+len, sec->enckey);

 	return len + sec->maclen;

@@ -2160,8 +2186,9 @@

 }

 static int

-ccpoly_aead_dec(Secret *sec, uchar *aad, int aadlen, uchar *data, int len)

+ccpoly_aead_dec(Secret *sec, uchar *aad, int aadlen, uchar *reciv, uchar *data, int len)

 {

+	USED(reciv);

 	len -= sec->maclen;

 	if(len < 0)

 		return -1;

@@ -2170,6 +2197,37 @@

 		return -1;

 	return len;

 }

+

+static int

+aesgcm_aead_enc(Secret *sec, uchar *aad, int aadlen, uchar *reciv, uchar *data, int len)

+{

+	uchar iv[12];

+	int i;

+

+	memmove(iv, sec->mackey, 4+8);

+	for(i=0; i<8; i++) iv[4+i] ^= aad[i];

+	memmove(reciv, iv+4, 8);

+	aesgcm_setiv(sec->enckey, iv, 12);

+	aesgcm_encrypt(data, len, aad, aadlen, data+len, sec->enckey);

+	return len + sec->maclen;

+}

+

+static int

+aesgcm_aead_dec(Secret *sec, uchar *aad, int aadlen, uchar *reciv, uchar *data, int len)

+{

+	uchar iv[12];

+

+	len -= sec->maclen;

+	if(len < 0)

+		return -1;

+	memmove(iv, sec->mackey, 4);

+	memmove(iv+4, reciv, 8);

+	aesgcm_setiv(sec->enckey, iv, 12);

+	if(aesgcm_decrypt(data, len, aad, aadlen, data+len, sec->enckey) != 0)

+		return -1;

+	return len;

+}

+

 static DigestState*

 nomac(uchar *p, ulong len, uchar *key, ulong keylen, uchar *digest, DigestState *s)

--- a/kern/fns.h

+++ b/kern/fns.h

@@ -13,7 +13,7 @@

 Block*		bl2mem(uchar*, Block*, int);

 int		blocklen(Block*);

 void		callwithureg(void(*)(Ureg*));

-char*		c2name(Chan*);

+char*		chanpath(Chan*);

 int		cangetc(void*);

 int		canlock(Lock*);

 int		canpage(Proc*);

--- a/libauth/auth_attr.c

+++ b/libauth/auth_attr.c

@@ -1,7 +1,6 @@

 #include <u.h>

 #include <libc.h>

 #include <auth.h>

-#include <authsrv.h>

 #include "authlocal.h"

 Attr*

--- a/libauth/auth_challenge.c

+++ b/libauth/auth_challenge.c

@@ -1,7 +1,6 @@

 #include <u.h>

 #include <libc.h>

 #include <auth.h>

-#include <authsrv.h>

 #include "authlocal.h"

 Chalstate*

--- a/libauth/auth_proxy.c

+++ b/libauth/auth_proxy.c

@@ -128,8 +128,8 @@

 		return nil;

 	}

-	rerrstr(oerr, sizeof oerr);

-	werrstr("UNKNOWN AUTH ERROR");

+	strcpy(oerr, "UNKNOWN AUTH ERROR");

+	errstr(oerr, sizeof oerr);

 	if(dorpc(rpc, "start", params, strlen(params), getkey) != ARok){

 		werrstr("fauth_proxy start: %r");

--- a/libauth/auth_respond.c

+++ b/libauth/auth_respond.c

@@ -1,7 +1,6 @@

 #include <u.h>

 #include <libc.h>

 #include <auth.h>

-#include <authsrv.h>

 #include "authlocal.h"

 enum {

--- a/libmp/mpmodop.c

+++ b/libmp/mpmodop.c

@@ -1,5 +1,4 @@

-#include <u.h>

-#include <libc.h>

+#include "os.h"

 #include <mp.h>

 /* operands need to have m->top+1 digits of space and satisfy 0 ≤ a ≤ m-1 */

--- a/libsec/Makefile

+++ b/libsec/Makefile

@@ -4,6 +4,7 @@

 OFILES=\

 	aes.$O\

+	aes_gcm.$O\

 	aes_xts.$O\

 	blowfish.$O\

 	ccpoly.$O\

--- a/libsec/aes.c

+++ b/libsec/aes.c

@@ -28,9 +28,7 @@

  * OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE,

  * EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

  */

-#include <u.h>

-#include <libc.h>

-#include <mp.h>

+#include "os.h"

 #include <libsec.h>

 typedef uchar	u8;

--- /dev/null

+++ b/libsec/aes_gcm.c

@@ -1,0 +1,198 @@

+#include "os.h"

+#include <libsec.h>

+

+static void

+load128(uchar b[16], ulong W[4])

+{

+	W[0] = (ulong)b[15] | (ulong)b[14]<<8 | (ulong)b[13]<<16 | (ulong)b[12]<<24;

+	W[1] = (ulong)b[11] | (ulong)b[10]<<8 | (ulong)b[ 9]<<16 | (ulong)b[ 8]<<24;

+	W[2] = (ulong)b[ 7] | (ulong)b[ 6]<<8 | (ulong)b[ 5]<<16 | (ulong)b[ 4]<<24;

+	W[3] = (ulong)b[ 3] | (ulong)b[ 2]<<8 | (ulong)b[ 1]<<16 | (ulong)b[ 0]<<24;

+}

+

+static void

+store128(ulong W[4], uchar b[16])

+{

+	b[15] = W[0], b[14] = W[0]>>8, b[13] = W[0]>>16, b[12] = W[0]>>24;

+	b[11] = W[1], b[10] = W[1]>>8, b[ 9] = W[1]>>16, b[ 8] = W[1]>>24;

+	b[ 7] = W[2], b[ 6] = W[2]>>8, b[ 5] = W[2]>>16, b[ 4] = W[2]>>24;

+	b[ 3] = W[3], b[ 2] = W[3]>>8, b[ 1] = W[3]>>16, b[ 0] = W[3]>>24;

+}

+

+static void

+gfmul(ulong X[4], ulong Y[4], ulong Z[4])

+{

+	long m, i;

+

+	Z[0] = Z[1] = Z[2] = Z[3] = 0;

+	for(i=127; i>=0; i--){

+		m = ((long)Y[i>>5] << (31-(i&31))) >> 31;

+		Z[0] ^= X[0] & m;

+		Z[1] ^= X[1] & m;

+		Z[2] ^= X[2] & m;

+		Z[3] ^= X[3] & m;

+		m = ((long)X[0]<<31) >> 31;

+		X[0] = X[0]>>1 | X[1]<<31;

+		X[1] = X[1]>>1 | X[2]<<31;

+		X[2] = X[2]>>1 | X[3]<<31;

+		X[3] = X[3]>>1 ^ (0xE1000000 & m);

+	}

+}

+

+static void

+prepareM(ulong H[4], ulong M[16][256][4])

+{

+	ulong X[4], i, j;

+

+	for(i=0; i<16; i++){

+		for(j=0; j<256; j++){

+			X[0] = X[1] = X[2] = X[3] = 0;

+			X[i>>2] = j<<((i&3)<<3);

+			gfmul(X, H, M[i][j]);

+		}

+	}

+}

+

+static void

+ghash1(AESGCMstate *s, ulong X[4], ulong Y[4])

+{

+	ulong *Xi, i;

+

+	X[0] ^= Y[0], X[1] ^= Y[1], X[2] ^= Y[2], X[3] ^= Y[3];

+	if(0){

+		gfmul(X, s->H, Y);

+		return;

+	}

+

+	Y[0] = Y[1] = Y[2] = Y[3] = 0;

+	for(i=0; i<16; i++){

+		Xi = s->M[i][(X[i>>2]>>((i&3)<<3))&0xFF];

+		Y[0] ^= Xi[0];

+		Y[1] ^= Xi[1];

+		Y[2] ^= Xi[2];

+		Y[3] ^= Xi[3];

+	}

+}

+

+static void

+ghashn(AESGCMstate *s, uchar *dat, ulong len, ulong Y[4])

+{

+	uchar tmp[16];

+	ulong X[4];

+

+	while(len >= 16){

+		load128(dat, X);

+		ghash1(s, X, Y);

+		dat += 16, len -= 16;

+	}

+	if(len > 0){

+		memmove(tmp, dat, len);

+		memset(tmp+len, 0, 16-len);

+		load128(tmp, X);

+		ghash1(s, X, Y);

+	}

+}

+

+static ulong

+aesxctr1(AESstate *s, uchar ctr[AESbsize], uchar *dat, ulong len)

+{

+	uchar tmp[AESbsize];

+	ulong i;

+

+	aes_encrypt(s->ekey, s->rounds, ctr, tmp);

+	if(len > AESbsize)

+		len = AESbsize;

+	for(i=0; i<len; i++)

+		dat[i] ^= tmp[i];

+	return len;

+}

+

+static void

+aesxctrn(AESstate *s, uchar *dat, ulong len)

+{

+	uchar ctr[AESbsize];

+	ulong i;

+

+	memmove(ctr, s->ivec, AESbsize);

+	while(len > 0){

+		for(i=AESbsize-1; i>=AESbsize-4; i--)

+			if(++ctr[i] != 0)

+				break;

+

+		if(aesxctr1(s, ctr, dat, len) < AESbsize)

+			break;

+		dat += AESbsize;

+		len -= AESbsize;

+	}

+}

+

+void

+aesgcm_setiv(AESGCMstate *s, uchar *iv, int ivlen)

+{

+	if(ivlen == 96/8){

+		memmove(s->a.ivec, iv, ivlen);

+		memset(s->a.ivec+ivlen, 0, AESbsize-ivlen);

+		s->a.ivec[AESbsize-1] = 1;

+	} else {

+		ulong L[4], Y[4] = {0};

+

+		ghashn(s, iv, ivlen, Y);

+		L[0] = ivlen << 3;

+		L[1] = ivlen >> 29;

+		L[2] = L[3] = 0;

+		ghash1(s, L, Y);

+		store128(Y, s->a.ivec);

+	}

+}

+

+void

+setupAESGCMstate(AESGCMstate *s, uchar *key, int keylen, uchar *iv, int ivlen)

+{

+	setupAESstate(&s->a, key, keylen, nil);

+

+	memset(s->a.mackey, 0, AESbsize);

+	aes_encrypt(s->a.ekey, s->a.rounds, s->a.mackey, s->a.mackey);

+	load128(s->a.mackey, s->H);

+	prepareM(s->H, s->M);

+

+	if(iv != nil && ivlen > 0)

+		aesgcm_setiv(s, iv, ivlen);

+}

+

+void

+aesgcm_encrypt(uchar *dat, ulong ndat, uchar *aad, ulong naad, uchar tag[16], AESGCMstate *s)

+{

+	ulong L[4], Y[4] = {0};

+

+	ghashn(s, aad, naad, Y);

+	aesxctrn(&s->a, dat, ndat);

+	ghashn(s, dat, ndat, Y);

+	L[0] = ndat << 3;

+	L[1] = ndat >> 29;

+	L[2] = naad << 3;

+	L[3] = naad >> 29;

+	ghash1(s, L, Y);

+	store128(Y, tag);

+	aesxctr1(&s->a, s->a.ivec, tag, 16);

+}

+

+int

+aesgcm_decrypt(uchar *dat, ulong ndat, uchar *aad, ulong naad, uchar tag[16], AESGCMstate *s)

+{

+	ulong L[4], Y[4] = {0};

+	uchar tmp[16];

+

+	ghashn(s, aad, naad, Y);

+	ghashn(s, dat, ndat, Y);

+	L[0] = ndat << 3;

+	L[1] = ndat >> 29;

+	L[2] = naad << 3;

+	L[3] = naad >> 29;

+	ghash1(s, L, Y);

+	store128(Y, tmp);

+	aesxctr1(&s->a, s->a.ivec, tmp, 16);

+	if(tsmemcmp(tag, tmp, 16) != 0)

+		return -1;

+	aesxctrn(&s->a, dat, ndat);

+	return 0;

+}

--- a/libsec/aes_xts.c

+++ b/libsec/aes_xts.c

@@ -1,7 +1,6 @@

 // Author Taru Karttunen <taruti@taruti.net>

 // This file can be used as both Public Domain or Creative Commons CC0.

-#include <u.h>

-#include <libc.h>

+#include "os.h"

 #include <libsec.h>

 #define AesBlockSize 16

--- /dev/null

+++ b/libsec/aesgcmtest.c

@@ -1,0 +1,314 @@

+#include <u.h>

+#include <libc.h>

+#include <mp.h>

+#include <libsec.h>

+

+typedef struct Test Test;

+struct Test

+{

+	char *K;

+	char *P;

+	char *A;

+	char *IV;

+	char *T;

+};

+

+Test tests[] = {

+	{	/* Test Case 1 */

+		"00000000000000000000000000000000",

+		"",

+		"",

+		"000000000000000000000000",

+

+		"58E2FCCEFA7E3061367F1D57A4E7455A"

+	},

+	{	/* Test Case 2 */

+		"00000000000000000000000000000000",

+		"00000000000000000000000000000000",

+		"",

+		"000000000000000000000000",

+

+		"AB6E47D42CEC13BDF53A67B21257BDDF",

+	},

+	{	/* Test Case 3 */

+		"feffe9928665731c6d6a8f9467308308",

+		"d9313225f88406e5a55909c5aff5269a"

+		"86a7a9531534f7da2e4c303d8a318a72"

+		"1c3c0c95956809532fcf0e2449a6b525"

+		"b16aedf5aa0de657ba637b391aafd255",

+		"",

+		"cafebabefacedbaddecaf888",

+

+		"4D5C2AF327CD64A62CF35ABD2BA6FAB4"

+	},

+	{	/* Test Case 4 */

+		"feffe9928665731c6d6a8f9467308308",

+		"d9313225f88406e5a55909c5aff5269a"

+		"86a7a9531534f7da2e4c303d8a318a72"

+		"1c3c0c95956809532fcf0e2449a6b525"

+		"b16aedf5aa0de657ba637b39",

+		"feedfacedeadbeeffeedfacedeadbeef"

+		"abaddad2",

+		"cafebabefacedbaddecaf888",

+

+		"5BC94FBC3221A5DB94FAE95AE7121A47"

+	},

+	{	/* Test Case 5 */

+		"feffe9928665731c6d6a8f9467308308",

+		"d9313225f88406e5a55909c5aff5269a"

+		"86a7a9531534f7da2e4c303d8a318a72"

+		"1c3c0c95956809532fcf0e2449a6b525"

+		"b16aedf5aa0de657ba637b39",

+		"feedfacedeadbeeffeedfacedeadbeef"

+		"abaddad2",

+		"cafebabefacedbad",

+

+		"3612D2E79E3B0785561BE14AACA2FCCB"

+	},

+	{	/* Test Case 6 */

+		"feffe9928665731c6d6a8f9467308308",

+		"d9313225f88406e5a55909c5aff5269a"

+		"86a7a9531534f7da2e4c303d8a318a72"

+		"1c3c0c95956809532fcf0e2449a6b525"

+		"b16aedf5aa0de657ba637b39",

+		"feedfacedeadbeeffeedfacedeadbeef"

+		"abaddad2",

+		"9313225df88406e555909c5aff5269aa"

+		"6a7a9538534f7da1e4c303d2a318a728"

+		"c3c0c95156809539fcf0e2429a6b5254"

+		"16aedbf5a0de6a57a637b39b",

+

+		"619CC5AEFFFE0BFA462AF43C1699D050"

+	},

+	{	/* Test Case 7 */

+		"00000000000000000000000000000000"

+		"0000000000000000",

+		"",

+		"",

+		"000000000000000000000000",

+

+		"CD33B28AC773F74BA00ED1F312572435"

+	},

+	{	/* Test Case 8 */

+		"00000000000000000000000000000000"

+		"0000000000000000",

+		"00000000000000000000000000000000",

+		"",

+		"000000000000000000000000",

+

+		"2FF58D80033927AB8EF4D4587514F0FB"

+	},

+	{	/* Test Case 9 */

+		"feffe9928665731c6d6a8f9467308308"

+		"feffe9928665731c",

+		"d9313225f88406e5a55909c5aff5269a"

+		"86a7a9531534f7da2e4c303d8a318a72"

+		"1c3c0c95956809532fcf0e2449a6b525"

+		"b16aedf5aa0de657ba637b391aafd255",

+		"",

+		"cafebabefacedbaddecaf888",

+

+		"9924A7C8587336BFB118024DB8674A14"

+	},

+	{	/* Test Case 10 */

+		"feffe9928665731c6d6a8f9467308308"

+		"feffe9928665731c",

+		"d9313225f88406e5a55909c5aff5269a"

+		"86a7a9531534f7da2e4c303d8a318a72"

+		"1c3c0c95956809532fcf0e2449a6b525"

+		"b16aedf5aa0de657ba637b39",

+		"feedfacedeadbeeffeedfacedeadbeef"

+		"abaddad2",

+		"cafebabefacedbaddecaf888",

+

+		"2519498E80F1478F37BA55BD6D27618C"

+	},

+	{	/* Test Case 11 */

+		"feffe9928665731c6d6a8f9467308308"

+		"feffe9928665731c",

+		"d9313225f88406e5a55909c5aff5269a"

+		"86a7a9531534f7da2e4c303d8a318a72"

+		"1c3c0c95956809532fcf0e2449a6b525"

+		"b16aedf5aa0de657ba637b39",

+		"feedfacedeadbeeffeedfacedeadbeef"

+		"abaddad2",

+		"cafebabefacedbad",

+

+		"65DCC57FCF623A24094FCCA40D3533F8"

+	},

+	{	/* Test Case 12 */

+		"feffe9928665731c6d6a8f9467308308"

+		"feffe9928665731c",

+		"d9313225f88406e5a55909c5aff5269a"

+		"86a7a9531534f7da2e4c303d8a318a72"

+		"1c3c0c95956809532fcf0e2449a6b525"

+		"b16aedf5aa0de657ba637b39",

+		"feedfacedeadbeeffeedfacedeadbeef"

+		"abaddad2",

+		"9313225df88406e555909c5aff5269aa"

+		"6a7a9538534f7da1e4c303d2a318a728"

+		"c3c0c95156809539fcf0e2429a6b5254"

+		"16aedbf5a0de6a57a637b39b",

+

+		"DCF566FF291C25BBB8568FC3D376A6D9"

+	},

+	{	/* Test Case 13 */

+		"00000000000000000000000000000000"

+		"00000000000000000000000000000000",

+		"",

+		"",

+		"000000000000000000000000",

+

+		"530F8AFBC74536B9A963B4F1C4CB738B"

+	},

+	{	/* Test Case 14 */

+		"00000000000000000000000000000000"

+		"00000000000000000000000000000000",

+		"00000000000000000000000000000000",

+		"",

+		"000000000000000000000000",

+

+		"D0D1C8A799996BF0265B98B5D48AB919"

+	},

+	{	/* Test Case 15 */

+		"feffe9928665731c6d6a8f9467308308"

+		"feffe9928665731c6d6a8f9467308308",

+		"d9313225f88406e5a55909c5aff5269a"

+		"86a7a9531534f7da2e4c303d8a318a72"

+		"1c3c0c95956809532fcf0e2449a6b525"

+		"b16aedf5aa0de657ba637b391aafd255",

+		"",

+		"cafebabefacedbaddecaf888",

+

+		"B094DAC5D93471BDEC1A502270E3CC6C"

+	},

+	{	/* Test Case 16 */

+		"feffe9928665731c6d6a8f9467308308"

+		"feffe9928665731c6d6a8f9467308308",

+		"d9313225f88406e5a55909c5aff5269a"

+		"86a7a9531534f7da2e4c303d8a318a72"

+		"1c3c0c95956809532fcf0e2449a6b525"

+		"b16aedf5aa0de657ba637b39",

+		"feedfacedeadbeeffeedfacedeadbeef"

+		"abaddad2",

+		"cafebabefacedbaddecaf888",

+

+		"76FC6ECE0F4E1768CDDF8853BB2D551B"

+	},

+	{	/* Test Case 17 */

+		"feffe9928665731c6d6a8f9467308308"

+		"feffe9928665731c6d6a8f9467308308",

+		"d9313225f88406e5a55909c5aff5269a"

+		"86a7a9531534f7da2e4c303d8a318a72"

+		"1c3c0c95956809532fcf0e2449a6b525"

+		"b16aedf5aa0de657ba637b39",

+		"feedfacedeadbeeffeedfacedeadbeef"

+		"abaddad2",

+		"cafebabefacedbad",

+

+		"3A337DBF46A792C45E454913FE2EA8F2"

+	},

+	{	/* Test Case 18 */

+		"feffe9928665731c6d6a8f9467308308"

+		"feffe9928665731c6d6a8f9467308308",

+		"d9313225f88406e5a55909c5aff5269a"

+		"86a7a9531534f7da2e4c303d8a318a72"

+		"1c3c0c95956809532fcf0e2449a6b525"

+		"b16aedf5aa0de657ba637b39",

+		"feedfacedeadbeeffeedfacedeadbeef"

+		"abaddad2",

+		"9313225df88406e555909c5aff5269aa"

+		"6a7a9538534f7da1e4c303d2a318a728"

+		"c3c0c95156809539fcf0e2429a6b5254"

+		"16aedbf5a0de6a57a637b39b",

+

+		"A44A8266EE1C8EB0C8B5D4CF5AE9F19A"

+	},

+};

+

+int

+parsehex(char *s, uchar *h, char *l)

+{

+	char *e;

+	mpint *m;

+	int n;

+

+	n = strlen(s);

+	if(n == 0)

+		return 0;

+	assert((n & 1) == 0);

+	n >>= 1;

+	e = nil;

+	m = strtomp(s, &e, 16, nil);

+	if(m == nil || *e != '\0')

+		abort();

+	mptober(m, h, n);

+	if(l != nil)

+		print("%s = %.*H\n", l, n, h);

+	return n;

+}

+

+void

+runtest(Test *t)

+{

+	AESGCMstate s;

+	uchar key[1024], plain[1024], aad[1024], iv[1024], tag[16], tmp[16];

+	int nkey, nplain, naad, niv;

+

+	nkey = parsehex(t->K, key, "K");

+	nplain = parsehex(t->P, plain, "P");

+	naad = parsehex(t->A, aad, "A");

+	niv = parsehex(t->IV, iv, "IV");

+

+	setupAESGCMstate(&s, key, nkey, iv, niv);

+	aesgcm_encrypt(plain, nplain, aad, naad, tag, &s);

+	print("C = %.*H\n", nplain, plain);

+	print("T = %.*H\n", 16, tag);

+

+	parsehex(t->T, tmp, nil);

+	assert(memcmp(tmp, tag, 16) == 0);

+}

+

+void

+perftest(void)

+{

+	AESGCMstate s;

+	static uchar zeros[16];

+	uchar buf[1024*1024], tag[16];

+	vlong now;

+	int i, delta;

+

+	now = nsec();

+	for(i=0; i<100; i++){

+		memset(buf, 0, sizeof(buf));

+		if(1){

+			setupAESGCMstate(&s, zeros, 16, zeros, 12);

+			aesgcm_encrypt(buf, sizeof(buf), nil, 0, tag, &s);

+		} else {

+			setupAESstate(&s, zeros, 16, zeros);

+			aesCBCencrypt(buf, sizeof(buf), &s);

+		}

+	}

+	delta = (nsec() - now) / 1000000000LL;

+	fprint(2, "%ds = %d/s\n", delta, i*sizeof(buf) / delta);

+}

+

+void

+main(int argc, char **argv)

+{

+	int i;

+

+	fmtinstall('H', encodefmt);

+

+	ARGBEGIN {

+	case 'p':

+		perftest();

+		exits(nil);

+	} ARGEND;

+

+	for(i=0; i<nelem(tests); i++){

+		print("Test Case %d\n", i+1);

+		runtest(&tests[i]);

+		print("\n");

+	}

+}

--- /dev/null

+++ b/libsec/bftest.c

@@ -1,0 +1,279 @@

+#include <u.h>

+#include <libc.h>

+#include <libsec.h>

+

+enum{

+	Bsz = 8,

+};

+

+typedef struct Testvector Testvector;

+

+struct Testvector{

+	uchar key[Bsz];

+	uchar plain[Bsz];

+	uchar cipher[Bsz];

+};

+

+/*

+ * Blowfish test vectors from https://www.schneier.com/code/vectors.txt

+ */

+Testvector vector [] = {

+	{{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},

+	 {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},

+	 {0x4E, 0xF9, 0x97, 0x45, 0x61, 0x98, 0xDD, 0x78}},

+

+	{{0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF},

+	 {0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF},

+	 {0x51, 0x86, 0x6F, 0xD5, 0xB8, 0x5E, 0xCB, 0x8A}},

+

+	{{0x30, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},

+	 {0x10, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01},

+	 {0x7D, 0x85, 0x6F, 0x9A, 0x61, 0x30, 0x63, 0xF2}},

+

+	{{0x11, 0x11, 0x11, 0x11, 0x11, 0x11, 0x11, 0x11},

+	 {0x11, 0x11, 0x11, 0x11, 0x11, 0x11, 0x11, 0x11},

+	 {0x24, 0x66, 0xDD, 0x87, 0x8B, 0x96, 0x3C, 0x9D}},

+

+	{{0x01, 0x23, 0x45, 0x67, 0x89, 0xAB, 0xCD, 0xEF},

+	 {0x11, 0x11, 0x11, 0x11, 0x11, 0x11, 0x11, 0x11},

+	 {0x61, 0xF9, 0xC3, 0x80, 0x22, 0x81, 0xB0, 0x96}},

+

+	{{0x11, 0x11, 0x11, 0x11, 0x11, 0x11, 0x11, 0x11},

+	 {0x01, 0x23, 0x45, 0x67, 0x89, 0xAB, 0xCD, 0xEF},

+	 {0x7D, 0x0C, 0xC6, 0x30, 0xAF, 0xDA, 0x1E, 0xC7}},

+

+	{{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},

+	 {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},

+	 {0x4E, 0xF9, 0x97, 0x45, 0x61, 0x98, 0xDD, 0x78}},

+

+	{{0xFE, 0xDC, 0xBA, 0x98, 0x76, 0x54, 0x32, 0x10},

+	 {0x01, 0x23, 0x45, 0x67, 0x89, 0xAB, 0xCD, 0xEF},

+	 {0x0A, 0xCE, 0xAB, 0x0F, 0xC6, 0xA0, 0xA2, 0x8D}},

+

+	{{0x7C, 0xA1, 0x10, 0x45, 0x4A, 0x1A, 0x6E, 0x57},

+	 {0x01, 0xA1, 0xD6, 0xD0, 0x39, 0x77, 0x67, 0x42},

+	 {0x59, 0xC6, 0x82, 0x45, 0xEB, 0x05, 0x28, 0x2B}},

+

+	{{0x01, 0x31, 0xD9, 0x61, 0x9D, 0xC1, 0x37, 0x6E},

+	 {0x5C, 0xD5, 0x4C, 0xA8, 0x3D, 0xEF, 0x57, 0xDA},

+	 {0xB1, 0xB8, 0xCC, 0x0B, 0x25, 0x0F, 0x09, 0xA0}},

+

+	{{0x07, 0xA1, 0x13, 0x3E, 0x4A, 0x0B, 0x26, 0x86},

+	 {0x02, 0x48, 0xD4, 0x38, 0x06, 0xF6, 0x71, 0x72},

+	 {0x17, 0x30, 0xE5, 0x77, 0x8B, 0xEA, 0x1D, 0xA4}},

+

+	{{0x38, 0x49, 0x67, 0x4C, 0x26, 0x02, 0x31, 0x9E},

+	 {0x51, 0x45, 0x4B, 0x58, 0x2D, 0xDF, 0x44, 0x0A},

+	 {0xA2, 0x5E, 0x78, 0x56, 0xCF, 0x26, 0x51, 0xEB}},

+

+	{{0x04, 0xB9, 0x15, 0xBA, 0x43, 0xFE, 0xB5, 0xB6},

+	 {0x42, 0xFD, 0x44, 0x30, 0x59, 0x57, 0x7F, 0xA2},

+	 {0x35, 0x38, 0x82, 0xB1, 0x09, 0xCE, 0x8F, 0x1A}},

+

+	{{0x01, 0x13, 0xB9, 0x70, 0xFD, 0x34, 0xF2, 0xCE},

+	 {0x05, 0x9B, 0x5E, 0x08, 0x51, 0xCF, 0x14, 0x3A},

+	 {0x48, 0xF4, 0xD0, 0x88, 0x4C, 0x37, 0x99, 0x18}},

+

+	{{0x01, 0x70, 0xF1, 0x75, 0x46, 0x8F, 0xB5, 0xE6},

+	 {0x07, 0x56, 0xD8, 0xE0, 0x77, 0x47, 0x61, 0xD2},

+	 {0x43, 0x21, 0x93, 0xB7, 0x89, 0x51, 0xFC, 0x98}},

+

+	{{0x43, 0x29, 0x7F, 0xAD, 0x38, 0xE3, 0x73, 0xFE},

+	 {0x76, 0x25, 0x14, 0xB8, 0x29, 0xBF, 0x48, 0x6A},

+	 {0x13, 0xF0, 0x41, 0x54, 0xD6, 0x9D, 0x1A, 0xE5}},

+

+	{{0x07, 0xA7, 0x13, 0x70, 0x45, 0xDA, 0x2A, 0x16},

+	 {0x3B, 0xDD, 0x11, 0x90, 0x49, 0x37, 0x28, 0x02},

+	 {0x2E, 0xED, 0xDA, 0x93, 0xFF, 0xD3, 0x9C, 0x79}},

+

+	{{0x04, 0x68, 0x91, 0x04, 0xC2, 0xFD, 0x3B, 0x2F},

+	 {0x26, 0x95, 0x5F, 0x68, 0x35, 0xAF, 0x60, 0x9A},

+	 {0xD8, 0x87, 0xE0, 0x39, 0x3C, 0x2D, 0xA6, 0xE3}},

+

+	{{0x37, 0xD0, 0x6B, 0xB5, 0x16, 0xCB, 0x75, 0x46},

+	 {0x16, 0x4D, 0x5E, 0x40, 0x4F, 0x27, 0x52, 0x32},

+	 {0x5F, 0x99, 0xD0, 0x4F, 0x5B, 0x16, 0x39, 0x69}},

+

+	{{0x1F, 0x08, 0x26, 0x0D, 0x1A, 0xC2, 0x46, 0x5E},

+	 {0x6B, 0x05, 0x6E, 0x18, 0x75, 0x9F, 0x5C, 0xCA},

+	 {0x4A, 0x05, 0x7A, 0x3B, 0x24, 0xD3, 0x97, 0x7B}},

+

+	{{0x58, 0x40, 0x23, 0x64, 0x1A, 0xBA, 0x61, 0x76},

+	 {0x00, 0x4B, 0xD6, 0xEF, 0x09, 0x17, 0x60, 0x62},

+	 {0x45, 0x20, 0x31, 0xC1, 0xE4, 0xFA, 0xDA, 0x8E}},

+

+	{{0x02, 0x58, 0x16, 0x16, 0x46, 0x29, 0xB0, 0x07},

+	 {0x48, 0x0D, 0x39, 0x00, 0x6E, 0xE7, 0x62, 0xF2},

+	 {0x75, 0x55, 0xAE, 0x39, 0xF5, 0x9B, 0x87, 0xBD}},

+

+	{{0x49, 0x79, 0x3E, 0xBC, 0x79, 0xB3, 0x25, 0x8F},

+	 {0x43, 0x75, 0x40, 0xC8, 0x69, 0x8F, 0x3C, 0xFA},

+	 {0x53, 0xC5, 0x5F, 0x9C, 0xB4, 0x9F, 0xC0, 0x19}},

+

+	{{0x4F, 0xB0, 0x5E, 0x15, 0x15, 0xAB, 0x73, 0xA7},

+	 {0x07, 0x2D, 0x43, 0xA0, 0x77, 0x07, 0x52, 0x92},

+	 {0x7A, 0x8E, 0x7B, 0xFA, 0x93, 0x7E, 0x89, 0xA3}},

+

+	{{0x49, 0xE9, 0x5D, 0x6D, 0x4C, 0xA2, 0x29, 0xBF},

+	 {0x02, 0xFE, 0x55, 0x77, 0x81, 0x17, 0xF1, 0x2A},

+	 {0xCF, 0x9C, 0x5D, 0x7A, 0x49, 0x86, 0xAD, 0xB5}},

+

+	{{0x01, 0x83, 0x10, 0xDC, 0x40, 0x9B, 0x26, 0xD6},

+	 {0x1D, 0x9D, 0x5C, 0x50, 0x18, 0xF7, 0x28, 0xC2},

+	 {0xD1, 0xAB, 0xB2, 0x90, 0x65, 0x8B, 0xC7, 0x78}},

+

+	{{0x1C, 0x58, 0x7F, 0x1C, 0x13, 0x92, 0x4F, 0xEF},

+	 {0x30, 0x55, 0x32, 0x28, 0x6D, 0x6F, 0x29, 0x5A},

+	 {0x55, 0xCB, 0x37, 0x74, 0xD1, 0x3E, 0xF2, 0x01}},

+

+	{{0x01, 0x01, 0x01, 0x01, 0x01, 0x01, 0x01, 0x01},

+	 {0x01, 0x23, 0x45, 0x67, 0x89, 0xAB, 0xCD, 0xEF},

+	 {0xFA, 0x34, 0xEC, 0x48, 0x47, 0xB2, 0x68, 0xB2}},

+

+	{{0x1F, 0x1F, 0x1F, 0x1F, 0x0E, 0x0E, 0x0E, 0x0E},

+	 {0x01, 0x23, 0x45, 0x67, 0x89, 0xAB, 0xCD, 0xEF},

+	 {0xA7, 0x90, 0x79, 0x51, 0x08, 0xEA, 0x3C, 0xAE}},

+

+	{{0xE0, 0xFE, 0xE0, 0xFE, 0xF1, 0xFE, 0xF1, 0xFE},

+	 {0x01, 0x23, 0x45, 0x67, 0x89, 0xAB, 0xCD, 0xEF},

+	 {0xC3, 0x9E, 0x07, 0x2D, 0x9F, 0xAC, 0x63, 0x1D}},

+

+	{{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},

+	 {0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF},

+	 {0x01, 0x49, 0x33, 0xE0, 0xCD, 0xAF, 0xF6, 0xE4}},

+

+	{{0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF},

+	 {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},

+	 {0xF2, 0x1E, 0x9A, 0x77, 0xB7, 0x1C, 0x49, 0xBC}},

+

+	{{0x01, 0x23, 0x45, 0x67, 0x89, 0xAB, 0xCD, 0xEF},

+	 {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},

+	 {0x24, 0x59, 0x46, 0x88, 0x57, 0x54, 0x36, 0x9A}},

+

+	{{0xFE, 0xDC, 0xBA, 0x98, 0x76, 0x54, 0x32, 0x10},

+	 {0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF},

+	 {0x6B, 0x5C, 0x5A, 0x9C, 0x5D, 0x9E, 0x0A, 0x5A}}

+};

+

+uchar CBCkey[16] = { 

+	 0x01, 0x23, 0x45, 0x67, 0x89, 0xAB, 0xCD, 0xEF, 

+	 0xF0, 0xE1, 0xD2, 0xC3, 0xB4, 0xA5, 0x96, 0x87

+};

+

+uchar CBCiv[8] = {

+	 0xFE, 0xDC, 0xBA, 0x98, 0x76, 0x54, 0x32, 0x10

+};

+

+uchar CBCdata[29] = {

+	 0x37, 0x36, 0x35, 0x34, 0x33, 0x32, 0x31, 0x20, 

+	 0x4E, 0x6F, 0x77, 0x20, 0x69, 0x73, 0x20, 0x74, 

+	 0x68, 0x65, 0x20, 0x74, 0x69, 0x6D, 0x65, 0x20, 

+	 0x66, 0x6F, 0x72, 0x20, 0x00

+};

+

+uchar CBCcipher[32] = {

+	 0x6B, 0x77, 0xB4, 0xD6, 0x30, 0x06, 0xDE, 0xE6,

+	 0x05, 0xB1, 0x56, 0xE2, 0x74, 0x03, 0x97, 0x93,

+	 0x58, 0xDE, 0xB9, 0xE7, 0x15, 0x46, 0x16, 0xD9,

+	 0x59, 0xF1, 0x65, 0x2B, 0xD5, 0xFF, 0x92, 0xCC

+};

+

+int

+testECB(Testvector *t)

+{

+	BFstate s;

+	int i;

+	uchar aux[Bsz];

+

+	memcpy(aux, t->plain, Bsz);

+

+	memset(&s, 0, sizeof(BFstate));

+	setupBFstate(&s, t->key, Bsz, nil);

+	bfECBencrypt(aux, Bsz, &s);

+

+	if(memcmp(aux, t->cipher, Bsz) != 0){

+		fprint(2, "ECB encrypt failed, ciphertext is:\n");

+		for(i = 0; i < Bsz; i++)

+			fprint(2, "%02X", aux[i]);

+		fprint(2, "\nand should be:\n");

+		for(i = 0; i < Bsz; i++)

+			fprint(2, "%02X", t->cipher[i]);

+		fprint(2, "\n");

+		return -1;

+	}

+

+	memset(&s, 0, sizeof(BFstate));

+	setupBFstate(&s, t->key, Bsz, nil);

+	bfECBdecrypt(aux, Bsz, &s);

+

+	if(memcmp(aux, t->plain, Bsz) != 0){

+		fprint(2, "ECB decrypt failed, plaintext is:\n");

+		for(i = 0; i < Bsz; i++)

+			fprint(2, "%02X", aux[i]);

+		fprint(2, "\nand should be:\n");

+		for(i = 0; i < Bsz; i++)

+			fprint(2, "%02X", t->plain[i]);

+		fprint(2, "\n");

+		return -1;

+	}

+	return 0;

+}

+

+int

+testCBC(void)

+{

+	BFstate s;

+	uchar aux[32];

+	int i;

+

+	memset(aux, 0 , sizeof(aux));

+	memcpy(aux, CBCdata, sizeof(CBCdata));

+	memset(&s, 0, sizeof(BFstate));

+	setupBFstate(&s, CBCkey, sizeof(CBCkey), CBCiv);

+	bfCBCencrypt(aux, 32, &s);

+	

+	if(memcmp(aux, CBCcipher, sizeof(CBCcipher)) != 0){

+		fprint(2, "CBC encrypt failed, ciphertext is:\n");

+		for(i = 0; i < sizeof(aux); i++)

+			fprint(2, "%02X", aux[i]);

+		fprint(2, "\nand should be:\n");

+		for(i = 0; i < sizeof(CBCcipher); i++)

+			fprint(2, "%02X", CBCcipher[i]);

+		fprint(2, "\n");

+		return -1;

+	}

+

+	memset(&s, 0, sizeof(BFstate));

+	setupBFstate(&s, CBCkey, sizeof(CBCkey), CBCiv);

+	bfCBCdecrypt(aux, 32, &s);

+

+	if(memcmp(aux, CBCdata, sizeof(CBCdata)) != 0){

+		fprint(2, "CBC decrypt failed, plaintext is:\n");

+		for(i = 0; i < sizeof(aux); i++)

+			fprint(2, "%02X", aux[i]);

+		fprint(2, "\nand should be:\n");

+		for(i = 0; i < sizeof(CBCdata); i++)

+			fprint(2, "%02X", CBCdata[i]);

+		fprint(2, "\n");

+		return -1;

+	}

+

+	return 0;

+}

+

+void

+main(int argc, char **argv)

+{

+	int i;

+

+	if(argc != 1)

+		sysfatal("usage: %s", argv[0]);

+

+	for(i=0; i < nelem(vector); i++)

+		if(testECB(&vector[i]) < 0)

+			sysfatal("TestECB %d failed", i);

+

+	if(testCBC() < 0)

+		sysfatal("TestCBC failed");

+	exits(nil);

+}

--- a/libsec/blowfish.c

+++ b/libsec/blowfish.c

@@ -1,5 +1,4 @@

 #include "os.h"

-#include <mp.h>

 #include <libsec.h>

 // Blowfish block cipher.  See:

--- a/libsec/ccpoly.c

+++ b/libsec/ccpoly.c

@@ -1,5 +1,4 @@

-#include <u.h>

-#include <libc.h>

+#include "os.h"

 #include <libsec.h>

 static void

--- a/libsec/chacha.c

+++ b/libsec/chacha.c

@@ -7,8 +7,7 @@

 and including the changes to block number and nonce defined in RFC7539

 */

-#include <u.h>

-#include <libc.h>

+#include "os.h"

 #include <libsec.h>

 enum{

--- /dev/null

+++ b/libsec/chachatest.c

@@ -1,0 +1,176 @@

+#include <u.h>

+#include <libc.h>

+#include <libsec.h>

+

+static void

+printblock(uchar *b, usize n)

+{

+	int i;

+

+	for(i=0; i+8<=n; i+=8){

+		print("%#.2ux %#.2ux %#.2ux %#.2ux %#.2ux %#.2ux %#.2ux %#.2ux\n",

+			b[0], b[1], b[2], b[3], b[4], b[5], b[6], b[7]);

+		b += 8;

+	}

+	if(i < n){

+		print("%#.2ux", *b++);

+		while(++i < n)

+			print(" %#.2ux", *b++);

+		print("\n");

+	}

+}

+

+/* test vector from RFC7539 */

+uchar	rfckey[] = {

+	0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07,

+	0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f,

+	0x10, 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17,

+	0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f};

+uchar	rfcnonce[] = {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x4a, 0x00, 0x00, 0x00, 0x00};

+u32int	rfccount = 1;

+char	rfctext[] = "Ladies and Gentlemen of the class of '99: If I could offer you only one tip for the future, "

+	"sunscreen would be it.";

+uchar	rfcout[3*ChachaBsize];

+uchar	rfcref[] = {

+	0x6e, 0x2e, 0x35, 0x9a, 0x25, 0x68, 0xf9, 0x80, 0x41, 0xba, 0x07, 0x28, 0xdd, 0x0d, 0x69, 0x81,

+	0xe9, 0x7e, 0x7a, 0xec, 0x1d, 0x43, 0x60, 0xc2, 0x0a, 0x27, 0xaf, 0xcc, 0xfd, 0x9f, 0xae, 0x0b,

+	0xf9, 0x1b, 0x65, 0xc5, 0x52, 0x47, 0x33, 0xab, 0x8f, 0x59, 0x3d, 0xab, 0xcd, 0x62, 0xb3, 0x57,

+	0x16, 0x39, 0xd6, 0x24, 0xe6, 0x51, 0x52, 0xab, 0x8f, 0x53, 0x0c, 0x35, 0x9f, 0x08, 0x61, 0xd8,

+	0x07, 0xca, 0x0d, 0xbf, 0x50, 0x0d, 0x6a, 0x61, 0x56, 0xa3, 0x8e, 0x08, 0x8a, 0x22, 0xb6, 0x5e,

+	0x52, 0xbc, 0x51, 0x4d, 0x16, 0xcc, 0xf8, 0x06, 0x81, 0x8c, 0xe9, 0x1a, 0xb7, 0x79, 0x37, 0x36,

+	0x5a, 0xf9, 0x0b, 0xbf, 0x74, 0xa3, 0x5b, 0xe6, 0xb4, 0x0b, 0x8e, 0xed, 0xf2, 0x78, 0x5e, 0x42,

+	0x87, 0x4d

+};

+

+uchar	ccpaad[] = {

+	0x50, 0x51, 0x52, 0x53, 0xc0, 0xc1, 0xc2, 0xc3, 0xc4, 0xc5, 0xc6, 0xc7,

+};

+uchar	ccpkey[] = {

+	0x80, 0x81, 0x82, 0x83, 0x84, 0x85, 0x86, 0x87, 0x88, 0x89, 0x8a, 0x8b, 0x8c, 0x8d, 0x8e, 0x8f,

+	0x90, 0x91, 0x92, 0x93, 0x94, 0x95, 0x96, 0x97, 0x98, 0x99, 0x9a, 0x9b, 0x9c, 0x9d, 0x9e, 0x9f,

+};

+uchar	ccpiv[] = {

+	0x07, 0x00, 0x00, 0x00,  

+	0x40, 0x41, 0x42, 0x43, 0x44, 0x45, 0x46, 0x47,

+};

+uchar	ccptag[] = {

+	0x1a, 0xe1, 0x0b, 0x59, 0x4f, 0x09, 0xe2, 0x6a, 0x7e, 0x90, 0x2e, 0xcb, 0xd0, 0x60, 0x06, 0x91,

+};

+

+uchar	ccp64aad[] = {

+	0x87, 0xe2, 0x29, 0xd4, 0x50, 0x08, 0x45, 0xa0, 0x79, 0xc0,

+};

+uchar	ccp64key[] = {

+	0x42, 0x90, 0xbc, 0xb1, 0x54, 0x17, 0x35, 0x31, 0xf3, 0x14, 0xaf, 0x57, 0xf3, 0xbe, 0x3b, 0x50,

+	0x06, 0xda, 0x37, 0x1e, 0xce, 0x27, 0x2a, 0xfa, 0x1b, 0x5d, 0xbd, 0xd1, 0x10, 0x0a, 0x10, 0x07,

+};

+uchar	ccp64iv[] = {

+	0xcd, 0x7c, 0xf6, 0x7b, 0xe3, 0x9c, 0x79, 0x4a,

+};

+uchar	ccp64inp[] = {

+	0x86, 0xd0, 0x99, 0x74, 0x84, 0x0b, 0xde, 0xd2, 0xa5, 0xca, 

+};

+uchar	ccp64out[] = {

+	0xe3, 0xe4, 0x46, 0xf7, 0xed, 0xe9, 0xa1, 0x9b, 0x62, 0xa4,

+};

+uchar	ccp64tag[] = {

+	0x67, 0x7d, 0xab, 0xf4, 0xe3, 0xd2, 0x4b, 0x87, 0x6b, 0xb2, 0x84, 0x75, 0x38, 0x96, 0xe1, 0xd6,

+};

+

+void

+main(int argc, char **argv)

+{

+	Chachastate s;

+	uchar tag[16];

+	int n;

+

+	ARGBEGIN{

+	}ARGEND

+	print("rfc7539:\n");

+	print("key:\n");

+	printblock(rfckey, sizeof(rfckey));

+	n = strlen(rfctext);

+	setupChachastate(&s, rfckey, sizeof(rfckey), rfcnonce, sizeof(rfcnonce), 0);

+	chacha_setblock(&s, rfccount);

+	print("rfc in:\n");

+	printblock((uchar*)rfctext, n);

+	chacha_encrypt2((uchar*)rfctext, rfcout, n, &s);

+	print("rfc out:\n");

+	printblock(rfcout, n);

+	if(memcmp(rfcout, rfcref, sizeof(rfcref)) != 0){

+		print("failure of vision\n");

+		exits("wrong");

+	}

+	print("\n");

+

+	print("ccpoly key:\n");

+	printblock(ccpkey, sizeof(ccpkey));

+

+	print("ccpoly iv:\n");

+	printblock(ccpiv, sizeof(ccpiv));

+

+	setupChachastate(&s, ccpkey, sizeof(ccpkey), ccpiv, sizeof(ccpiv), 20);

+

+	memmove(rfcout, rfctext, sizeof(rfctext)-1);

+	ccpoly_encrypt(rfcout, sizeof(rfctext)-1, ccpaad, sizeof(ccpaad), tag, &s);

+

+	print("ccpoly cipher:\n");

+	printblock(rfcout, sizeof(rfctext)-1);

+

+	print("ccpoly tag:\n");

+	printblock(tag, sizeof(tag));

+

+	if(memcmp(tag, ccptag, sizeof(tag)) != 0){

+		print("bad ccpoly tag\n");

+		exits("wrong");

+	}

+

+	if(ccpoly_decrypt(rfcout, sizeof(rfctext)-1, ccpaad, sizeof(ccpaad), tag, &s) != 0){

+		print("ccpoly decryption failed\n");

+		exits("wrong");

+	}

+

+	if(memcmp(rfcout, rfctext, sizeof(rfctext)-1) != 0){

+		print("ccpoly bad decryption\n");

+		exits("wrong");

+	}

+	print("\n");

+

+	print("ccpoly64 key:\n");

+	printblock(ccp64key, sizeof(ccp64key));

+

+	print("ccpoly64 iv:\n");

+	printblock(ccp64iv, sizeof(ccp64iv));

+

+	setupChachastate(&s, ccp64key, sizeof(ccp64key), ccp64iv, sizeof(ccp64iv), 20);

+

+	memmove(rfcout, ccp64inp, sizeof(ccp64inp));

+	ccpoly_encrypt(rfcout, sizeof(ccp64inp), ccp64aad, sizeof(ccp64aad), tag, &s);

+

+	print("ccpoly64 cipher:\n");

+	printblock(rfcout, sizeof(ccp64inp));

+

+	print("ccpoly64 tag:\n");

+	printblock(tag, sizeof(tag));

+

+	if(memcmp(rfcout, ccp64out, sizeof(ccp64out)) != 0){

+		print("ccpoly64 bad ciphertext\n");

+		exits("wrong");

+	}

+	if(memcmp(tag, ccp64tag, sizeof(ccp64tag)) != 0){

+		print("ccpoly64 bad encryption tag\n");

+		exits("wrong");

+	}

+

+	if(ccpoly_decrypt(rfcout, sizeof(ccp64inp), ccp64aad, sizeof(ccp64aad), tag, &s) != 0){

+		print("ccpoly64 decryption failed\n");

+		exits("wrong");

+	}

+	if(memcmp(rfcout, ccp64inp, sizeof(ccp64inp)) != 0){

+		print("ccpoly64 bad decryption\n");

+		exits("wrong");

+	}

+

+	print("passed\n");

+	exits(nil);

+}

--- a/libsec/curve25519.c

+++ b/libsec/curve25519.c

@@ -45,8 +45,7 @@

  * uses many of the tricks described therein. Only the crecip function is taken

  * from the sample implementation.

  */

-#include <u.h>

-#include <libc.h>

+#include "os.h"

 #include <libsec.h>

 typedef vlong felem;

--- a/libsec/decodepem.c

+++ b/libsec/decodepem.c

@@ -1,6 +1,4 @@

-#include <u.h>

-#include <libc.h>

-#include <mp.h>

+#include "os.h"

 #include <libsec.h>

 #define STRLEN(s)	(sizeof(s)-1)

--- a/libsec/des3CBC.c

+++ b/libsec/des3CBC.c

@@ -1,5 +1,4 @@

 #include "os.h"

-#include <mp.h>

 #include <libsec.h>

 // Because of the way that non multiple of 8

--- a/libsec/des3ECB.c

+++ b/libsec/des3ECB.c

@@ -1,5 +1,4 @@

 #include "os.h"

-#include <mp.h>

 #include <libsec.h>

 // I wasn't sure what to do when the buffer was not

--- a/libsec/desCBC.c

+++ b/libsec/desCBC.c

@@ -1,5 +1,4 @@

 #include "os.h"

-#include <mp.h>

 #include <libsec.h>

 // Because of the way that non multiple of 8

--- a/libsec/desECB.c

+++ b/libsec/desECB.c

@@ -1,5 +1,4 @@

 #include "os.h"

-#include <mp.h>

 #include <libsec.h>

 // I wasn't sure what to do when the buffer was not

--- a/libsec/egtest.c

+++ b/libsec/egtest.c

@@ -9,7 +9,7 @@

 	mpint *m, *gamma, *delta, *in, *out;

 	int plen, shift;

-	fmtinstall('B', mpconv);

+	fmtinstall('B', mpfmt);

 	sk = egprivalloc();

 	sk->pub.p = uitomp(2357, nil);

--- a/libsec/fastrand.c

+++ b/libsec/fastrand.c

@@ -1,6 +1,5 @@

-#include	<u.h>

-#include	<libc.h>

-#include	<libsec.h>

+#include "os.h"

+#include <libsec.h>

 /* 

  *  use the X917 random number generator to create random

--- a/libsec/genrandom.c

+++ b/libsec/genrandom.c

@@ -1,5 +1,4 @@

 #include "os.h"

-#include <mp.h>

 #include <libsec.h>

 typedef struct State{

--- a/libsec/hkdf.c

+++ b/libsec/hkdf.c

@@ -1,5 +1,4 @@

 #include "os.h"

-#include <mp.h>

 #include <libsec.h>

 /* rfc5869 */

--- /dev/null

+++ b/libsec/hmactest.c

@@ -1,0 +1,19 @@

+#include "os.h"

+#include <mp.h>

+#include <libsec.h>

+

+uchar key[] = "Jefe";

+uchar data[] = "what do ya want for nothing?";

+

+void

+main(void)

+{

+	int i;

+	uchar hash[MD5dlen];

+

+	hmac_md5(data, strlen((char*)data), key, 4, hash, nil);

+	for(i=0; i<MD5dlen; i++)

+		print("%2.2x", hash[i]);

+	print("\n");

+	print("750c783e6ab0b503eaa86e310a5db738\n");

+}

--- /dev/null

+++ b/libsec/md4test.c

@@ -1,0 +1,31 @@

+#include "os.h"

+#include <mp.h>

+#include <libsec.h>

+

+char *tests[] = {

+	"",

+	"a",

+	"abc",

+	"message digest",

+	"abcdefghijklmnopqrstuvwxyz",

+	"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789",

+	"12345678901234567890123456789012345678901234567890123456789012345678901234567890",

+	0

+};

+

+void

+main(void)

+{

+	char **pp;

+	uchar *p;

+	int i;

+	uchar digest[MD5dlen];

+

+	for(pp = tests; *pp; pp++){

+		p = (uchar*)*pp;

+		md4(p, strlen(*pp), digest, 0);

+		for(i = 0; i < MD5dlen; i++)

+			print("%2.2ux", digest[i]);

+		print("\n");

+	}

+}

--- a/libsec/nfastrand.c

+++ b/libsec/nfastrand.c

@@ -1,5 +1,4 @@

-#include <u.h>

-#include <libc.h>

+#include "os.h"

 #include <libsec.h>

 #define Maxrand	((1UL<<31)-1)

--- a/libsec/pbkdf2.c

+++ b/libsec/pbkdf2.c

@@ -1,5 +1,4 @@

 #include "os.h"

-#include <mp.h>

 #include <libsec.h>

 /* rfc2898 */

--- a/libsec/poly1305.c

+++ b/libsec/poly1305.c

@@ -1,5 +1,4 @@

-#include <u.h>

-#include <libc.h>

+#include "os.h"

 #include <libsec.h>

 /*

--- a/libsec/primetest.c

+++ b/libsec/primetest.c

@@ -10,7 +10,7 @@

 	mpint *q = mpnew(0);

 	mpint *nine = mpnew(0);

-	fmtinstall('B', mpconv);

+	fmtinstall('B', mpfmt);

 	strtomp("2492491", nil, 16, z);	// 38347921 = x*y = (2**28-9)/7, 

 				//    an example of 3**(n-1)=1 mod n

 	strtomp("15662C00E811", nil, 16, p);// 23528569104401, a prime

--- a/libsec/prng.c

+++ b/libsec/prng.c

@@ -1,5 +1,4 @@

 #include "os.h"

-#include <mp.h>

 #include <libsec.h>

 //

--- a/libsec/readcert.c

+++ b/libsec/readcert.c

@@ -1,7 +1,4 @@

-#include <u.h>

-#include <libc.h>

-#include <auth.h>

-#include <mp.h>

+#include "os.h"

 #include <libsec.h>

 static char*

--- a/libsec/rsatest.c

+++ b/libsec/rsatest.c

@@ -6,16 +6,15 @@

 void

 main(void)

 {

-	RSApriv *rsa;

-	Biobuf b;

-	char *p;

 	int n;

-	mpint *clr, *enc, *clr2;

-	uchar buf[4096];

-	uchar *e;

 	vlong start;

+	char *p;

+	uchar buf[4096];

+	Biobuf b;

+	RSApriv *rsa;

+	mpint *clr, *enc, *clr2;

-	fmtinstall('B', mpconv);

+	fmtinstall('B', mpfmt);

 	rsa = rsagen(1024, 16, 0);

 	if(rsa == nil)

--- a/libsec/salsa.c

+++ b/libsec/salsa.c

@@ -1,5 +1,4 @@

-#include <u.h>

-#include <libc.h>

+#include "os.h"

 #include <libsec.h>

 enum{

--- a/libsec/secp256k1.c

+++ b/libsec/secp256k1.c

@@ -1,5 +1,4 @@

-#include <u.h>

-#include <libc.h>

+#include "os.h"

 #include <mp.h>

 void secp256k1(mpint *p, mpint *a, mpint *b, mpint *x, mpint *y, mpint *n, mpint *h){

 	strtomp("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F", nil, 16, p);

--- a/libsec/secp256r1.c

+++ b/libsec/secp256r1.c

@@ -1,5 +1,4 @@

-#include <u.h>

-#include <libc.h>

+#include "os.h"

 #include <mp.h>

 void secp256r1(mpint *p, mpint *a, mpint *b, mpint *x, mpint *y, mpint *n, mpint *h){

 	strtomp("FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF", nil, 16, p);

--- /dev/null

+++ b/libsec/sha2test.c

@@ -1,0 +1,63 @@

+#include <u.h>

+#include <libc.h>

+#include "libsec.h"

+

+char *tests[] = {

+	"",

+	"a",

+	"abc",

+	"message digest",

+	"abcdefghijklmnopqrstuvwxyz",

+	"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789",

+	"123456789012345678901234567890123456789012345678901234567890"

+		"12345678901234567890",

+	"abcdbcdecdefdefgefghfghighijhijkijkljklmklmnlmnomnopnopq",

+	"abcdefghbcdefghicdefghijdefghijkefghijklfghijklmghijklmnhi"

+		"jklmnoijklmnopjklmnopqklmnopqrlmnopqrsmnopqrstnopqrstu",

+	0

+};

+

+void

+main(void)

+{

+	int i;

+	char **pp;

+	uchar *p;

+	uchar digest[SHA2_512dlen];

+

+	print("SHA2_224 tests:\n");

+	for(pp = tests; *pp; pp++){

+		p = (uchar*)*pp;

+		sha2_224(p, strlen(*pp), digest, 0);

+		for(i = 0; i < SHA2_224dlen; i++)

+			print("%2.2ux", digest[i]);

+		print("\n");

+	}

+

+	print("\nSHA256 tests:\n");

+	for(pp = tests; *pp; pp++){

+		p = (uchar*)*pp;

+		sha2_256(p, strlen(*pp), digest, 0);

+		for(i = 0; i < SHA2_256dlen; i++)

+			print("%2.2ux", digest[i]);

+		print("\n");

+	}

+

+	print("\nSHA384 tests:\n");

+	for(pp = tests; *pp; pp++){

+		p = (uchar*)*pp;

+		sha2_384(p, strlen(*pp), digest, 0);

+		for(i = 0; i < SHA2_384dlen; i++)

+			print("%2.2ux", digest[i]);

+		print("\n");

+	}

+

+	print("\nSHA512 tests:\n");

+	for(pp = tests; *pp; pp++){

+		p = (uchar*)*pp;

+		sha2_512(p, strlen(*pp), digest, 0);

+		for(i = 0; i < SHA2_512dlen; i++)

+			print("%2.2ux", digest[i]);

+		print("\n");

+	}

+}

--- /dev/null

+++ b/libsec/smallprimetest.c

@@ -1,0 +1,1039 @@

+#include "os.h"

+#include <mp.h>

+#include <libsec.h>

+

+static ulong smallprimes[] = {

+	2,	3,	5,	7,	11,	13,	17,	19,	23,	29,

+	31,	37,	41,	43,	47,	53,	59,	61,	67,	71,

+	73,	79,	83,	89,	97,	101,	103,	107,	109,	113,

+	127,	131,	137,	139,	149,	151,	157,	163,	167,	173,

+	179,	181,	191,	193,	197,	199,	211,	223,	227,	229,

+	233,	239,	241,	251,	257,	263,	269,	271,	277,	281,

+	283,	293,	307,	311,	313,	317,	331,	337,	347,	349,

+	353,	359,	367,	373,	379,	383,	389,	397,	401,	409,

+	419,	421,	431,	433,	439,	443,	449,	457,	461,	463,

+	467,	479,	487,	491,	499,	503,	509,	521,	523,	541,

+	547,	557,	563,	569,	571,	577,	587,	593,	599,	601,

+	607,	613,	617,	619,	631,	641,	643,	647,	653,	659,

+	661,	673,	677,	683,	691,	701,	709,	719,	727,	733,

+	739,	743,	751,	757,	761,	769,	773,	787,	797,	809,

+	811,	821,	823,	827,	829,	839,	853,	857,	859,	863,

+	877,	881,	883,	887,	907,	911,	919,	929,	937,	941,

+	947,	953,	967,	971,	977,	983,	991,	997,	1009,	1013,

+	1019,	1021,	1031,	1033,	1039,	1049,	1051,	1061,	1063,	1069,

+	1087,	1091,	1093,	1097,	1103,	1109,	1117,	1123,	1129,	1151,

+	1153,	1163,	1171,	1181,	1187,	1193,	1201,	1213,	1217,	1223,

+	1229,	1231,	1237,	1249,	1259,	1277,	1279,	1283,	1289,	1291,

+	1297,	1301,	1303,	1307,	1319,	1321,	1327,	1361,	1367,	1373,

+	1381,	1399,	1409,	1423,	1427,	1429,	1433,	1439,	1447,	1451,

+	1453,	1459,	1471,	1481,	1483,	1487,	1489,	1493,	1499,	1511,

+	1523,	1531,	1543,	1549,	1553,	1559,	1567,	1571,	1579,	1583,

+	1597,	1601,	1607,	1609,	1613,	1619,	1621,	1627,	1637,	1657,

+	1663,	1667,	1669,	1693,	1697,	1699,	1709,	1721,	1723,	1733,

+	1741,	1747,	1753,	1759,	1777,	1783,	1787,	1789,	1801,	1811,

+	1823,	1831,	1847,	1861,	1867,	1871,	1873,	1877,	1879,	1889,

+	1901,	1907,	1913,	1931,	1933,	1949,	1951,	1973,	1979,	1987,

+	1993,	1997,	1999,	2003,	2011,	2017,	2027,	2029,	2039,	2053,

+	2063,	2069,	2081,	2083,	2087,	2089,	2099,	2111,	2113,	2129,

+	2131,	2137,	2141,	2143,	2153,	2161,	2179,	2203,	2207,	2213,

+	2221,	2237,	2239,	2243,	2251,	2267,	2269,	2273,	2281,	2287,

+	2293,	2297,	2309,	2311,	2333,	2339,	2341,	2347,	2351,	2357,

+	2371,	2377,	2381,	2383,	2389,	2393,	2399,	2411,	2417,	2423,

+	2437,	2441,	2447,	2459,	2467,	2473,	2477,	2503,	2521,	2531,

+	2539,	2543,	2549,	2551,	2557,	2579,	2591,	2593,	2609,	2617,

+	2621,	2633,	2647,	2657,	2659,	2663,	2671,	2677,	2683,	2687,

+	2689,	2693,	2699,	2707,	2711,	2713,	2719,	2729,	2731,	2741,

+	2749,	2753,	2767,	2777,	2789,	2791,	2797,	2801,	2803,	2819,

+	2833,	2837,	2843,	2851,	2857,	2861,	2879,	2887,	2897,	2903,

+	2909,	2917,	2927,	2939,	2953,	2957,	2963,	2969,	2971,	2999,

+	3001,	3011,	3019,	3023,	3037,	3041,	3049,	3061,	3067,	3079,

+	3083,	3089,	3109,	3119,	3121,	3137,	3163,	3167,	3169,	3181,

+	3187,	3191,	3203,	3209,	3217,	3221,	3229,	3251,	3253,	3257,

+	3259,	3271,	3299,	3301,	3307,	3313,	3319,	3323,	3329,	3331,

+	3343,	3347,	3359,	3361,	3371,	3373,	3389,	3391,	3407,	3413,

+	3433,	3449,	3457,	3461,	3463,	3467,	3469,	3491,	3499,	3511,

+	3517,	3527,	3529,	3533,	3539,	3541,	3547,	3557,	3559,	3571,

+	3581,	3583,	3593,	3607,	3613,	3617,	3623,	3631,	3637,	3643,

+	3659,	3671,	3673,	3677,	3691,	3697,	3701,	3709,	3719,	3727,

+	3733,	3739,	3761,	3767,	3769,	3779,	3793,	3797,	3803,	3821,

+	3823,	3833,	3847,	3851,	3853,	3863,	3877,	3881,	3889,	3907,

+	3911,	3917,	3919,	3923,	3929,	3931,	3943,	3947,	3967,	3989,

+	4001,	4003,	4007,	4013,	4019,	4021,	4027,	4049,	4051,	4057,

+	4073,	4079,	4091,	4093,	4099,	4111,	4127,	4129,	4133,	4139,

+	4153,	4157,	4159,	4177,	4201,	4211,	4217,	4219,	4229,	4231,

+	4241,	4243,	4253,	4259,	4261,	4271,	4273,	4283,	4289,	4297,

+	4327,	4337,	4339,	4349,	4357,	4363,	4373,	4391,	4397,	4409,

+	4421,	4423,	4441,	4447,	4451,	4457,	4463,	4481,	4483,	4493,

+	4507,	4513,	4517,	4519,	4523,	4547,	4549,	4561,	4567,	4583,

+	4591,	4597,	4603,	4621,	4637,	4639,	4643,	4649,	4651,	4657,

+	4663,	4673,	4679,	4691,	4703,	4721,	4723,	4729,	4733,	4751,

+	4759,	4783,	4787,	4789,	4793,	4799,	4801,	4813,	4817,	4831,

+	4861,	4871,	4877,	4889,	4903,	4909,	4919,	4931,	4933,	4937,

+	4943,	4951,	4957,	4967,	4969,	4973,	4987,	4993,	4999,	5003,

+	5009,	5011,	5021,	5023,	5039,	5051,	5059,	5077,	5081,	5087,

+	5099,	5101,	5107,	5113,	5119,	5147,	5153,	5167,	5171,	5179,

+	5189,	5197,	5209,	5227,	5231,	5233,	5237,	5261,	5273,	5279,

+	5281,	5297,	5303,	5309,	5323,	5333,	5347,	5351,	5381,	5387,

+	5393,	5399,	5407,	5413,	5417,	5419,	5431,	5437,	5441,	5443,

+	5449,	5471,	5477,	5479,	5483,	5501,	5503,	5507,	5519,	5521,

+	5527,	5531,	5557,	5563,	5569,	5573,	5581,	5591,	5623,	5639,

+	5641,	5647,	5651,	5653,	5657,	5659,	5669,	5683,	5689,	5693,

+	5701,	5711,	5717,	5737,	5741,	5743,	5749,	5779,	5783,	5791,

+	5801,	5807,	5813,	5821,	5827,	5839,	5843,	5849,	5851,	5857,

+	5861,	5867,	5869,	5879,	5881,	5897,	5903,	5923,	5927,	5939,

+	5953,	5981,	5987,	6007,	6011,	6029,	6037,	6043,	6047,	6053,

+	6067,	6073,	6079,	6089,	6091,	6101,	6113,	6121,	6131,	6133,

+	6143,	6151,	6163,	6173,	6197,	6199,	6203,	6211,	6217,	6221,

+	6229,	6247,	6257,	6263,	6269,	6271,	6277,	6287,	6299,	6301,

+	6311,	6317,	6323,	6329,	6337,	6343,	6353,	6359,	6361,	6367,

+	6373,	6379,	6389,	6397,	6421,	6427,	6449,	6451,	6469,	6473,

+	6481,	6491,	6521,	6529,	6547,	6551,	6553,	6563,	6569,	6571,

+	6577,	6581,	6599,	6607,	6619,	6637,	6653,	6659,	6661,	6673,

+	6679,	6689,	6691,	6701,	6703,	6709,	6719,	6733,	6737,	6761,

+	6763,	6779,	6781,	6791,	6793,	6803,	6823,	6827,	6829,	6833,

+	6841,	6857,	6863,	6869,	6871,	6883,	6899,	6907,	6911,	6917,

+	6947,	6949,	6959,	6961,	6967,	6971,	6977,	6983,	6991,	6997,

+	7001,	7013,	7019,	7027,	7039,	7043,	7057,	7069,	7079,	7103,

+	7109,	7121,	7127,	7129,	7151,	7159,	7177,	7187,	7193,	7207,

+	7211,	7213,	7219,	7229,	7237,	7243,	7247,	7253,	7283,	7297,

+	7307,	7309,	7321,	7331,	7333,	7349,	7351,	7369,	7393,	7411,

+	7417,	7433,	7451,	7457,	7459,	7477,	7481,	7487,	7489,	7499,

+	7507,	7517,	7523,	7529,	7537,	7541,	7547,	7549,	7559,	7561,

+	7573,	7577,	7583,	7589,	7591,	7603,	7607,	7621,	7639,	7643,

+	7649,	7669,	7673,	7681,	7687,	7691,	7699,	7703,	7717,	7723,

+	7727,	7741,	7753,	7757,	7759,	7789,	7793,	7817,	7823,	7829,

+	7841,	7853,	7867,	7873,	7877,	7879,	7883,	7901,	7907,	7919,

+	7927,	7933,	7937,	7949,	7951,	7963,	7993,	8009,	8011,	8017,

+	8039,	8053,	8059,	8069,	8081,	8087,	8089,	8093,	8101,	8111,

+	8117,	8123,	8147,	8161,	8167,	8171,	8179,	8191,	8209,	8219,

+	8221,	8231,	8233,	8237,	8243,	8263,	8269,	8273,	8287,	8291,

+	8293,	8297,	8311,	8317,	8329,	8353,	8363,	8369,	8377,	8387,

+	8389,	8419,	8423,	8429,	8431,	8443,	8447,	8461,	8467,	8501,

+	8513,	8521,	8527,	8537,	8539,	8543,	8563,	8573,	8581,	8597,

+	8599,	8609,	8623,	8627,	8629,	8641,	8647,	8663,	8669,	8677,

+	8681,	8689,	8693,	8699,	8707,	8713,	8719,	8731,	8737,	8741,

+	8747,	8753,	8761,	8779,	8783,	8803,	8807,	8819,	8821,	8831,

+	8837,	8839,	8849,	8861,	8863,	8867,	8887,	8893,	8923,	8929,

+	8933,	8941,	8951,	8963,	8969,	8971,	8999,	9001,	9007,	9011,

+	9013,	9029,	9041,	9043,	9049,	9059,	9067,	9091,	9103,	9109,

+	9127,	9133,	9137,	9151,	9157,	9161,	9173,	9181,	9187,	9199,

+	9203,	9209,	9221,	9227,	9239,	9241,	9257,	9277,	9281,	9283,

+	9293,	9311,	9319,	9323,	9337,	9341,	9343,	9349,	9371,	9377,

+	9391,	9397,	9403,	9413,	9419,	9421,	9431,	9433,	9437,	9439,

+	9461,	9463,	9467,	9473,	9479,	9491,	9497,	9511,	9521,	9533,

+	9539,	9547,	9551,	9587,	9601,	9613,	9619,	9623,	9629,	9631,

+	9643,	9649,	9661,	9677,	9679,	9689,	9697,	9719,	9721,	9733,

+	9739,	9743,	9749,	9767,	9769,	9781,	9787,	9791,	9803,	9811,

+	9817,	9829,	9833,	9839,	9851,	9857,	9859,	9871,	9883,	9887,

+	9901,	9907,	9923,	9929,	9931,	9941,	9949,	9967,	9973,	10007,

+	10009,	10037,	10039,	10061,	10067,	10069,	10079,	10091,	10093,	10099,

+	10103,	10111,	10133,	10139,	10141,	10151,	10159,	10163,	10169,	10177,

+	10181,	10193,	10211,	10223,	10243,	10247,	10253,	10259,	10267,	10271,

+	10273,	10289,	10301,	10303,	10313,	10321,	10331,	10333,	10337,	10343,

+	10357,	10369,	10391,	10399,	10427,	10429,	10433,	10453,	10457,	10459,

+	10463,	10477,	10487,	10499,	10501,	10513,	10529,	10531,	10559,	10567,

+	10589,	10597,	10601,	10607,	10613,	10627,	10631,	10639,	10651,	10657,

+	10663,	10667,	10687,	10691,	10709,	10711,	10723,	10729,	10733,	10739,

+	10753,	10771,	10781,	10789,	10799,	10831,	10837,	10847,	10853,	10859,

+	10861,	10867,	10883,	10889,	10891,	10903,	10909,	10937,	10939,	10949,

+	10957,	10973,	10979,	10987,	10993,	11003,	11027,	11047,	11057,	11059,

+	11069,	11071,	11083,	11087,	11093,	11113,	11117,	11119,	11131,	11149,

+	11159,	11161,	11171,	11173,	11177,	11197,	11213,	11239,	11243,	11251,

+	11257,	11261,	11273,	11279,	11287,	11299,	11311,	11317,	11321,	11329,

+	11351,	11353,	11369,	11383,	11393,	11399,	11411,	11423,	11437,	11443,

+	11447,	11467,	11471,	11483,	11489,	11491,	11497,	11503,	11519,	11527,

+	11549,	11551,	11579,	11587,	11593,	11597,	11617,	11621,	11633,	11657,

+	11677,	11681,	11689,	11699,	11701,	11717,	11719,	11731,	11743,	11777,

+	11779,	11783,	11789,	11801,	11807,	11813,	11821,	11827,	11831,	11833,

+	11839,	11863,	11867,	11887,	11897,	11903,	11909,	11923,	11927,	11933,

+	11939,	11941,	11953,	11959,	11969,	11971,	11981,	11987,	12007,	12011,

+	12037,	12041,	12043,	12049,	12071,	12073,	12097,	12101,	12107,	12109,

+	12113,	12119,	12143,	12149,	12157,	12161,	12163,	12197,	12203,	12211,

+	12227,	12239,	12241,	12251,	12253,	12263,	12269,	12277,	12281,	12289,

+	12301,	12323,	12329,	12343,	12347,	12373,	12377,	12379,	12391,	12401,

+	12409,	12413,	12421,	12433,	12437,	12451,	12457,	12473,	12479,	12487,

+	12491,	12497,	12503,	12511,	12517,	12527,	12539,	12541,	12547,	12553,

+	12569,	12577,	12583,	12589,	12601,	12611,	12613,	12619,	12637,	12641,

+	12647,	12653,	12659,	12671,	12689,	12697,	12703,	12713,	12721,	12739,

+	12743,	12757,	12763,	12781,	12791,	12799,	12809,	12821,	12823,	12829,

+	12841,	12853,	12889,	12893,	12899,	12907,	12911,	12917,	12919,	12923,

+	12941,	12953,	12959,	12967,	12973,	12979,	12983,	13001,	13003,	13007,

+	13009,	13033,	13037,	13043,	13049,	13063,	13093,	13099,	13103,	13109,

+	13121,	13127,	13147,	13151,	13159,	13163,	13171,	13177,	13183,	13187,

+	13217,	13219,	13229,	13241,	13249,	13259,	13267,	13291,	13297,	13309,

+	13313,	13327,	13331,	13337,	13339,	13367,	13381,	13397,	13399,	13411,

+	13417,	13421,	13441,	13451,	13457,	13463,	13469,	13477,	13487,	13499,

+	13513,	13523,	13537,	13553,	13567,	13577,	13591,	13597,	13613,	13619,

+	13627,	13633,	13649,	13669,	13679,	13681,	13687,	13691,	13693,	13697,

+	13709,	13711,	13721,	13723,	13729,	13751,	13757,	13759,	13763,	13781,

+	13789,	13799,	13807,	13829,	13831,	13841,	13859,	13873,	13877,	13879,

+	13883,	13901,	13903,	13907,	13913,	13921,	13931,	13933,	13963,	13967,

+	13997,	13999,	14009,	14011,	14029,	14033,	14051,	14057,	14071,	14081,

+	14083,	14087,	14107,	14143,	14149,	14153,	14159,	14173,	14177,	14197,

+	14207,	14221,	14243,	14249,	14251,	14281,	14293,	14303,	14321,	14323,

+	14327,	14341,	14347,	14369,	14387,	14389,	14401,	14407,	14411,	14419,

+	14423,	14431,	14437,	14447,	14449,	14461,	14479,	14489,	14503,	14519,

+	14533,	14537,	14543,	14549,	14551,	14557,	14561,	14563,	14591,	14593,

+	14621,	14627,	14629,	14633,	14639,	14653,	14657,	14669,	14683,	14699,

+	14713,	14717,	14723,	14731,	14737,	14741,	14747,	14753,	14759,	14767,

+	14771,	14779,	14783,	14797,	14813,	14821,	14827,	14831,	14843,	14851,

+	14867,	14869,	14879,	14887,	14891,	14897,	14923,	14929,	14939,	14947,

+	14951,	14957,	14969,	14983,	15013,	15017,	15031,	15053,	15061,	15073,

+	15077,	15083,	15091,	15101,	15107,	15121,	15131,	15137,	15139,	15149,

+	15161,	15173,	15187,	15193,	15199,	15217,	15227,	15233,	15241,	15259,

+	15263,	15269,	15271,	15277,	15287,	15289,	15299,	15307,	15313,	15319,

+	15329,	15331,	15349,	15359,	15361,	15373,	15377,	15383,	15391,	15401,

+	15413,	15427,	15439,	15443,	15451,	15461,	15467,	15473,	15493,	15497,

+	15511,	15527,	15541,	15551,	15559,	15569,	15581,	15583,	15601,	15607,

+	15619,	15629,	15641,	15643,	15647,	15649,	15661,	15667,	15671,	15679,

+	15683,	15727,	15731,	15733,	15737,	15739,	15749,	15761,	15767,	15773,

+	15787,	15791,	15797,	15803,	15809,	15817,	15823,	15859,	15877,	15881,

+	15887,	15889,	15901,	15907,	15913,	15919,	15923,	15937,	15959,	15971,

+	15973,	15991,	16001,	16007,	16033,	16057,	16061,	16063,	16067,	16069,

+	16073,	16087,	16091,	16097,	16103,	16111,	16127,	16139,	16141,	16183,

+	16187,	16189,	16193,	16217,	16223,	16229,	16231,	16249,	16253,	16267,

+	16273,	16301,	16319,	16333,	16339,	16349,	16361,	16363,	16369,	16381,

+	16411,	16417,	16421,	16427,	16433,	16447,	16451,	16453,	16477,	16481,

+	16487,	16493,	16519,	16529,	16547,	16553,	16561,	16567,	16573,	16603,

+	16607,	16619,	16631,	16633,	16649,	16651,	16657,	16661,	16673,	16691,

+	16693,	16699,	16703,	16729,	16741,	16747,	16759,	16763,	16787,	16811,

+	16823,	16829,	16831,	16843,	16871,	16879,	16883,	16889,	16901,	16903,

+	16921,	16927,	16931,	16937,	16943,	16963,	16979,	16981,	16987,	16993,

+	17011,	17021,	17027,	17029,	17033,	17041,	17047,	17053,	17077,	17093,

+	17099,	17107,	17117,	17123,	17137,	17159,	17167,	17183,	17189,	17191,

+	17203,	17207,	17209,	17231,	17239,	17257,	17291,	17293,	17299,	17317,

+	17321,	17327,	17333,	17341,	17351,	17359,	17377,	17383,	17387,	17389,

+	17393,	17401,	17417,	17419,	17431,	17443,	17449,	17467,	17471,	17477,

+	17483,	17489,	17491,	17497,	17509,	17519,	17539,	17551,	17569,	17573,

+	17579,	17581,	17597,	17599,	17609,	17623,	17627,	17657,	17659,	17669,

+	17681,	17683,	17707,	17713,	17729,	17737,	17747,	17749,	17761,	17783,

+	17789,	17791,	17807,	17827,	17837,	17839,	17851,	17863,	17881,	17891,

+	17903,	17909,	17911,	17921,	17923,	17929,	17939,	17957,	17959,	17971,

+	17977,	17981,	17987,	17989,	18013,	18041,	18043,	18047,	18049,	18059,

+	18061,	18077,	18089,	18097,	18119,	18121,	18127,	18131,	18133,	18143,

+	18149,	18169,	18181,	18191,	18199,	18211,	18217,	18223,	18229,	18233,

+	18251,	18253,	18257,	18269,	18287,	18289,	18301,	18307,	18311,	18313,

+	18329,	18341,	18353,	18367,	18371,	18379,	18397,	18401,	18413,	18427,

+	18433,	18439,	18443,	18451,	18457,	18461,	18481,	18493,	18503,	18517,

+	18521,	18523,	18539,	18541,	18553,	18583,	18587,	18593,	18617,	18637,

+	18661,	18671,	18679,	18691,	18701,	18713,	18719,	18731,	18743,	18749,

+	18757,	18773,	18787,	18793,	18797,	18803,	18839,	18859,	18869,	18899,

+	18911,	18913,	18917,	18919,	18947,	18959,	18973,	18979,	19001,	19009,

+	19013,	19031,	19037,	19051,	19069,	19073,	19079,	19081,	19087,	19121,

+	19139,	19141,	19157,	19163,	19181,	19183,	19207,	19211,	19213,	19219,

+	19231,	19237,	19249,	19259,	19267,	19273,	19289,	19301,	19309,	19319,

+	19333,	19373,	19379,	19381,	19387,	19391,	19403,	19417,	19421,	19423,

+	19427,	19429,	19433,	19441,	19447,	19457,	19463,	19469,	19471,	19477,

+	19483,	19489,	19501,	19507,	19531,	19541,	19543,	19553,	19559,	19571,

+	19577,	19583,	19597,	19603,	19609,	19661,	19681,	19687,	19697,	19699,

+	19709,	19717,	19727,	19739,	19751,	19753,	19759,	19763,	19777,	19793,

+	19801,	19813,	19819,	19841,	19843,	19853,	19861,	19867,	19889,	19891,

+	19913,	19919,	19927,	19937,	19949,	19961,	19963,	19973,	19979,	19991,

+	19993,	19997,	20011,	20021,	20023,	20029,	20047,	20051,	20063,	20071,

+	20089,	20101,	20107,	20113,	20117,	20123,	20129,	20143,	20147,	20149,

+	20161,	20173,	20177,	20183,	20201,	20219,	20231,	20233,	20249,	20261,

+	20269,	20287,	20297,	20323,	20327,	20333,	20341,	20347,	20353,	20357,

+	20359,	20369,	20389,	20393,	20399,	20407,	20411,	20431,	20441,	20443,

+	20477,	20479,	20483,	20507,	20509,	20521,	20533,	20543,	20549,	20551,

+	20563,	20593,	20599,	20611,	20627,	20639,	20641,	20663,	20681,	20693,

+	20707,	20717,	20719,	20731,	20743,	20747,	20749,	20753,	20759,	20771,

+	20773,	20789,	20807,	20809,	20849,	20857,	20873,	20879,	20887,	20897,

+	20899,	20903,	20921,	20929,	20939,	20947,	20959,	20963,	20981,	20983,

+	21001,	21011,	21013,	21017,	21019,	21023,	21031,	21059,	21061,	21067,

+	21089,	21101,	21107,	21121,	21139,	21143,	21149,	21157,	21163,	21169,

+	21179,	21187,	21191,	21193,	21211,	21221,	21227,	21247,	21269,	21277,

+	21283,	21313,	21317,	21319,	21323,	21341,	21347,	21377,	21379,	21383,

+	21391,	21397,	21401,	21407,	21419,	21433,	21467,	21481,	21487,	21491,

+	21493,	21499,	21503,	21517,	21521,	21523,	21529,	21557,	21559,	21563,

+	21569,	21577,	21587,	21589,	21599,	21601,	21611,	21613,	21617,	21647,

+	21649,	21661,	21673,	21683,	21701,	21713,	21727,	21737,	21739,	21751,

+	21757,	21767,	21773,	21787,	21799,	21803,	21817,	21821,	21839,	21841,

+	21851,	21859,	21863,	21871,	21881,	21893,	21911,	21929,	21937,	21943,

+	21961,	21977,	21991,	21997,	22003,	22013,	22027,	22031,	22037,	22039,

+	22051,	22063,	22067,	22073,	22079,	22091,	22093,	22109,	22111,	22123,

+	22129,	22133,	22147,	22153,	22157,	22159,	22171,	22189,	22193,	22229,

+	22247,	22259,	22271,	22273,	22277,	22279,	22283,	22291,	22303,	22307,

+	22343,	22349,	22367,	22369,	22381,	22391,	22397,	22409,	22433,	22441,

+	22447,	22453,	22469,	22481,	22483,	22501,	22511,	22531,	22541,	22543,

+	22549,	22567,	22571,	22573,	22613,	22619,	22621,	22637,	22639,	22643,

+	22651,	22669,	22679,	22691,	22697,	22699,	22709,	22717,	22721,	22727,

+	22739,	22741,	22751,	22769,	22777,	22783,	22787,	22807,	22811,	22817,

+	22853,	22859,	22861,	22871,	22877,	22901,	22907,	22921,	22937,	22943,

+	22961,	22963,	22973,	22993,	23003,	23011,	23017,	23021,	23027,	23029,

+	23039,	23041,	23053,	23057,	23059,	23063,	23071,	23081,	23087,	23099,

+	23117,	23131,	23143,	23159,	23167,	23173,	23189,	23197,	23201,	23203,

+	23209,	23227,	23251,	23269,	23279,	23291,	23293,	23297,	23311,	23321,

+	23327,	23333,	23339,	23357,	23369,	23371,	23399,	23417,	23431,	23447,

+	23459,	23473,	23497,	23509,	23531,	23537,	23539,	23549,	23557,	23561,

+	23563,	23567,	23581,	23593,	23599,	23603,	23609,	23623,	23627,	23629,

+	23633,	23663,	23669,	23671,	23677,	23687,	23689,	23719,	23741,	23743,

+	23747,	23753,	23761,	23767,	23773,	23789,	23801,	23813,	23819,	23827,

+	23831,	23833,	23857,	23869,	23873,	23879,	23887,	23893,	23899,	23909,

+	23911,	23917,	23929,	23957,	23971,	23977,	23981,	23993,	24001,	24007,

+	24019,	24023,	24029,	24043,	24049,	24061,	24071,	24077,	24083,	24091,

+	24097,	24103,	24107,	24109,	24113,	24121,	24133,	24137,	24151,	24169,

+	24179,	24181,	24197,	24203,	24223,	24229,	24239,	24247,	24251,	24281,

+	24317,	24329,	24337,	24359,	24371,	24373,	24379,	24391,	24407,	24413,

+	24419,	24421,	24439,	24443,	24469,	24473,	24481,	24499,	24509,	24517,

+	24527,	24533,	24547,	24551,	24571,	24593,	24611,	24623,	24631,	24659,

+	24671,	24677,	24683,	24691,	24697,	24709,	24733,	24749,	24763,	24767,

+	24781,	24793,	24799,	24809,	24821,	24841,	24847,	24851,	24859,	24877,

+	24889,	24907,	24917,	24919,	24923,	24943,	24953,	24967,	24971,	24977,

+	24979,	24989,	25013,	25031,	25033,	25037,	25057,	25073,	25087,	25097,

+	25111,	25117,	25121,	25127,	25147,	25153,	25163,	25169,	25171,	25183,

+	25189,	25219,	25229,	25237,	25243,	25247,	25253,	25261,	25301,	25303,

+	25307,	25309,	25321,	25339,	25343,	25349,	25357,	25367,	25373,	25391,

+	25409,	25411,	25423,	25439,	25447,	25453,	25457,	25463,	25469,	25471,

+	25523,	25537,	25541,	25561,	25577,	25579,	25583,	25589,	25601,	25603,

+	25609,	25621,	25633,	25639,	25643,	25657,	25667,	25673,	25679,	25693,

+	25703,	25717,	25733,	25741,	25747,	25759,	25763,	25771,	25793,	25799,

+	25801,	25819,	25841,	25847,	25849,	25867,	25873,	25889,	25903,	25913,

+	25919,	25931,	25933,	25939,	25943,	25951,	25969,	25981,	25997,	25999,

+	26003,	26017,	26021,	26029,	26041,	26053,	26083,	26099,	26107,	26111,

+	26113,	26119,	26141,	26153,	26161,	26171,	26177,	26183,	26189,	26203,

+	26209,	26227,	26237,	26249,	26251,	26261,	26263,	26267,	26293,	26297,

+	26309,	26317,	26321,	26339,	26347,	26357,	26371,	26387,	26393,	26399,

+	26407,	26417,	26423,	26431,	26437,	26449,	26459,	26479,	26489,	26497,

+	26501,	26513,	26539,	26557,	26561,	26573,	26591,	26597,	26627,	26633,

+	26641,	26647,	26669,	26681,	26683,	26687,	26693,	26699,	26701,	26711,

+	26713,	26717,	26723,	26729,	26731,	26737,	26759,	26777,	26783,	26801,

+	26813,	26821,	26833,	26839,	26849,	26861,	26863,	26879,	26881,	26891,

+	26893,	26903,	26921,	26927,	26947,	26951,	26953,	26959,	26981,	26987,

+	26993,	27011,	27017,	27031,	27043,	27059,	27061,	27067,	27073,	27077,

+	27091,	27103,	27107,	27109,	27127,	27143,	27179,	27191,	27197,	27211,

+	27239,	27241,	27253,	27259,	27271,	27277,	27281,	27283,	27299,	27329,

+	27337,	27361,	27367,	27397,	27407,	27409,	27427,	27431,	27437,	27449,

+	27457,	27479,	27481,	27487,	27509,	27527,	27529,	27539,	27541,	27551,

+	27581,	27583,	27611,	27617,	27631,	27647,	27653,	27673,	27689,	27691,

+	27697,	27701,	27733,	27737,	27739,	27743,	27749,	27751,	27763,	27767,

+	27773,	27779,	27791,	27793,	27799,	27803,	27809,	27817,	27823,	27827,

+	27847,	27851,	27883,	27893,	27901,	27917,	27919,	27941,	27943,	27947,

+	27953,	27961,	27967,	27983,	27997,	28001,	28019,	28027,	28031,	28051,

+	28057,	28069,	28081,	28087,	28097,	28099,	28109,	28111,	28123,	28151,

+	28163,	28181,	28183,	28201,	28211,	28219,	28229,	28277,	28279,	28283,

+	28289,	28297,	28307,	28309,	28319,	28349,	28351,	28387,	28393,	28403,

+	28409,	28411,	28429,	28433,	28439,	28447,	28463,	28477,	28493,	28499,

+	28513,	28517,	28537,	28541,	28547,	28549,	28559,	28571,	28573,	28579,

+	28591,	28597,	28603,	28607,	28619,	28621,	28627,	28631,	28643,	28649,

+	28657,	28661,	28663,	28669,	28687,	28697,	28703,	28711,	28723,	28729,

+	28751,	28753,	28759,	28771,	28789,	28793,	28807,	28813,	28817,	28837,

+	28843,	28859,	28867,	28871,	28879,	28901,	28909,	28921,	28927,	28933,

+	28949,	28961,	28979,	29009,	29017,	29021,	29023,	29027,	29033,	29059,

+	29063,	29077,	29101,	29123,	29129,	29131,	29137,	29147,	29153,	29167,

+	29173,	29179,	29191,	29201,	29207,	29209,	29221,	29231,	29243,	29251,

+	29269,	29287,	29297,	29303,	29311,	29327,	29333,	29339,	29347,	29363,

+	29383,	29387,	29389,	29399,	29401,	29411,	29423,	29429,	29437,	29443,

+	29453,	29473,	29483,	29501,	29527,	29531,	29537,	29567,	29569,	29573,

+	29581,	29587,	29599,	29611,	29629,	29633,	29641,	29663,	29669,	29671,

+	29683,	29717,	29723,	29741,	29753,	29759,	29761,	29789,	29803,	29819,

+	29833,	29837,	29851,	29863,	29867,	29873,	29879,	29881,	29917,	29921,

+	29927,	29947,	29959,	29983,	29989,	30011,	30013,	30029,	30047,	30059,

+	30071,	30089,	30091,	30097,	30103,	30109,	30113,	30119,	30133,	30137,

+	30139,	30161,	30169,	30181,	30187,	30197,	30203,	30211,	30223,	30241,

+	30253,	30259,	30269,	30271,	30293,	30307,	30313,	30319,	30323,	30341,

+	30347,	30367,	30389,	30391,	30403,	30427,	30431,	30449,	30467,	30469,

+	30491,	30493,	30497,	30509,	30517,	30529,	30539,	30553,	30557,	30559,

+	30577,	30593,	30631,	30637,	30643,	30649,	30661,	30671,	30677,	30689,

+	30697,	30703,	30707,	30713,	30727,	30757,	30763,	30773,	30781,	30803,

+	30809,	30817,	30829,	30839,	30841,	30851,	30853,	30859,	30869,	30871,

+	30881,	30893,	30911,	30931,	30937,	30941,	30949,	30971,	30977,	30983,

+	31013,	31019,	31033,	31039,	31051,	31063,	31069,	31079,	31081,	31091,

+	31121,	31123,	31139,	31147,	31151,	31153,	31159,	31177,	31181,	31183,

+	31189,	31193,	31219,	31223,	31231,	31237,	31247,	31249,	31253,	31259,

+	31267,	31271,	31277,	31307,	31319,	31321,	31327,	31333,	31337,	31357,

+	31379,	31387,	31391,	31393,	31397,	31469,	31477,	31481,	31489,	31511,

+	31513,	31517,	31531,	31541,	31543,	31547,	31567,	31573,	31583,	31601,

+	31607,	31627,	31643,	31649,	31657,	31663,	31667,	31687,	31699,	31721,

+	31723,	31727,	31729,	31741,	31751,	31769,	31771,	31793,	31799,	31817,

+	31847,	31849,	31859,	31873,	31883,	31891,	31907,	31957,	31963,	31973,

+	31981,	31991,	32003,	32009,	32027,	32029,	32051,	32057,	32059,	32063,

+	32069,	32077,	32083,	32089,	32099,	32117,	32119,	32141,	32143,	32159,

+	32173,	32183,	32189,	32191,	32203,	32213,	32233,	32237,	32251,	32257,

+	32261,	32297,	32299,	32303,	32309,	32321,	32323,	32327,	32341,	32353,

+	32359,	32363,	32369,	32371,	32377,	32381,	32401,	32411,	32413,	32423,

+	32429,	32441,	32443,	32467,	32479,	32491,	32497,	32503,	32507,	32531,

+	32533,	32537,	32561,	32563,	32569,	32573,	32579,	32587,	32603,	32609,

+	32611,	32621,	32633,	32647,	32653,	32687,	32693,	32707,	32713,	32717,

+	32719,	32749,	32771,	32779,	32783,	32789,	32797,	32801,	32803,	32831,

+	32833,	32839,	32843,	32869,	32887,	32909,	32911,	32917,	32933,	32939,

+	32941,	32957,	32969,	32971,	32983,	32987,	32993,	32999,	33013,	33023,

+	33029,	33037,	33049,	33053,	33071,	33073,	33083,	33091,	33107,	33113,

+	33119,	33149,	33151,	33161,	33179,	33181,	33191,	33199,	33203,	33211,

+	33223,	33247,	33287,	33289,	33301,	33311,	33317,	33329,	33331,	33343,

+	33347,	33349,	33353,	33359,	33377,	33391,	33403,	33409,	33413,	33427,

+	33457,	33461,	33469,	33479,	33487,	33493,	33503,	33521,	33529,	33533,

+	33547,	33563,	33569,	33577,	33581,	33587,	33589,	33599,	33601,	33613,

+	33617,	33619,	33623,	33629,	33637,	33641,	33647,	33679,	33703,	33713,

+	33721,	33739,	33749,	33751,	33757,	33767,	33769,	33773,	33791,	33797,

+	33809,	33811,	33827,	33829,	33851,	33857,	33863,	33871,	33889,	33893,

+	33911,	33923,	33931,	33937,	33941,	33961,	33967,	33997,	34019,	34031,

+	34033,	34039,	34057,	34061,	34123,	34127,	34129,	34141,	34147,	34157,

+	34159,	34171,	34183,	34211,	34213,	34217,	34231,	34253,	34259,	34261,

+	34267,	34273,	34283,	34297,	34301,	34303,	34313,	34319,	34327,	34337,

+	34351,	34361,	34367,	34369,	34381,	34403,	34421,	34429,	34439,	34457,

+	34469,	34471,	34483,	34487,	34499,	34501,	34511,	34513,	34519,	34537,

+	34543,	34549,	34583,	34589,	34591,	34603,	34607,	34613,	34631,	34649,

+	34651,	34667,	34673,	34679,	34687,	34693,	34703,	34721,	34729,	34739,

+	34747,	34757,	34759,	34763,	34781,	34807,	34819,	34841,	34843,	34847,

+	34849,	34871,	34877,	34883,	34897,	34913,	34919,	34939,	34949,	34961,

+	34963,	34981,	35023,	35027,	35051,	35053,	35059,	35069,	35081,	35083,

+	35089,	35099,	35107,	35111,	35117,	35129,	35141,	35149,	35153,	35159,

+	35171,	35201,	35221,	35227,	35251,	35257,	35267,	35279,	35281,	35291,

+	35311,	35317,	35323,	35327,	35339,	35353,	35363,	35381,	35393,	35401,

+	35407,	35419,	35423,	35437,	35447,	35449,	35461,	35491,	35507,	35509,

+	35521,	35527,	35531,	35533,	35537,	35543,	35569,	35573,	35591,	35593,

+	35597,	35603,	35617,	35671,	35677,	35729,	35731,	35747,	35753,	35759,

+	35771,	35797,	35801,	35803,	35809,	35831,	35837,	35839,	35851,	35863,

+	35869,	35879,	35897,	35899,	35911,	35923,	35933,	35951,	35963,	35969,

+	35977,	35983,	35993,	35999,	36007,	36011,	36013,	36017,	36037,	36061,

+	36067,	36073,	36083,	36097,	36107,	36109,	36131,	36137,	36151,	36161,

+	36187,	36191,	36209,	36217,	36229,	36241,	36251,	36263,	36269,	36277,

+	36293,	36299,	36307,	36313,	36319,	36341,	36343,	36353,	36373,	36383,

+	36389,	36433,	36451,	36457,	36467,	36469,	36473,	36479,	36493,	36497,

+	36523,	36527,	36529,	36541,	36551,	36559,	36563,	36571,	36583,	36587,

+	36599,	36607,	36629,	36637,	36643,	36653,	36671,	36677,	36683,	36691,

+	36697,	36709,	36713,	36721,	36739,	36749,	36761,	36767,	36779,	36781,

+	36787,	36791,	36793,	36809,	36821,	36833,	36847,	36857,	36871,	36877,

+	36887,	36899,	36901,	36913,	36919,	36923,	36929,	36931,	36943,	36947,

+	36973,	36979,	36997,	37003,	37013,	37019,	37021,	37039,	37049,	37057,

+	37061,	37087,	37097,	37117,	37123,	37139,	37159,	37171,	37181,	37189,

+	37199,	37201,	37217,	37223,	37243,	37253,	37273,	37277,	37307,	37309,

+	37313,	37321,	37337,	37339,	37357,	37361,	37363,	37369,	37379,	37397,

+	37409,	37423,	37441,	37447,	37463,	37483,	37489,	37493,	37501,	37507,

+	37511,	37517,	37529,	37537,	37547,	37549,	37561,	37567,	37571,	37573,

+	37579,	37589,	37591,	37607,	37619,	37633,	37643,	37649,	37657,	37663,

+	37691,	37693,	37699,	37717,	37747,	37781,	37783,	37799,	37811,	37813,

+	37831,	37847,	37853,	37861,	37871,	37879,	37889,	37897,	37907,	37951,

+	37957,	37963,	37967,	37987,	37991,	37993,	37997,	38011,	38039,	38047,

+	38053,	38069,	38083,	38113,	38119,	38149,	38153,	38167,	38177,	38183,

+	38189,	38197,	38201,	38219,	38231,	38237,	38239,	38261,	38273,	38281,

+	38287,	38299,	38303,	38317,	38321,	38327,	38329,	38333,	38351,	38371,

+	38377,	38393,	38431,	38447,	38449,	38453,	38459,	38461,	38501,	38543,

+	38557,	38561,	38567,	38569,	38593,	38603,	38609,	38611,	38629,	38639,

+	38651,	38653,	38669,	38671,	38677,	38693,	38699,	38707,	38711,	38713,

+	38723,	38729,	38737,	38747,	38749,	38767,	38783,	38791,	38803,	38821,

+	38833,	38839,	38851,	38861,	38867,	38873,	38891,	38903,	38917,	38921,

+	38923,	38933,	38953,	38959,	38971,	38977,	38993,	39019,	39023,	39041,

+	39043,	39047,	39079,	39089,	39097,	39103,	39107,	39113,	39119,	39133,

+	39139,	39157,	39161,	39163,	39181,	39191,	39199,	39209,	39217,	39227,

+	39229,	39233,	39239,	39241,	39251,	39293,	39301,	39313,	39317,	39323,

+	39341,	39343,	39359,	39367,	39371,	39373,	39383,	39397,	39409,	39419,

+	39439,	39443,	39451,	39461,	39499,	39503,	39509,	39511,	39521,	39541,

+	39551,	39563,	39569,	39581,	39607,	39619,	39623,	39631,	39659,	39667,

+	39671,	39679,	39703,	39709,	39719,	39727,	39733,	39749,	39761,	39769,

+	39779,	39791,	39799,	39821,	39827,	39829,	39839,	39841,	39847,	39857,

+	39863,	39869,	39877,	39883,	39887,	39901,	39929,	39937,	39953,	39971,

+	39979,	39983,	39989,	40009,	40013,	40031,	40037,	40039,	40063,	40087,

+	40093,	40099,	40111,	40123,	40127,	40129,	40151,	40153,	40163,	40169,

+	40177,	40189,	40193,	40213,	40231,	40237,	40241,	40253,	40277,	40283,

+	40289,	40343,	40351,	40357,	40361,	40387,	40423,	40427,	40429,	40433,

+	40459,	40471,	40483,	40487,	40493,	40499,	40507,	40519,	40529,	40531,

+	40543,	40559,	40577,	40583,	40591,	40597,	40609,	40627,	40637,	40639,

+	40693,	40697,	40699,	40709,	40739,	40751,	40759,	40763,	40771,	40787,

+	40801,	40813,	40819,	40823,	40829,	40841,	40847,	40849,	40853,	40867,

+	40879,	40883,	40897,	40903,	40927,	40933,	40939,	40949,	40961,	40973,

+	40993,	41011,	41017,	41023,	41039,	41047,	41051,	41057,	41077,	41081,

+	41113,	41117,	41131,	41141,	41143,	41149,	41161,	41177,	41179,	41183,

+	41189,	41201,	41203,	41213,	41221,	41227,	41231,	41233,	41243,	41257,

+	41263,	41269,	41281,	41299,	41333,	41341,	41351,	41357,	41381,	41387,

+	41389,	41399,	41411,	41413,	41443,	41453,	41467,	41479,	41491,	41507,

+	41513,	41519,	41521,	41539,	41543,	41549,	41579,	41593,	41597,	41603,

+	41609,	41611,	41617,	41621,	41627,	41641,	41647,	41651,	41659,	41669,

+	41681,	41687,	41719,	41729,	41737,	41759,	41761,	41771,	41777,	41801,

+	41809,	41813,	41843,	41849,	41851,	41863,	41879,	41887,	41893,	41897,

+	41903,	41911,	41927,	41941,	41947,	41953,	41957,	41959,	41969,	41981,

+	41983,	41999,	42013,	42017,	42019,	42023,	42043,	42061,	42071,	42073,

+	42083,	42089,	42101,	42131,	42139,	42157,	42169,	42179,	42181,	42187,

+	42193,	42197,	42209,	42221,	42223,	42227,	42239,	42257,	42281,	42283,

+	42293,	42299,	42307,	42323,	42331,	42337,	42349,	42359,	42373,	42379,

+	42391,	42397,	42403,	42407,	42409,	42433,	42437,	42443,	42451,	42457,

+	42461,	42463,	42467,	42473,	42487,	42491,	42499,	42509,	42533,	42557,

+	42569,	42571,	42577,	42589,	42611,	42641,	42643,	42649,	42667,	42677,

+	42683,	42689,	42697,	42701,	42703,	42709,	42719,	42727,	42737,	42743,

+	42751,	42767,	42773,	42787,	42793,	42797,	42821,	42829,	42839,	42841,

+	42853,	42859,	42863,	42899,	42901,	42923,	42929,	42937,	42943,	42953,

+	42961,	42967,	42979,	42989,	43003,	43013,	43019,	43037,	43049,	43051,

+	43063,	43067,	43093,	43103,	43117,	43133,	43151,	43159,	43177,	43189,

+	43201,	43207,	43223,	43237,	43261,	43271,	43283,	43291,	43313,	43319,

+	43321,	43331,	43391,	43397,	43399,	43403,	43411,	43427,	43441,	43451,

+	43457,	43481,	43487,	43499,	43517,	43541,	43543,	43573,	43577,	43579,

+	43591,	43597,	43607,	43609,	43613,	43627,	43633,	43649,	43651,	43661,

+	43669,	43691,	43711,	43717,	43721,	43753,	43759,	43777,	43781,	43783,

+	43787,	43789,	43793,	43801,	43853,	43867,	43889,	43891,	43913,	43933,

+	43943,	43951,	43961,	43963,	43969,	43973,	43987,	43991,	43997,	44017,

+	44021,	44027,	44029,	44041,	44053,	44059,	44071,	44087,	44089,	44101,

+	44111,	44119,	44123,	44129,	44131,	44159,	44171,	44179,	44189,	44201,

+	44203,	44207,	44221,	44249,	44257,	44263,	44267,	44269,	44273,	44279,

+	44281,	44293,	44351,	44357,	44371,	44381,	44383,	44389,	44417,	44449,

+	44453,	44483,	44491,	44497,	44501,	44507,	44519,	44531,	44533,	44537,

+	44543,	44549,	44563,	44579,	44587,	44617,	44621,	44623,	44633,	44641,

+	44647,	44651,	44657,	44683,	44687,	44699,	44701,	44711,	44729,	44741,

+	44753,	44771,	44773,	44777,	44789,	44797,	44809,	44819,	44839,	44843,

+	44851,	44867,	44879,	44887,	44893,	44909,	44917,	44927,	44939,	44953,

+	44959,	44963,	44971,	44983,	44987,	45007,	45013,	45053,	45061,	45077,

+	45083,	45119,	45121,	45127,	45131,	45137,	45139,	45161,	45179,	45181,

+	45191,	45197,	45233,	45247,	45259,	45263,	45281,	45289,	45293,	45307,

+	45317,	45319,	45329,	45337,	45341,	45343,	45361,	45377,	45389,	45403,

+	45413,	45427,	45433,	45439,	45481,	45491,	45497,	45503,	45523,	45533,

+	45541,	45553,	45557,	45569,	45587,	45589,	45599,	45613,	45631,	45641,

+	45659,	45667,	45673,	45677,	45691,	45697,	45707,	45737,	45751,	45757,

+	45763,	45767,	45779,	45817,	45821,	45823,	45827,	45833,	45841,	45853,

+	45863,	45869,	45887,	45893,	45943,	45949,	45953,	45959,	45971,	45979,

+	45989,	46021,	46027,	46049,	46051,	46061,	46073,	46091,	46093,	46099,

+	46103,	46133,	46141,	46147,	46153,	46171,	46181,	46183,	46187,	46199,

+	46219,	46229,	46237,	46261,	46271,	46273,	46279,	46301,	46307,	46309,

+	46327,	46337,	46349,	46351,	46381,	46399,	46411,	46439,	46441,	46447,

+	46451,	46457,	46471,	46477,	46489,	46499,	46507,	46511,	46523,	46549,

+	46559,	46567,	46573,	46589,	46591,	46601,	46619,	46633,	46639,	46643,

+	46649,	46663,	46679,	46681,	46687,	46691,	46703,	46723,	46727,	46747,

+	46751,	46757,	46769,	46771,	46807,	46811,	46817,	46819,	46829,	46831,

+	46853,	46861,	46867,	46877,	46889,	46901,	46919,	46933,	46957,	46993,

+	46997,	47017,	47041,	47051,	47057,	47059,	47087,	47093,	47111,	47119,

+	47123,	47129,	47137,	47143,	47147,	47149,	47161,	47189,	47207,	47221,

+	47237,	47251,	47269,	47279,	47287,	47293,	47297,	47303,	47309,	47317,

+	47339,	47351,	47353,	47363,	47381,	47387,	47389,	47407,	47417,	47419,

+	47431,	47441,	47459,	47491,	47497,	47501,	47507,	47513,	47521,	47527,

+	47533,	47543,	47563,	47569,	47581,	47591,	47599,	47609,	47623,	47629,

+	47639,	47653,	47657,	47659,	47681,	47699,	47701,	47711,	47713,	47717,

+	47737,	47741,	47743,	47777,	47779,	47791,	47797,	47807,	47809,	47819,

+	47837,	47843,	47857,	47869,	47881,	47903,	47911,	47917,	47933,	47939,

+	47947,	47951,	47963,	47969,	47977,	47981,	48017,	48023,	48029,	48049,

+	48073,	48079,	48091,	48109,	48119,	48121,	48131,	48157,	48163,	48179,

+	48187,	48193,	48197,	48221,	48239,	48247,	48259,	48271,	48281,	48299,

+	48311,	48313,	48337,	48341,	48353,	48371,	48383,	48397,	48407,	48409,

+	48413,	48437,	48449,	48463,	48473,	48479,	48481,	48487,	48491,	48497,

+	48523,	48527,	48533,	48539,	48541,	48563,	48571,	48589,	48593,	48611,

+	48619,	48623,	48647,	48649,	48661,	48673,	48677,	48679,	48731,	48733,

+	48751,	48757,	48761,	48767,	48779,	48781,	48787,	48799,	48809,	48817,

+	48821,	48823,	48847,	48857,	48859,	48869,	48871,	48883,	48889,	48907,

+	48947,	48953,	48973,	48989,	48991,	49003,	49009,	49019,	49031,	49033,

+	49037,	49043,	49057,	49069,	49081,	49103,	49109,	49117,	49121,	49123,

+	49139,	49157,	49169,	49171,	49177,	49193,	49199,	49201,	49207,	49211,

+	49223,	49253,	49261,	49277,	49279,	49297,	49307,	49331,	49333,	49339,

+	49363,	49367,	49369,	49391,	49393,	49409,	49411,	49417,	49429,	49433,

+	49451,	49459,	49463,	49477,	49481,	49499,	49523,	49529,	49531,	49537,

+	49547,	49549,	49559,	49597,	49603,	49613,	49627,	49633,	49639,	49663,

+	49667,	49669,	49681,	49697,	49711,	49727,	49739,	49741,	49747,	49757,

+	49783,	49787,	49789,	49801,	49807,	49811,	49823,	49831,	49843,	49853,

+	49871,	49877,	49891,	49919,	49921,	49927,	49937,	49939,	49943,	49957,

+	49991,	49993,	49999,	50021,	50023,	50033,	50047,	50051,	50053,	50069,

+	50077,	50087,	50093,	50101,	50111,	50119,	50123,	50129,	50131,	50147,

+	50153,	50159,	50177,	50207,	50221,	50227,	50231,	50261,	50263,	50273,

+	50287,	50291,	50311,	50321,	50329,	50333,	50341,	50359,	50363,	50377,

+	50383,	50387,	50411,	50417,	50423,	50441,	50459,	50461,	50497,	50503,

+	50513,	50527,	50539,	50543,	50549,	50551,	50581,	50587,	50591,	50593,

+	50599,	50627,	50647,	50651,	50671,	50683,	50707,	50723,	50741,	50753,

+	50767,	50773,	50777,	50789,	50821,	50833,	50839,	50849,	50857,	50867,

+	50873,	50891,	50893,	50909,	50923,	50929,	50951,	50957,	50969,	50971,

+	50989,	50993,	51001,	51031,	51043,	51047,	51059,	51061,	51071,	51109,

+	51131,	51133,	51137,	51151,	51157,	51169,	51193,	51197,	51199,	51203,

+	51217,	51229,	51239,	51241,	51257,	51263,	51283,	51287,	51307,	51329,

+	51341,	51343,	51347,	51349,	51361,	51383,	51407,	51413,	51419,	51421,

+	51427,	51431,	51437,	51439,	51449,	51461,	51473,	51479,	51481,	51487,

+	51503,	51511,	51517,	51521,	51539,	51551,	51563,	51577,	51581,	51593,

+	51599,	51607,	51613,	51631,	51637,	51647,	51659,	51673,	51679,	51683,

+	51691,	51713,	51719,	51721,	51749,	51767,	51769,	51787,	51797,	51803,

+	51817,	51827,	51829,	51839,	51853,	51859,	51869,	51871,	51893,	51899,

+	51907,	51913,	51929,	51941,	51949,	51971,	51973,	51977,	51991,	52009,

+	52021,	52027,	52051,	52057,	52067,	52069,	52081,	52103,	52121,	52127,

+	52147,	52153,	52163,	52177,	52181,	52183,	52189,	52201,	52223,	52237,

+	52249,	52253,	52259,	52267,	52289,	52291,	52301,	52313,	52321,	52361,

+	52363,	52369,	52379,	52387,	52391,	52433,	52453,	52457,	52489,	52501,

+	52511,	52517,	52529,	52541,	52543,	52553,	52561,	52567,	52571,	52579,

+	52583,	52609,	52627,	52631,	52639,	52667,	52673,	52691,	52697,	52709,

+	52711,	52721,	52727,	52733,	52747,	52757,	52769,	52783,	52807,	52813,

+	52817,	52837,	52859,	52861,	52879,	52883,	52889,	52901,	52903,	52919,

+	52937,	52951,	52957,	52963,	52967,	52973,	52981,	52999,	53003,	53017,

+	53047,	53051,	53069,	53077,	53087,	53089,	53093,	53101,	53113,	53117,

+	53129,	53147,	53149,	53161,	53171,	53173,	53189,	53197,	53201,	53231,

+	53233,	53239,	53267,	53269,	53279,	53281,	53299,	53309,	53323,	53327,

+	53353,	53359,	53377,	53381,	53401,	53407,	53411,	53419,	53437,	53441,

+	53453,	53479,	53503,	53507,	53527,	53549,	53551,	53569,	53591,	53593,

+	53597,	53609,	53611,	53617,	53623,	53629,	53633,	53639,	53653,	53657,

+	53681,	53693,	53699,	53717,	53719,	53731,	53759,	53773,	53777,	53783,

+	53791,	53813,	53819,	53831,	53849,	53857,	53861,	53881,	53887,	53891,

+	53897,	53899,	53917,	53923,	53927,	53939,	53951,	53959,	53987,	53993,

+	54001,	54011,	54013,	54037,	54049,	54059,	54083,	54091,	54101,	54121,

+	54133,	54139,	54151,	54163,	54167,	54181,	54193,	54217,	54251,	54269,

+	54277,	54287,	54293,	54311,	54319,	54323,	54331,	54347,	54361,	54367,

+	54371,	54377,	54401,	54403,	54409,	54413,	54419,	54421,	54437,	54443,

+	54449,	54469,	54493,	54497,	54499,	54503,	54517,	54521,	54539,	54541,

+	54547,	54559,	54563,	54577,	54581,	54583,	54601,	54617,	54623,	54629,

+	54631,	54647,	54667,	54673,	54679,	54709,	54713,	54721,	54727,	54751,

+	54767,	54773,	54779,	54787,	54799,	54829,	54833,	54851,	54869,	54877,

+	54881,	54907,	54917,	54919,	54941,	54949,	54959,	54973,	54979,	54983,

+	55001,	55009,	55021,	55049,	55051,	55057,	55061,	55073,	55079,	55103,

+	55109,	55117,	55127,	55147,	55163,	55171,	55201,	55207,	55213,	55217,

+	55219,	55229,	55243,	55249,	55259,	55291,	55313,	55331,	55333,	55337,

+	55339,	55343,	55351,	55373,	55381,	55399,	55411,	55439,	55441,	55457,

+	55469,	55487,	55501,	55511,	55529,	55541,	55547,	55579,	55589,	55603,

+	55609,	55619,	55621,	55631,	55633,	55639,	55661,	55663,	55667,	55673,

+	55681,	55691,	55697,	55711,	55717,	55721,	55733,	55763,	55787,	55793,

+	55799,	55807,	55813,	55817,	55819,	55823,	55829,	55837,	55843,	55849,

+	55871,	55889,	55897,	55901,	55903,	55921,	55927,	55931,	55933,	55949,

+	55967,	55987,	55997,	56003,	56009,	56039,	56041,	56053,	56081,	56087,

+	56093,	56099,	56101,	56113,	56123,	56131,	56149,	56167,	56171,	56179,

+	56197,	56207,	56209,	56237,	56239,	56249,	56263,	56267,	56269,	56299,

+	56311,	56333,	56359,	56369,	56377,	56383,	56393,	56401,	56417,	56431,

+	56437,	56443,	56453,	56467,	56473,	56477,	56479,	56489,	56501,	56503,

+	56509,	56519,	56527,	56531,	56533,	56543,	56569,	56591,	56597,	56599,

+	56611,	56629,	56633,	56659,	56663,	56671,	56681,	56687,	56701,	56711,

+	56713,	56731,	56737,	56747,	56767,	56773,	56779,	56783,	56807,	56809,

+	56813,	56821,	56827,	56843,	56857,	56873,	56891,	56893,	56897,	56909,

+	56911,	56921,	56923,	56929,	56941,	56951,	56957,	56963,	56983,	56989,

+	56993,	56999,	57037,	57041,	57047,	57059,	57073,	57077,	57089,	57097,

+	57107,	57119,	57131,	57139,	57143,	57149,	57163,	57173,	57179,	57191,

+	57193,	57203,	57221,	57223,	57241,	57251,	57259,	57269,	57271,	57283,

+	57287,	57301,	57329,	57331,	57347,	57349,	57367,	57373,	57383,	57389,

+	57397,	57413,	57427,	57457,	57467,	57487,	57493,	57503,	57527,	57529,

+	57557,	57559,	57571,	57587,	57593,	57601,	57637,	57641,	57649,	57653,

+	57667,	57679,	57689,	57697,	57709,	57713,	57719,	57727,	57731,	57737,

+	57751,	57773,	57781,	57787,	57791,	57793,	57803,	57809,	57829,	57839,

+	57847,	57853,	57859,	57881,	57899,	57901,	57917,	57923,	57943,	57947,

+	57973,	57977,	57991,	58013,	58027,	58031,	58043,	58049,	58057,	58061,

+	58067,	58073,	58099,	58109,	58111,	58129,	58147,	58151,	58153,	58169,

+	58171,	58189,	58193,	58199,	58207,	58211,	58217,	58229,	58231,	58237,

+	58243,	58271,	58309,	58313,	58321,	58337,	58363,	58367,	58369,	58379,

+	58391,	58393,	58403,	58411,	58417,	58427,	58439,	58441,	58451,	58453,

+	58477,	58481,	58511,	58537,	58543,	58549,	58567,	58573,	58579,	58601,

+	58603,	58613,	58631,	58657,	58661,	58679,	58687,	58693,	58699,	58711,

+	58727,	58733,	58741,	58757,	58763,	58771,	58787,	58789,	58831,	58889,

+	58897,	58901,	58907,	58909,	58913,	58921,	58937,	58943,	58963,	58967,

+	58979,	58991,	58997,	59009,	59011,	59021,	59023,	59029,	59051,	59053,

+	59063,	59069,	59077,	59083,	59093,	59107,	59113,	59119,	59123,	59141,

+	59149,	59159,	59167,	59183,	59197,	59207,	59209,	59219,	59221,	59233,

+	59239,	59243,	59263,	59273,	59281,	59333,	59341,	59351,	59357,	59359,

+	59369,	59377,	59387,	59393,	59399,	59407,	59417,	59419,	59441,	59443,

+	59447,	59453,	59467,	59471,	59473,	59497,	59509,	59513,	59539,	59557,

+	59561,	59567,	59581,	59611,	59617,	59621,	59627,	59629,	59651,	59659,

+	59663,	59669,	59671,	59693,	59699,	59707,	59723,	59729,	59743,	59747,

+	59753,	59771,	59779,	59791,	59797,	59809,	59833,	59863,	59879,	59887,

+	59921,	59929,	59951,	59957,	59971,	59981,	59999,	60013,	60017,	60029,

+	60037,	60041,	60077,	60083,	60089,	60091,	60101,	60103,	60107,	60127,

+	60133,	60139,	60149,	60161,	60167,	60169,	60209,	60217,	60223,	60251,

+	60257,	60259,	60271,	60289,	60293,	60317,	60331,	60337,	60343,	60353,

+	60373,	60383,	60397,	60413,	60427,	60443,	60449,	60457,	60493,	60497,

+	60509,	60521,	60527,	60539,	60589,	60601,	60607,	60611,	60617,	60623,

+	60631,	60637,	60647,	60649,	60659,	60661,	60679,	60689,	60703,	60719,

+	60727,	60733,	60737,	60757,	60761,	60763,	60773,	60779,	60793,	60811,

+	60821,	60859,	60869,	60887,	60889,	60899,	60901,	60913,	60917,	60919,

+	60923,	60937,	60943,	60953,	60961,	61001,	61007,	61027,	61031,	61043,

+	61051,	61057,	61091,	61099,	61121,	61129,	61141,	61151,	61153,	61169,

+	61211,	61223,	61231,	61253,	61261,	61283,	61291,	61297,	61331,	61333,

+	61339,	61343,	61357,	61363,	61379,	61381,	61403,	61409,	61417,	61441,

+	61463,	61469,	61471,	61483,	61487,	61493,	61507,	61511,	61519,	61543,

+	61547,	61553,	61559,	61561,	61583,	61603,	61609,	61613,	61627,	61631,

+	61637,	61643,	61651,	61657,	61667,	61673,	61681,	61687,	61703,	61717,

+	61723,	61729,	61751,	61757,	61781,	61813,	61819,	61837,	61843,	61861,

+	61871,	61879,	61909,	61927,	61933,	61949,	61961,	61967,	61979,	61981,

+	61987,	61991,	62003,	62011,	62017,	62039,	62047,	62053,	62057,	62071,

+	62081,	62099,	62119,	62129,	62131,	62137,	62141,	62143,	62171,	62189,

+	62191,	62201,	62207,	62213,	62219,	62233,	62273,	62297,	62299,	62303,

+	62311,	62323,	62327,	62347,	62351,	62383,	62401,	62417,	62423,	62459,

+	62467,	62473,	62477,	62483,	62497,	62501,	62507,	62533,	62539,	62549,

+	62563,	62581,	62591,	62597,	62603,	62617,	62627,	62633,	62639,	62653,

+	62659,	62683,	62687,	62701,	62723,	62731,	62743,	62753,	62761,	62773,

+	62791,	62801,	62819,	62827,	62851,	62861,	62869,	62873,	62897,	62903,

+	62921,	62927,	62929,	62939,	62969,	62971,	62981,	62983,	62987,	62989,

+	63029,	63031,	63059,	63067,	63073,	63079,	63097,	63103,	63113,	63127,

+	63131,	63149,	63179,	63197,	63199,	63211,	63241,	63247,	63277,	63281,

+	63299,	63311,	63313,	63317,	63331,	63337,	63347,	63353,	63361,	63367,

+	63377,	63389,	63391,	63397,	63409,	63419,	63421,	63439,	63443,	63463,

+	63467,	63473,	63487,	63493,	63499,	63521,	63527,	63533,	63541,	63559,

+	63577,	63587,	63589,	63599,	63601,	63607,	63611,	63617,	63629,	63647,

+	63649,	63659,	63667,	63671,	63689,	63691,	63697,	63703,	63709,	63719,

+	63727,	63737,	63743,	63761,	63773,	63781,	63793,	63799,	63803,	63809,

+	63823,	63839,	63841,	63853,	63857,	63863,	63901,	63907,	63913,	63929,

+	63949,	63977,	63997,	64007,	64013,	64019,	64033,	64037,	64063,	64067,

+	64081,	64091,	64109,	64123,	64151,	64153,	64157,	64171,	64187,	64189,

+	64217,	64223,	64231,	64237,	64271,	64279,	64283,	64301,	64303,	64319,

+	64327,	64333,	64373,	64381,	64399,	64403,	64433,	64439,	64451,	64453,

+	64483,	64489,	64499,	64513,	64553,	64567,	64577,	64579,	64591,	64601,

+	64609,	64613,	64621,	64627,	64633,	64661,	64663,	64667,	64679,	64693,

+	64709,	64717,	64747,	64763,	64781,	64783,	64793,	64811,	64817,	64849,

+	64853,	64871,	64877,	64879,	64891,	64901,	64919,	64921,	64927,	64937,

+	64951,	64969,	64997,	65003,	65011,	65027,	65029,	65033,	65053,	65063,

+	65071,	65089,	65099,	65101,	65111,	65119,	65123,	65129,	65141,	65147,

+	65167,	65171,	65173,	65179,	65183,	65203,	65213,	65239,	65257,	65267,

+	65269,	65287,	65293,	65309,	65323,	65327,	65353,	65357,	65371,	65381,

+	65393,	65407,	65413,	65419,	65423,	65437,	65447,	65449,	65479,	65497,

+	65519,	65521,	65537,	65539,	65543,	65551,	65557,	65563,	65579,	65581,

+	65587,	65599,	65609,	65617,	65629,	65633,	65647,	65651,	65657,	65677,

+	65687,	65699,	65701,	65707,	65713,	65717,	65719,	65729,	65731,	65761,

+	65777,	65789,	65809,	65827,	65831,	65837,	65839,	65843,	65851,	65867,

+	65881,	65899,	65921,	65927,	65929,	65951,	65957,	65963,	65981,	65983,

+	65993,	66029,	66037,	66041,	66047,	66067,	66071,	66083,	66089,	66103,

+	66107,	66109,	66137,	66161,	66169,	66173,	66179,	66191,	66221,	66239,

+	66271,	66293,	66301,	66337,	66343,	66347,	66359,	66361,	66373,	66377,

+	66383,	66403,	66413,	66431,	66449,	66457,	66463,	66467,	66491,	66499,

+	66509,	66523,	66529,	66533,	66541,	66553,	66569,	66571,	66587,	66593,

+	66601,	66617,	66629,	66643,	66653,	66683,	66697,	66701,	66713,	66721,

+	66733,	66739,	66749,	66751,	66763,	66791,	66797,	66809,	66821,	66841,

+	66851,	66853,	66863,	66877,	66883,	66889,	66919,	66923,	66931,	66943,

+	66947,	66949,	66959,	66973,	66977,	67003,	67021,	67033,	67043,	67049,

+	67057,	67061,	67073,	67079,	67103,	67121,	67129,	67139,	67141,	67153,

+	67157,	67169,	67181,	67187,	67189,	67211,	67213,	67217,	67219,	67231,

+	67247,	67261,	67271,	67273,	67289,	67307,	67339,	67343,	67349,	67369,

+	67391,	67399,	67409,	67411,	67421,	67427,	67429,	67433,	67447,	67453,

+	67477,	67481,	67489,	67493,	67499,	67511,	67523,	67531,	67537,	67547,

+	67559,	67567,	67577,	67579,	67589,	67601,	67607,	67619,	67631,	67651,

+	67679,	67699,	67709,	67723,	67733,	67741,	67751,	67757,	67759,	67763,

+	67777,	67783,	67789,	67801,	67807,	67819,	67829,	67843,	67853,	67867,

+	67883,	67891,	67901,	67927,	67931,	67933,	67939,	67943,	67957,	67961,

+	67967,	67979,	67987,	67993,	68023,	68041,	68053,	68059,	68071,	68087,

+	68099,	68111,	68113,	68141,	68147,	68161,	68171,	68207,	68209,	68213,

+	68219,	68227,	68239,	68261,	68279,	68281,	68311,	68329,	68351,	68371,

+	68389,	68399,	68437,	68443,	68447,	68449,	68473,	68477,	68483,	68489,

+	68491,	68501,	68507,	68521,	68531,	68539,	68543,	68567,	68581,	68597,

+	68611,	68633,	68639,	68659,	68669,	68683,	68687,	68699,	68711,	68713,

+	68729,	68737,	68743,	68749,	68767,	68771,	68777,	68791,	68813,	68819,

+	68821,	68863,	68879,	68881,	68891,	68897,	68899,	68903,	68909,	68917,

+	68927,	68947,	68963,	68993,	69001,	69011,	69019,	69029,	69031,	69061,

+	69067,	69073,	69109,	69119,	69127,	69143,	69149,	69151,	69163,	69191,

+	69193,	69197,	69203,	69221,	69233,	69239,	69247,	69257,	69259,	69263,

+	69313,	69317,	69337,	69341,	69371,	69379,	69383,	69389,	69401,	69403,

+	69427,	69431,	69439,	69457,	69463,	69467,	69473,	69481,	69491,	69493,

+	69497,	69499,	69539,	69557,	69593,	69623,	69653,	69661,	69677,	69691,

+	69697,	69709,	69737,	69739,	69761,	69763,	69767,	69779,	69809,	69821,

+	69827,	69829,	69833,	69847,	69857,	69859,	69877,	69899,	69911,	69929,

+	69931,	69941,	69959,	69991,	69997,	70001,	70003,	70009,	70019,	70039,

+	70051,	70061,	70067,	70079,	70099,	70111,	70117,	70121,	70123,	70139,

+	70141,	70157,	70163,	70177,	70181,	70183,	70199,	70201,	70207,	70223,

+	70229,	70237,	70241,	70249,	70271,	70289,	70297,	70309,	70313,	70321,

+	70327,	70351,	70373,	70379,	70381,	70393,	70423,	70429,	70439,	70451,

+	70457,	70459,	70481,	70487,	70489,	70501,	70507,	70529,	70537,	70549,

+	70571,	70573,	70583,	70589,	70607,	70619,	70621,	70627,	70639,	70657,

+	70663,	70667,	70687,	70709,	70717,	70729,	70753,	70769,	70783,	70793,

+	70823,	70841,	70843,	70849,	70853,	70867,	70877,	70879,	70891,	70901,

+	70913,	70919,	70921,	70937,	70949,	70951,	70957,	70969,	70979,	70981,

+	70991,	70997,	70999,	71011,	71023,	71039,	71059,	71069,	71081,	71089,

+	71119,	71129,	71143,	71147,	71153,	71161,	71167,	71171,	71191,	71209,

+	71233,	71237,	71249,	71257,	71261,	71263,	71287,	71293,	71317,	71327,

+	71329,	71333,	71339,	71341,	71347,	71353,	71359,	71363,	71387,	71389,

+	71399,	71411,	71413,	71419,	71429,	71437,	71443,	71453,	71471,	71473,

+	71479,	71483,	71503,	71527,	71537,	71549,	71551,	71563,	71569,	71593,

+	71597,	71633,	71647,	71663,	71671,	71693,	71699,	71707,	71711,	71713,

+	71719,	71741,	71761,	71777,	71789,	71807,	71809,	71821,	71837,	71843,

+	71849,	71861,	71867,	71879,	71881,	71887,	71899,	71909,	71917,	71933,

+	71941,	71947,	71963,	71971,	71983,	71987,	71993,	71999,	72019,	72031,

+	72043,	72047,	72053,	72073,	72077,	72089,	72091,	72101,	72103,	72109,

+	72139,	72161,	72167,	72169,	72173,	72211,	72221,	72223,	72227,	72229,

+	72251,	72253,	72269,	72271,	72277,	72287,	72307,	72313,	72337,	72341,

+	72353,	72367,	72379,	72383,	72421,	72431,	72461,	72467,	72469,	72481,

+	72493,	72497,	72503,	72533,	72547,	72551,	72559,	72577,	72613,	72617,

+	72623,	72643,	72647,	72649,	72661,	72671,	72673,	72679,	72689,	72701,

+	72707,	72719,	72727,	72733,	72739,	72763,	72767,	72797,	72817,	72823,

+	72859,	72869,	72871,	72883,	72889,	72893,	72901,	72907,	72911,	72923,

+	72931,	72937,	72949,	72953,	72959,	72973,	72977,	72997,	73009,	73013,

+	73019,	73037,	73039,	73043,	73061,	73063,	73079,	73091,	73121,	73127,

+	73133,	73141,	73181,	73189,	73237,	73243,	73259,	73277,	73291,	73303,

+	73309,	73327,	73331,	73351,	73361,	73363,	73369,	73379,	73387,	73417,

+	73421,	73433,	73453,	73459,	73471,	73477,	73483,	73517,	73523,	73529,

+	73547,	73553,	73561,	73571,	73583,	73589,	73597,	73607,	73609,	73613,

+	73637,	73643,	73651,	73673,	73679,	73681,	73693,	73699,	73709,	73721,

+	73727,	73751,	73757,	73771,	73783,	73819,	73823,	73847,	73849,	73859,

+	73867,	73877,	73883,	73897,	73907,	73939,	73943,	73951,	73961,	73973,

+	73999,	74017,	74021,	74027,	74047,	74051,	74071,	74077,	74093,	74099,

+	74101,	74131,	74143,	74149,	74159,	74161,	74167,	74177,	74189,	74197,

+	74201,	74203,	74209,	74219,	74231,	74257,	74279,	74287,	74293,	74297,

+	74311,	74317,	74323,	74353,	74357,	74363,	74377,	74381,	74383,	74411,

+	74413,	74419,	74441,	74449,	74453,	74471,	74489,	74507,	74509,	74521,

+	74527,	74531,	74551,	74561,	74567,	74573,	74587,	74597,	74609,	74611,

+	74623,	74653,	74687,	74699,	74707,	74713,	74717,	74719,	74729,	74731,

+	74747,	74759,	74761,	74771,	74779,	74797,	74821,	74827,	74831,	74843,

+	74857,	74861,	74869,	74873,	74887,	74891,	74897,	74903,	74923,	74929,

+	74933,	74941,	74959,	75011,	75013,	75017,	75029,	75037,	75041,	75079,

+	75083,	75109,	75133,	75149,	75161,	75167,	75169,	75181,	75193,	75209,

+	75211,	75217,	75223,	75227,	75239,	75253,	75269,	75277,	75289,	75307,

+	75323,	75329,	75337,	75347,	75353,	75367,	75377,	75389,	75391,	75401,

+	75403,	75407,	75431,	75437,	75479,	75503,	75511,	75521,	75527,	75533,

+	75539,	75541,	75553,	75557,	75571,	75577,	75583,	75611,	75617,	75619,

+	75629,	75641,	75653,	75659,	75679,	75683,	75689,	75703,	75707,	75709,

+	75721,	75731,	75743,	75767,	75773,	75781,	75787,	75793,	75797,	75821,

+	75833,	75853,	75869,	75883,	75913,	75931,	75937,	75941,	75967,	75979,

+	75983,	75989,	75991,	75997,	76001,	76003,	76031,	76039,	76079,	76081,

+	76091,	76099,	76103,	76123,	76129,	76147,	76157,	76159,	76163,	76207,

+	76213,	76231,	76243,	76249,	76253,	76259,	76261,	76283,	76289,	76303,

+	76333,	76343,	76367,	76369,	76379,	76387,	76403,	76421,	76423,	76441,

+	76463,	76471,	76481,	76487,	76493,	76507,	76511,	76519,	76537,	76541,

+	76543,	76561,	76579,	76597,	76603,	76607,	76631,	76649,	76651,	76667,

+	76673,	76679,	76697,	76717,	76733,	76753,	76757,	76771,	76777,	76781,

+	76801,	76819,	76829,	76831,	76837,	76847,	76871,	76873,	76883,	76907,

+	76913,	76919,	76943,	76949,	76961,	76963,	76991,	77003,	77017,	77023,

+	77029,	77041,	77047,	77069,	77081,	77093,	77101,	77137,	77141,	77153,

+	77167,	77171,	77191,	77201,	77213,	77237,	77239,	77243,	77249,	77261,

+	77263,	77267,	77269,	77279,	77291,	77317,	77323,	77339,	77347,	77351,

+	77359,	77369,	77377,	77383,	77417,	77419,	77431,	77447,	77471,	77477,

+	77479,	77489,	77491,	77509,	77513,	77521,	77527,	77543,	77549,	77551,

+	77557,	77563,	77569,	77573,	77587,	77591,	77611,	77617,	77621,	77641,

+	77647,	77659,	77681,	77687,	77689,	77699,	77711,	77713,	77719,	77723,

+	77731,	77743,	77747,	77761,	77773,	77783,	77797,	77801,	77813,	77839,

+	77849,	77863,	77867,	77893,	77899,	77929,	77933,	77951,	77969,	77977,

+	77983,	77999,	78007,	78017,	78031,	78041,	78049,	78059,	78079,	78101,

+	78121,	78137,	78139,	78157,	78163,	78167,	78173,	78179,	78191,	78193,

+	78203,	78229,	78233,	78241,	78259,	78277,	78283,	78301,	78307,	78311,

+	78317,	78341,	78347,	78367,	78401,	78427,	78437,	78439,	78467,	78479,

+	78487,	78497,	78509,	78511,	78517,	78539,	78541,	78553,	78569,	78571,

+	78577,	78583,	78593,	78607,	78623,	78643,	78649,	78653,	78691,	78697,

+	78707,	78713,	78721,	78737,	78779,	78781,	78787,	78791,	78797,	78803,

+	78809,	78823,	78839,	78853,	78857,	78877,	78887,	78889,	78893,	78901,

+	78919,	78929,	78941,	78977,	78979,	78989,	79031,	79039,	79043,	79063,

+	79087,	79103,	79111,	79133,	79139,	79147,	79151,	79153,	79159,	79181,

+	79187,	79193,	79201,	79229,	79231,	79241,	79259,	79273,	79279,	79283,

+	79301,	79309,	79319,	79333,	79337,	79349,	79357,	79367,	79379,	79393,

+	79397,	79399,	79411,	79423,	79427,	79433,	79451,	79481,	79493,	79531,

+	79537,	79549,	79559,	79561,	79579,	79589,	79601,	79609,	79613,	79621,

+	79627,	79631,	79633,	79657,	79669,	79687,	79691,	79693,	79697,	79699,

+	79757,	79769,	79777,	79801,	79811,	79813,	79817,	79823,	79829,	79841,

+	79843,	79847,	79861,	79867,	79873,	79889,	79901,	79903,	79907,	79939,

+	79943,	79967,	79973,	79979,	79987,	79997,	79999,	80021,	80039,	80051,

+	80071,	80077,	80107,	80111,	80141,	80147,	80149,	80153,	80167,	80173,

+	80177,	80191,	80207,	80209,	80221,	80231,	80233,	80239,	80251,	80263,

+	80273,	80279,	80287,	80309,	80317,	80329,	80341,	80347,	80363,	80369,

+	80387,	80407,	80429,	80447,	80449,	80471,	80473,	80489,	80491,	80513,

+	80527,	80537,	80557,	80567,	80599,	80603,	80611,	80621,	80627,	80629,

+	80651,	80657,	80669,	80671,	80677,	80681,	80683,	80687,	80701,	80713,

+	80737,	80747,	80749,	80761,	80777,	80779,	80783,	80789,	80803,	80809,

+	80819,	80831,	80833,	80849,	80863,	80897,	80909,	80911,	80917,	80923,

+	80929,	80933,	80953,	80963,	80989,	81001,	81013,	81017,	81019,	81023,

+	81031,	81041,	81043,	81047,	81049,	81071,	81077,	81083,	81097,	81101,

+	81119,	81131,	81157,	81163,	81173,	81181,	81197,	81199,	81203,	81223,

+	81233,	81239,	81281,	81283,	81293,	81299,	81307,	81331,	81343,	81349,

+	81353,	81359,	81371,	81373,	81401,	81409,	81421,	81439,	81457,	81463,

+	81509,	81517,	81527,	81533,	81547,	81551,	81553,	81559,	81563,	81569,

+	81611,	81619,	81629,	81637,	81647,	81649,	81667,	81671,	81677,	81689,

+	81701,	81703,	81707,	81727,	81737,	81749,	81761,	81769,	81773,	81799,

+	81817,	81839,	81847,	81853,	81869,	81883,	81899,	81901,	81919,	81929,

+	81931,	81937,	81943,	81953,	81967,	81971,	81973,	82003,	82007,	82009,

+	82013,	82021,	82031,	82037,	82039,	82051,	82067,	82073,	82129,	82139,

+	82141,	82153,	82163,	82171,	82183,	82189,	82193,	82207,	82217,	82219,

+	82223,	82231,	82237,	82241,	82261,	82267,	82279,	82301,	82307,	82339,

+	82349,	82351,	82361,	82373,	82387,	82393,	82421,	82457,	82463,	82469,

+	82471,	82483,	82487,	82493,	82499,	82507,	82529,	82531,	82549,	82559,

+	82561,	82567,	82571,	82591,	82601,	82609,	82613,	82619,	82633,	82651,

+	82657,	82699,	82721,	82723,	82727,	82729,	82757,	82759,	82763,	82781,

+	82787,	82793,	82799,	82811,	82813,	82837,	82847,	82883,	82889,	82891,

+	82903,	82913,	82939,	82963,	82981,	82997,	83003,	83009,	83023,	83047,

+	83059,	83063,	83071,	83077,	83089,	83093,	83101,	83117,	83137,	83177,

+	83203,	83207,	83219,	83221,	83227,	83231,	83233,	83243,	83257,	83267,

+	83269,	83273,	83299,	83311,	83339,	83341,	83357,	83383,	83389,	83399,

+	83401,	83407,	83417,	83423,	83431,	83437,	83443,	83449,	83459,	83471,

+	83477,	83497,	83537,	83557,	83561,	83563,	83579,	83591,	83597,	83609,

+	83617,	83621,	83639,	83641,	83653,	83663,	83689,	83701,	83717,	83719,

+	83737,	83761,	83773,	83777,	83791,	83813,	83833,	83843,	83857,	83869,

+	83873,	83891,	83903,	83911,	83921,	83933,	83939,	83969,	83983,	83987,

+	84011,	84017,	84047,	84053,	84059,	84061,	84067,	84089,	84121,	84127,

+	84131,	84137,	84143,	84163,	84179,	84181,	84191,	84199,	84211,	84221,

+	84223,	84229,	84239,	84247,	84263,	84299,	84307,	84313,	84317,	84319,

+	84347,	84349,	84377,	84389,	84391,	84401,	84407,	84421,	84431,	84437,

+	84443,	84449,	84457,	84463,	84467,	84481,	84499,	84503,	84509,	84521,

+	84523,	84533,	84551,	84559,	84589,	84629,	84631,	84649,	84653,	84659,

+	84673,	84691,	84697,	84701,	84713,	84719,	84731,	84737,	84751,	84761,

+	84787,	84793,	84809,	84811,	84827,	84857,	84859,	84869,	84871,	84913,

+	84919,	84947,	84961,	84967,	84977,	84979,	84991,	85009,	85021,	85027,

+	85037,	85049,	85061,	85081,	85087,	85091,	85093,	85103,	85109,	85121,

+	85133,	85147,	85159,	85193,	85199,	85201,	85213,	85223,	85229,	85237,

+	85243,	85247,	85259,	85297,	85303,	85313,	85331,	85333,	85361,	85363,

+	85369,	85381,	85411,	85427,	85429,	85439,	85447,	85451,	85453,	85469,

+	85487,	85513,	85517,	85523,	85531,	85549,	85571,	85577,	85597,	85601,

+	85607,	85619,	85621,	85627,	85639,	85643,	85661,	85667,	85669,	85691,

+	85703,	85711,	85717,	85733,	85751,	85781,	85793,	85817,	85819,	85829,

+	85831,	85837,	85843,	85847,	85853,	85889,	85903,	85909,	85931,	85933,

+	85991,	85999,	86011,	86017,	86027,	86029,	86069,	86077,	86083,	86111,

+	86113,	86117,	86131,	86137,	86143,	86161,	86171,	86179,	86183,	86197,

+	86201,	86209,	86239,	86243,	86249,	86257,	86263,	86269,	86287,	86291,

+	86293,	86297,	86311,	86323,	86341,	86351,	86353,	86357,	86369,	86371,

+	86381,	86389,	86399,	86413,	86423,	86441,	86453,	86461,	86467,	86477,

+	86491,	86501,	86509,	86531,	86533,	86539,	86561,	86573,	86579,	86587,

+	86599,	86627,	86629,	86677,	86689,	86693,	86711,	86719,	86729,	86743,

+	86753,	86767,	86771,	86783,	86813,	86837,	86843,	86851,	86857,	86861,

+	86869,	86923,	86927,	86929,	86939,	86951,	86959,	86969,	86981,	86993,

+	87011,	87013,	87037,	87041,	87049,	87071,	87083,	87103,	87107,	87119,

+	87121,	87133,	87149,	87151,	87179,	87181,	87187,	87211,	87221,	87223,

+	87251,	87253,	87257,	87277,	87281,	87293,	87299,	87313,	87317,	87323,

+	87337,	87359,	87383,	87403,	87407,	87421,	87427,	87433,	87443,	87473,

+	87481,	87491,	87509,	87511,	87517,	87523,	87539,	87541,	87547,	87553,

+	87557,	87559,	87583,	87587,	87589,	87613,	87623,	87629,	87631,	87641,

+	87643,	87649,	87671,	87679,	87683,	87691,	87697,	87701,	87719,	87721,

+	87739,	87743,	87751,	87767,	87793,	87797,	87803,	87811,	87833,	87853,

+	87869,	87877,	87881,	87887,	87911,	87917,	87931,	87943,	87959,	87961,

+	87973,	87977,	87991,	88001,	88003,	88007,	88019,	88037,	88069,	88079,

+	88093,	88117,	88129,	88169,	88177,	88211,	88223,	88237,	88241,	88259,

+	88261,	88289,	88301,	88321,	88327,	88337,	88339,	88379,	88397,	88411,

+	88423,	88427,	88463,	88469,	88471,	88493,	88499,	88513,	88523,	88547,

+	88589,	88591,	88607,	88609,	88643,	88651,	88657,	88661,	88663,	88667,

+	88681,	88721,	88729,	88741,	88747,	88771,	88789,	88793,	88799,	88801,

+	88807,	88811,	88813,	88817,	88819,	88843,	88853,	88861,	88867,	88873,

+	88883,	88897,	88903,	88919,	88937,	88951,	88969,	88993,	88997,	89003,

+	89009,	89017,	89021,	89041,	89051,	89057,	89069,	89071,	89083,	89087,

+	89101,	89107,	89113,	89119,	89123,	89137,	89153,	89189,	89203,	89209,

+	89213,	89227,	89231,	89237,	89261,	89269,	89273,	89293,	89303,	89317,

+	89329,	89363,	89371,	89381,	89387,	89393,	89399,	89413,	89417,	89431,

+	89443,	89449,	89459,	89477,	89491,	89501,	89513,	89519,	89521,	89527,

+	89533,	89561,	89563,	89567,	89591,	89597,	89599,	89603,	89611,	89627,

+	89633,	89653,	89657,	89659,	89669,	89671,	89681,	89689,	89753,	89759,

+	89767,	89779,	89783,	89797,	89809,	89819,	89821,	89833,	89839,	89849,

+	89867,	89891,	89897,	89899,	89909,	89917,	89923,	89939,	89959,	89963,

+	89977,	89983,	89989,	90001,	90007,	90011,	90017,	90019,	90023,	90031,

+	90053,	90059,	90067,	90071,	90073,	90089,	90107,	90121,	90127,	90149,

+	90163,	90173,	90187,	90191,	90197,	90199,	90203,	90217,	90227,	90239,

+	90247,	90263,	90271,	90281,	90289,	90313,	90353,	90359,	90371,	90373,

+	90379,	90397,	90401,	90403,	90407,	90437,	90439,	90469,	90473,	90481,

+	90499,	90511,	90523,	90527,	90529,	90533,	90547,	90583,	90599,	90617,

+	90619,	90631,	90641,	90647,	90659,	90677,	90679,	90697,	90703,	90709,

+	90731,	90749,	90787,	90793,	90803,	90821,	90823,	90833,	90841,	90847,

+	90863,	90887,	90901,	90907,	90911,	90917,	90931,	90947,	90971,	90977,

+	90989,	90997,	91009,	91019,	91033,	91079,	91081,	91097,	91099,	91121,

+	91127,	91129,	91139,	91141,	91151,	91153,	91159,	91163,	91183,	91193,

+	91199,	91229,	91237,	91243,	91249,	91253,	91283,	91291,	91297,	91303,

+	91309,	91331,	91367,	91369,	91373,	91381,	91387,	91393,	91397,	91411,

+	91423,	91433,	91453,	91457,	91459,	91463,	91493,	91499,	91513,	91529,

+	91541,	91571,	91573,	91577,	91583,	91591,	91621,	91631,	91639,	91673,

+	91691,	91703,	91711,	91733,	91753,	91757,	91771,	91781,	91801,	91807,

+	91811,	91813,	91823,	91837,	91841,	91867,	91873,	91909,	91921,	91939,

+	91943,	91951,	91957,	91961,	91967,	91969,	91997,	92003,	92009,	92033,

+	92041,	92051,	92077,	92083,	92107,	92111,	92119,	92143,	92153,	92173,

+	92177,	92179,	92189,	92203,	92219,	92221,	92227,	92233,	92237,	92243,

+	92251,	92269,	92297,	92311,	92317,	92333,	92347,	92353,	92357,	92363,

+	92369,	92377,	92381,	92383,	92387,	92399,	92401,	92413,	92419,	92431,

+	92459,	92461,	92467,	92479,	92489,	92503,	92507,	92551,	92557,	92567,

+	92569,	92581,	92593,	92623,	92627,	92639,	92641,	92647,	92657,	92669,

+	92671,	92681,	92683,	92693,	92699,	92707,	92717,	92723,	92737,	92753,

+	92761,	92767,	92779,	92789,	92791,	92801,	92809,	92821,	92831,	92849,

+	92857,	92861,	92863,	92867,	92893,	92899,	92921,	92927,	92941,	92951,

+	92957,	92959,	92987,	92993,	93001,	93047,	93053,	93059,	93077,	93083,

+	93089,	93097,	93103,	93113,	93131,	93133,	93139,	93151,	93169,	93179,

+	93187,	93199,	93229,	93239,	93241,	93251,	93253,	93257,	93263,	93281,

+	93283,	93287,	93307,	93319,	93323,	93329,	93337,	93371,	93377,	93383,

+	93407,	93419,	93427,	93463,	93479,	93481,	93487,	93491,	93493,	93497,

+	93503,	93523,	93529,	93553,	93557,	93559,	93563,	93581,	93601,	93607,

+	93629,	93637,	93683,	93701,	93703,	93719,	93739,	93761,	93763,	93787,

+	93809,	93811,	93827,	93851,	93871,	93887,	93889,	93893,	93901,	93911,

+	93913,	93923,	93937,	93941,	93949,	93967,	93971,	93979,	93983,	93997,

+	94007,	94009,	94033,	94049,	94057,	94063,	94079,	94099,	94109,	94111,

+	94117,	94121,	94151,	94153,	94169,	94201,	94207,	94219,	94229,	94253,

+	94261,	94273,	94291,	94307,	94309,	94321,	94327,	94331,	94343,	94349,

+	94351,	94379,	94397,	94399,	94421,	94427,	94433,	94439,	94441,	94447,

+	94463,	94477,	94483,	94513,	94529,	94531,	94541,	94543,	94547,	94559,

+	94561,	94573,	94583,	94597,	94603,	94613,	94621,	94649,	94651,	94687,

+	94693,	94709,	94723,	94727,	94747,	94771,	94777,	94781,	94789,	94793,

+	94811,	94819,	94823,	94837,	94841,	94847,	94849,	94873,	94889,	94903,

+	94907,	94933,	94949,	94951,	94961,	94993,	94999,	95003,	95009,	95021,

+	95027,	95063,	95071,	95083,	95087,	95089,	95093,	95101,	95107,	95111,

+	95131,	95143,	95153,	95177,	95189,	95191,	95203,	95213,	95219,	95231,

+	95233,	95239,	95257,	95261,	95267,	95273,	95279,	95287,	95311,	95317,

+	95327,	95339,	95369,	95383,	95393,	95401,	95413,	95419,	95429,	95441,

+	95443,	95461,	95467,	95471,	95479,	95483,	95507,	95527,	95531,	95539,

+	95549,	95561,	95569,	95581,	95597,	95603,	95617,	95621,	95629,	95633,

+	95651,	95701,	95707,	95713,	95717,	95723,	95731,	95737,	95747,	95773,

+	95783,	95789,	95791,	95801,	95803,	95813,	95819,	95857,	95869,	95873,

+	95881,	95891,	95911,	95917,	95923,	95929,	95947,	95957,	95959,	95971,

+	95987,	95989,	96001,	96013,	96017,	96043,	96053,	96059,	96079,	96097,

+	96137,	96149,	96157,	96167,	96179,	96181,	96199,	96211,	96221,	96223,

+	96233,	96259,	96263,	96269,	96281,	96289,	96293,	96323,	96329,	96331,

+	96337,	96353,	96377,	96401,	96419,	96431,	96443,	96451,	96457,	96461,

+	96469,	96479,	96487,	96493,	96497,	96517,	96527,	96553,	96557,	96581,

+	96587,	96589,	96601,	96643,	96661,	96667,	96671,	96697,	96703,	96731,

+	96737,	96739,	96749,	96757,	96763,	96769,	96779,	96787,	96797,	96799,

+	96821,	96823,	96827,	96847,	96851,	96857,	96893,	96907,	96911,	96931,

+	96953,	96959,	96973,	96979,	96989,	96997,	97001,	97003,	97007,	97021,

+	97039,	97073,	97081,	97103,	97117,	97127,	97151,	97157,	97159,	97169,

+	97171,	97177,	97187,	97213,	97231,	97241,	97259,	97283,	97301,	97303,

+	97327,	97367,	97369,	97373,	97379,	97381,	97387,	97397,	97423,	97429,

+	97441,	97453,	97459,	97463,	97499,	97501,	97511,	97523,	97547,	97549,

+	97553,	97561,	97571,	97577,	97579,	97583,	97607,	97609,	97613,	97649,

+	97651,	97673,	97687,	97711,	97729,	97771,	97777,	97787,	97789,	97813,

+	97829,	97841,	97843,	97847,	97849,	97859,	97861,	97871,	97879,	97883,

+	97919,	97927,	97931,	97943,	97961,	97967,	97973,	97987,	98009,	98011,

+	98017,	98041,	98047,	98057,	98081,	98101,	98123,	98129,	98143,	98179,

+	98207,	98213,	98221,	98227,	98251,	98257,	98269,	98297,	98299,	98317,

+	98321,	98323,	98327,	98347,	98369,	98377,	98387,	98389,	98407,	98411,

+	98419,	98429,	98443,	98453,	98459,	98467,	98473,	98479,	98491,	98507,

+	98519,	98533,	98543,	98561,	98563,	98573,	98597,	98621,	98627,	98639,

+	98641,	98663,	98669,	98689,	98711,	98713,	98717,	98729,	98731,	98737,

+	98773,	98779,	98801,	98807,	98809,	98837,	98849,	98867,	98869,	98873,

+	98887,	98893,	98897,	98899,	98909,	98911,	98927,	98929,	98939,	98947,

+	98953,	98963,	98981,	98993,	98999,	99013,	99017,	99023,	99041,	99053,

+	99079,	99083,	99089,	99103,	99109,	99119,	99131,	99133,	99137,	99139,

+	99149,	99173,	99181,	99191,	99223,	99233,	99241,	99251,	99257,	99259,

+	99277,	99289,	99317,	99347,	99349,	99367,	99371,	99377,	99391,	99397,

+	99401,	99409,	99431,	99439,	99469,	99487,	99497,	99523,	99527,	99529,

+	99551,	99559,	99563,	99571,	99577,	99581,	99607,	99611,	99623,	99643,

+	99661,	99667,	99679,	99689,	99707,	99709,	99713,	99719,	99721,	99733,

+	99761,	99767,	99787,	99793,	99809,	99817,	99823,	99829,	99833,	99839,

+	99859,	99871,	99877,	99881,	99901,	99907,	99923,	99929,	99961,	99971,

+	99989,	99991,	100003,	100019,	100043,	100049,	100057,	100069,	100103,	100109,

+	100129,	100151,	100153,	100169,	100183,	100189,	100193,	100207,	100213,	100237,

+	100267,	100271,	100279,	100291,	100297,	100313,	100333,	100343,	100357,	100361,

+	100363,	100379,	100391,	100393,	100403,	100411,	100417,	100447,	100459,	100469,

+	100483,	100493,	100501,	100511,	100517,	100519,	100523,	100537,	100547,	100549,

+	100559,	100591,	100609,	100613,	100621,	100649,	100669,	100673,	100693,	100699,

+	100703,	100733,	100741,	100747,	100769,	100787,	100799,	100801,	100811,	100823,

+	100829,	100847,	100853,	100907,	100913,	100927,	100931,	100937,	100943,	100957,

+	100981,	100987,	100999,	101009,	101021,	101027,	101051,	101063,	101081,	101089,

+	101107,	101111,	101113,	101117,	101119,	101141,	101149,	101159,	101161,	101173,

+	101183,	101197,	101203,	101207,	101209,	101221,	101267,	101273,	101279,	101281,

+	101287,	101293,	101323,	101333,	101341,	101347,	101359,	101363,	101377,	101383,

+	101399,	101411,	101419,	101429,	101449,	101467,	101477,	101483,	101489,	101501,

+	101503,	101513,	101527,	101531,	101533,	101537,	101561,	101573,	101581,	101599,

+	101603,	101611,	101627,	101641,	101653,	101663,	101681,	101693,	101701,	101719,

+	101723,	101737,	101741,	101747,	101749,	101771,	101789,	101797,	101807,	101833,

+	101837,	101839,	101863,	101869,	101873,	101879,	101891,	101917,	101921,	101929,

+	101939,	101957,	101963,	101977,	101987,	101999,	102001,	102013,	102019,	102023,

+	102031,	102043,	102059,	102061,	102071,	102077,	102079,	102101,	102103,	102107,

+	102121,	102139,	102149,	102161,	102181,	102191,	102197,	102199,	102203,	102217,

+	102229,	102233,	102241,	102251,	102253,	102259,	102293,	102299,	102301,	102317,

+	102329,	102337,	102359,	102367,	102397,	102407,	102409,	102433,	102437,	102451,

+	102461,	102481,	102497,	102499,	102503,	102523,	102533,	102539,	102547,	102551,

+	102559,	102563,	102587,	102593,	102607,	102611,	102643,	102647,	102653,	102667,

+	102673,	102677,	102679,	102701,	102761,	102763,	102769,	102793,	102797,	102811,

+	102829,	102841,	102859,	102871,	102877,	102881,	102911,	102913,	102929,	102931,

+	102953,	102967,	102983,	103001,	103007,	103043,	103049,	103067,	103069,	103079,

+	103087,	103091,	103093,	103099,	103123,	103141,	103171,	103177,	103183,	103217,

+	103231,	103237,	103289,	103291,	103307,	103319,	103333,	103349,	103357,	103387,

+	103391,	103393,	103399,	103409,	103421,	103423,	103451,	103457,	103471,	103483,

+	103511,	103529,	103549,	103553,	103561,	103567,	103573,	103577,	103583,	103591,

+	103613,	103619,	103643,	103651,	103657,	103669,	103681,	103687,	103699,	103703,

+	103723,	103769,	103787,	103801,	103811,	103813,	103837,	103841,	103843,	103867,

+	103889,	103903,	103913,	103919,	103951,	103963,	103967,	103969,	103979,	103981,

+	103991,	103993,	103997,	104003,	104009,	104021,	104033,	104047,	104053,	104059,

+	104087,	104089,	104107,	104113,	104119,	104123,	104147,	104149,	104161,	104173,

+	104179,	104183,	104207,	104231,	104233,	104239,	104243,	104281,	104287,	104297,

+	104309,	104311,	104323,	104327,	104347,	104369,	104381,	104383,	104393,	104399,

+	104417,	104459,	104471,	104473,	104479,	104491,	104513,	104527,	104537,	104543,

+	104549,	104551,	104561,	104579,	104593,	104597,	104623,	104639,	104651,	104659,

+	104677,	104681,	104683,	104693,	104701,	104707,	104711,	104717,	104723,	104729,

+};

+

+//  return 1 if p is divisable by sp, 0 otherwise

+static int

+divides(mpint *dividend, ulong divisor)

+{

+	mpdigit d[2], q;

+	int i;

+

+	d[1] = 0;

+	for(i = dividend->top-1; i >= 0; i--){

+		d[0] = dividend->p[i];

+		mpdigdiv(d, divisor, &q);

+		d[1] = d[0] - divisor*q;

+	}

+	return d[1] == 0;

+}

+

+//  return -1 if p is divisable by one of the small primes, 0 otherwise

+int

+smallprimetest(mpint *p)

+{

+	int i;

+	ulong sp;

+

+	for(i = 0; i < nelem(smallprimes); i++){

+		sp = smallprimes[i];

+		if(p->top == 1 && p->p[0] <= sp)

+			break;

+		if(divides(p, sp))

+			return -1;

+	}

+	return 0;

+}

--- a/libsec/thumb.c

+++ b/libsec/thumb.c

@@ -1,8 +1,5 @@

-#include <u.h>

-#include <libc.h>

+#include "os.h"

 #include <bio.h>

-#include <auth.h>

-#include <mp.h>

 #include <libsec.h>

 enum{ ThumbTab = 1<<10 };

--- a/libsec/tlshand.c

+++ b/libsec/tlshand.c

@@ -20,14 +20,11 @@

 	MaxChunk = 1<<15,

 	MAXdlen = SHA2_512dlen,

 	RandomSize = 32,

-	SidSize = 32,

 	MasterSecretSize = 48,

 	AQueue = 0,

 	AFlush = 1,

 };

-typedef struct TlsSec TlsSec;

-

 typedef struct Bytes{

 	int len;

 	uchar data[1];  // [len]

@@ -62,21 +59,39 @@

 	SHA2_256state	sha2_256;

 } HandshakeHash;

+typedef struct TlsSec TlsSec;

+struct TlsSec {

+	RSApub *rsapub;

+	AuthRpc *rpc;	// factotum for rsa private key

+	uchar *psk;	// pre-shared key

+	int psklen;

+	int clientVers;			// version in ClientHello

+	uchar sec[MasterSecretSize];	// master secret

+	uchar crandom[RandomSize];	// client random

+	uchar srandom[RandomSize];	// server random

+	// byte generation and handshake checksum

+	void (*prf)(uchar*, int, uchar*, int, char*, uchar*, int, uchar*, int);

+	void (*setFinished)(TlsSec*, HandshakeHash, uchar*, int);

+	int nfin;

+};

+

 typedef struct TlsConnection{

-	TlsSec *sec;	// security management goo

+	TlsSec sec[1];	// security management goo

 	int hand, ctl;	// record layer file descriptors

 	int erred;		// set when tlsError called

 	int (*trace)(char*fmt, ...); // for debugging

 	int version;	// protocol we are speaking

-	int verset;		// version has been set

-	int ver2hi;		// server got a version 2 hello

-	int isClient;	// is this the client or server?

-	Bytes *sid;		// SessionID

-	Bytes *cert;	// only last - no chain

+	Bytes *cert;	// server certificate; only last - no chain

-	Lock statelk;

-	int state;		// must be set using setstate

+	int cipher;

+	int nsecret;	// amount of secret data to init keys

+	char *digest;	// name of digest algorithm to use

+	char *enc;		// name of encryption algorithm to use

+	// for finished messages

+	HandshakeHash	handhash;

+	Finished	finished;

+

 	// input buffer for handshake messages

 	uchar recvbuf[MaxChunk];

 	uchar *rp, *ep;

@@ -84,18 +99,6 @@

 	// output buffer

 	uchar sendbuf[MaxChunk];

 	uchar *sendp;

-

-	uchar crandom[RandomSize];	// client random

-	uchar srandom[RandomSize];	// server random

-	int clientVersion;	// version in ClientHello

-	int cipher;

-	char *digest;	// name of digest algorithm to use

-	char *enc;		// name of encryption algorithm to use

-	int nsecret;	// amount of secret data to init keys

-

-	// for finished messages

-	HandshakeHash	handhash;

-	Finished	finished;

 } TlsConnection;

 typedef struct Msg{

@@ -149,25 +152,7 @@

 	} u;

 } Msg;

-struct TlsSec{

-	char *server;	// name of remote; nil for server

-	int ok;	// <0 killed; == 0 in progress; >0 reusable

-	RSApub *rsapub;

-	AuthRpc *rpc;	// factotum for rsa private key

-	uchar *psk;	// pre-shared key

-	int psklen;

-	uchar sec[MasterSecretSize];	// master secret

-	uchar crandom[RandomSize];	// client random

-	uchar srandom[RandomSize];	// server random

-	int clientVers;		// version in ClientHello

-	int vers;			// final version

-	// byte generation and handshake checksum

-	void (*prf)(uchar*, int, uchar*, int, char*, uchar*, int, uchar*, int);

-	void (*setFinished)(TlsSec*, HandshakeHash, uchar*, int);

-	int nfin;

-};

-

 enum {

 	SSL3Version	= 0x0300,

 	TLS10Version	= 0x0301,

@@ -269,8 +254,25 @@

 	TLS_RSA_WITH_AES_128_CBC_SHA256		= 0X003C,

 	TLS_RSA_WITH_AES_256_CBC_SHA256		= 0X003D,

 	TLS_DHE_RSA_WITH_AES_128_CBC_SHA256	= 0X0067,

-	TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA	= 0XC013,

-	TLS_ECDHE_RSA_WITH_AES_256_CBC_SHA	= 0XC014,

+

+	TLS_RSA_WITH_AES_128_GCM_SHA256		= 0x009C,

+	TLS_RSA_WITH_AES_256_GCM_SHA384		= 0x009D,

+	TLS_DHE_RSA_WITH_AES_128_GCM_SHA256	= 0x009E,

+	TLS_DHE_RSA_WITH_AES_256_GCM_SHA384	= 0x009F,

+	TLS_DH_RSA_WITH_AES_128_GCM_SHA256	= 0x00A0,

+	TLS_DH_RSA_WITH_AES_256_GCM_SHA384	= 0x00A1,

+	TLS_DHE_DSS_WITH_AES_128_GCM_SHA256	= 0x00A2,

+	TLS_DHE_DSS_WITH_AES_256_GCM_SHA384	= 0x00A3,

+	TLS_DH_DSS_WITH_AES_128_GCM_SHA256	= 0x00A4,

+	TLS_DH_DSS_WITH_AES_256_GCM_SHA384	= 0x00A5,

+	TLS_DH_anon_WITH_AES_128_GCM_SHA256	= 0x00A6,

+	TLS_DH_anon_WITH_AES_256_GCM_SHA384	= 0x00A7,

+

+	TLS_ECDHE_ECDSA_WITH_AES_128_GCM_SHA256 = 0xC02B,

+	TLS_ECDHE_RSA_WITH_AES_128_GCM_SHA256	= 0xC02F,

+

+	TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA	= 0xC013,

+	TLS_ECDHE_RSA_WITH_AES_256_CBC_SHA	= 0xC014,

 	TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA256	= 0xC027,

 	TLS_ECDHE_ECDSA_WITH_AES_128_CBC_SHA256	= 0xC023,

@@ -302,6 +304,11 @@

 	{"ccpoly64_aead", "clear", 2*32, GOOGLE_ECDHE_ECDSA_WITH_CHACHA20_POLY1305},

 	{"ccpoly64_aead", "clear", 2*32, GOOGLE_DHE_RSA_WITH_CHACHA20_POLY1305},

+	{"aes_128_gcm_aead", "clear", 2*(16+4), TLS_ECDHE_RSA_WITH_AES_128_GCM_SHA256},

+	{"aes_128_gcm_aead", "clear", 2*(16+4), TLS_ECDHE_ECDSA_WITH_AES_128_GCM_SHA256},

+	{"aes_128_gcm_aead", "clear", 2*(16+4), TLS_DHE_RSA_WITH_AES_128_GCM_SHA256},

+	{"aes_128_gcm_aead", "clear", 2*(16+4), TLS_RSA_WITH_AES_128_GCM_SHA256},

+

 	{"aes_128_cbc", "sha256", 2*(16+16+SHA2_256dlen), TLS_ECDHE_ECDSA_WITH_AES_128_CBC_SHA256},

 	{"aes_128_cbc", "sha256", 2*(16+16+SHA2_256dlen), TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA256},

 	{"aes_128_cbc", "sha1", 2*(16+16+SHA1dlen), TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA},

@@ -364,7 +371,6 @@

 	char *pskid, uchar *psk, int psklen,

 	int (*trace)(char*fmt, ...), PEMChain *chain);

 static TlsConnection *tlsClient2(int ctl, int hand,

-	uchar *csid, int ncsid,

 	uchar *cert, int certlen,

 	char *pskid, uchar *psk, int psklen,

 	uchar *ext, int extlen, int (*trace)(char*fmt, ...));

@@ -374,6 +380,7 @@

 static int	msgSend(TlsConnection *c, Msg *m, int act);

 static void	tlsError(TlsConnection *c, int err, char *msg, ...);

 static int setVersion(TlsConnection *c, int version);

+static int setSecrets(TlsConnection *c, int isclient);

 static int finishedMatch(TlsConnection *c, Finished *f);

 static void tlsConnectionFree(TlsConnection *c);

@@ -383,31 +390,23 @@

 static int initCiphers(void);

 static Ints* makeciphers(int ispsk);

-static TlsSec*	tlsSecInits(int cvers, uchar *csid, int ncsid, uchar *crandom, uchar *ssid, int *nssid, uchar *srandom);

-static int	tlsSecRSAs(TlsSec *sec, int vers, Bytes *epm);

-static int	tlsSecPSKs(TlsSec *sec, int vers);

-static TlsSec*	tlsSecInitc(int cvers, uchar *crandom);

-static Bytes*	tlsSecRSAc(TlsSec *sec, uchar *sid, int nsid, uchar *srandom, uchar *cert, int ncert, int vers);

-static int	tlsSecPSKc(TlsSec *sec, uchar *srandom, int vers);

-static Bytes*	tlsSecDHEc(TlsSec *sec, uchar *srandom, int vers, Bytes *p, Bytes *g, Bytes *Ys);

-static Bytes*	tlsSecECDHEc(TlsSec *sec, uchar *srandom, int vers, int curve, Bytes *Ys);

+static void	tlsSecInits(TlsSec *sec, int cvers, uchar *crandom);

+static int	tlsSecRSAs(TlsSec *sec, Bytes *epm);

+static void	tlsSecPSKs(TlsSec *sec);

+static void	tlsSecInitc(TlsSec *sec, int cvers);

+static Bytes*	tlsSecRSAc(TlsSec *sec, uchar *cert, int ncert);

+static void	tlsSecPSKc(TlsSec *sec);

+static Bytes*	tlsSecDHEc(TlsSec *sec, Bytes *p, Bytes *g, Bytes *Ys);

+static Bytes*	tlsSecECDHEc(TlsSec *sec, int curve, Bytes *Ys);

+static void	tlsSecVers(TlsSec *sec, int v);

 static int	tlsSecFinished(TlsSec *sec, HandshakeHash hsh, uchar *fin, int nfin, int isclient);

-static void	tlsSecOk(TlsSec *sec);

-static void	tlsSecClose(TlsSec *sec);

 static void	setMasterSecret(TlsSec *sec, Bytes *pm);

-static void	setSecrets(TlsSec *sec, uchar *kd, int nkd);

 static Bytes*	pkcs1_encrypt(Bytes* data, RSApub* key, int blocktype);

 static Bytes*	pkcs1_decrypt(TlsSec *sec, Bytes *cipher);

-static void	tls10SetFinished(TlsSec *sec, HandshakeHash hsh, uchar *finished, int isClient);

-static void	tls12SetFinished(TlsSec *sec, HandshakeHash hsh, uchar *finished, int isClient);

-static void	sslSetFinished(TlsSec *sec, HandshakeHash hsh, uchar *finished, int isClient);

-static void	sslPRF(uchar *buf, int nbuf, uchar *key, int nkey, char *label,

-			uchar *seed0, int nseed0, uchar *seed1, int nseed1);

-static int setVers(TlsSec *sec, int version);

-static AuthRpc* factotum_rsa_open(uchar *cert, int certlen);

+static AuthRpc* factotum_rsa_open(RSApub *rsapub);

 static mpint* factotum_rsa_decrypt(AuthRpc *rpc, mpint *cipher);

-static void factotum_rsa_close(AuthRpc*rpc);

+static void factotum_rsa_close(AuthRpc *rpc);

 static void* emalloc(int);

 static void* erealloc(void*, int);

@@ -459,26 +458,27 @@

 		close(ctl);

 		return -1;

 	}

+	data = -1;

 	fprint(ctl, "fd %d 0x%x", fd, ProtocolVersion);

 	tls = tlsServer2(ctl, hand,

 		conn->cert, conn->certlen,

 		conn->pskID, conn->psk, conn->psklen,

 		conn->trace, conn->chain);

-	snprint(dname, sizeof(dname), "#a/tls/%s/data", buf);

-	data = open(dname, ORDWR);

+	if(tls != nil){

+		snprint(dname, sizeof(dname), "#a/tls/%s/data", buf);

+		data = open(dname, ORDWR);

+	}

 	close(hand);

 	close(ctl);

-	if(data < 0 || tls == nil){

-		if(tls != nil)

-			tlsConnectionFree(tls);

+	if(data < 0){

+		tlsConnectionFree(tls);

 		return -1;

 	}

 	free(conn->cert);

 	conn->cert = nil;  // client certificates are not yet implemented

 	conn->certlen = 0;

-	conn->sessionIDlen = tls->sid->len;

-	conn->sessionID = emalloc(conn->sessionIDlen);

-	memcpy(conn->sessionID, tls->sid->data, conn->sessionIDlen);

+	conn->sessionIDlen = 0;

+	conn->sessionID = nil;

 	if(conn->sessionKey != nil

 	&& conn->sessionType != nil

 	&& strcmp(conn->sessionType, "ttls") == 0)

@@ -601,7 +601,6 @@

 	fprint(ctl, "fd %d 0x%x", fd, ProtocolVersion);

 	ext = tlsClientExtensions(conn, &n);

 	tls = tlsClient2(ctl, hand,

-		conn->sessionID, conn->sessionIDlen,

 		conn->cert, conn->certlen, 

 		conn->pskID, conn->psk, conn->psklen,

 		ext, n, conn->trace);

@@ -612,6 +611,7 @@

 		close(data);

 		return -1;

 	}

+	free(conn->cert);

 	if(tls->cert != nil){

 		conn->certlen = tls->cert->len;

 		conn->cert = emalloc(conn->certlen);

@@ -620,9 +620,8 @@

 		conn->certlen = 0;

 		conn->cert = nil;

 	}

-	conn->sessionIDlen = tls->sid->len;

-	conn->sessionID = emalloc(conn->sessionIDlen);

-	memcpy(conn->sessionID, tls->sid->data, conn->sessionIDlen);

+	conn->sessionIDlen = 0;

+	conn->sessionID = nil;

 	if(conn->sessionKey != nil

 	&& conn->sessionType != nil

 	&& strcmp(conn->sessionType, "ttls") == 0)

@@ -657,15 +656,13 @@

 {

 	TlsConnection *c;

 	Msg m;

-	Bytes *csid;

-	uchar sid[SidSize], kd[MaxKeyData];

-	char *secrets;

-	int cipher, compressor, nsid, rv, numcerts, i;

+	int cipher, compressor, numcerts, i;

 	if(trace)

 		trace("tlsServer2\n");

 	if(!initCiphers())

 		return nil;

+

 	c = emalloc(sizeof(TlsConnection));

 	c->ctl = ctl;

 	c->hand = hand;

@@ -682,66 +679,55 @@

 		tlsError(c, EUnexpectedMessage, "expected a client hello");

 		goto Err;

 	}

-	c->clientVersion = m.u.clientHello.version;

 	if(trace)

-		trace("ClientHello version %x\n", c->clientVersion);

-	if(setVersion(c, c->clientVersion) < 0) {

+		trace("ClientHello version %x\n", m.u.clientHello.version);

+	if(setVersion(c, m.u.clientHello.version) < 0) {

 		tlsError(c, EIllegalParameter, "incompatible version");

 		goto Err;

 	}

-	memmove(c->crandom, m.u.clientHello.random, RandomSize);

 	cipher = okCipher(m.u.clientHello.ciphers, psklen > 0);

-	if(cipher < 0) {

+	if(cipher < 0 || !setAlgs(c, cipher)) {

 		tlsError(c, EHandshakeFailure, "no matching cipher suite");

 		goto Err;

 	}

-	if(!setAlgs(c, cipher)){

-		tlsError(c, EHandshakeFailure, "no matching cipher suite");

-		goto Err;

-	}

 	compressor = okCompression(m.u.clientHello.compressors);

 	if(compressor < 0) {

 		tlsError(c, EHandshakeFailure, "no matching compressor");

 		goto Err;

 	}

-

-	csid = m.u.clientHello.sid;

 	if(trace)

-		trace("  cipher %x, compressor %x, csidlen %d\n", cipher, compressor, csid->len);

-	c->sec = tlsSecInits(c->clientVersion, csid->data, csid->len, c->crandom, sid, &nsid, c->srandom);

-	if(c->sec == nil){

-		tlsError(c, EHandshakeFailure, "can't initialize security: %r");

-		goto Err;

-	}

+		trace("  cipher %x, compressor %x\n", cipher, compressor);

+

+	tlsSecInits(c->sec, m.u.clientHello.version, m.u.clientHello.random);

+	tlsSecVers(c->sec, c->version);

 	if(psklen > 0){

 		c->sec->psk = psk;

 		c->sec->psklen = psklen;

 	}

 	if(certlen > 0){

-		c->sec->rpc = factotum_rsa_open(cert, certlen);

-		if(c->sec->rpc == nil){

-			tlsError(c, EHandshakeFailure, "factotum_rsa_open: %r");

-			goto Err;

-		}

+		/* server certificate */

 		c->sec->rsapub = X509toRSApub(cert, certlen, nil, 0);

 		if(c->sec->rsapub == nil){

 			tlsError(c, EHandshakeFailure, "invalid X509/rsa certificate");

 			goto Err;

 		}

+		c->sec->rpc = factotum_rsa_open(c->sec->rsapub);

+		if(c->sec->rpc == nil){

+			tlsError(c, EHandshakeFailure, "factotum_rsa_open: %r");

+			goto Err;

+		}

 	}

 	msgClear(&m);

 	m.tag = HServerHello;

 	m.u.serverHello.version = c->version;

-	memmove(m.u.serverHello.random, c->srandom, RandomSize);

+	memmove(m.u.serverHello.random, c->sec->srandom, RandomSize);

 	m.u.serverHello.cipher = cipher;

 	m.u.serverHello.compressor = compressor;

-	c->sid = makebytes(sid, nsid);

-	m.u.serverHello.sid = makebytes(c->sid->data, c->sid->len);

+	m.u.serverHello.sid = makebytes(nil, 0);

 	if(!msgSend(c, &m, AQueue))

 		goto Err;

-	msgClear(&m);

 	if(certlen > 0){

 		m.tag = HCertificate;

@@ -753,13 +739,11 @@

 			m.u.certificate.certs[i+1] = makebytes(chp->pem, chp->pemlen);

 		if(!msgSend(c, &m, AQueue))

 			goto Err;

-		msgClear(&m);

 	}

 	m.tag = HServerHelloDone;

 	if(!msgSend(c, &m, AFlush))

 		goto Err;

-	msgClear(&m);

 	if(!msgRecv(c, &m))

 		goto Err;

@@ -776,34 +760,23 @@

 		}

 	}

 	if(certlen > 0){

-		if(tlsSecRSAs(c->sec, c->version, m.u.clientKeyExchange.key) < 0){

-			tlsError(c, EHandshakeFailure, "couldn't set secrets: %r");

+		if(tlsSecRSAs(c->sec, m.u.clientKeyExchange.key) < 0){

+			tlsError(c, EHandshakeFailure, "couldn't set keys: %r");

 			goto Err;

 		}

 	} else if(psklen > 0){

-		if(tlsSecPSKs(c->sec, c->version) < 0){

-			tlsError(c, EHandshakeFailure, "couldn't set secrets: %r");

-			goto Err;

-		}

+		tlsSecPSKs(c->sec);

 	} else {

 		tlsError(c, EInternalError, "no psk or certificate");

 		goto Err;

 	}

-	setSecrets(c->sec, kd, c->nsecret);

 	if(trace)

 		trace("tls secrets\n");

-	secrets = (char*)emalloc(2*c->nsecret);

-	enc64(secrets, 2*c->nsecret, kd, c->nsecret);

-	rv = fprint(c->ctl, "secret %s %s 0 %s", c->digest, c->enc, secrets);

-	memset(secrets, 0, 2*c->nsecret);

-	free(secrets);

-	memset(kd, 0, c->nsecret);

-	if(rv < 0){

-		tlsError(c, EHandshakeFailure, "can't set keys: %r");

+	if(setSecrets(c, 0) < 0){

+		tlsError(c, EHandshakeFailure, "can't set secrets: %r");

 		goto Err;

 	}

-	msgClear(&m);

 	/* no CertificateVerify; skip to Finished */

 	if(tlsSecFinished(c->sec, c->handhash, c->finished.verify, c->finished.n, 1) < 0){

@@ -836,19 +809,17 @@

 	m.u.finished = c->finished;

 	if(!msgSend(c, &m, AFlush))

 		goto Err;

-	msgClear(&m);

 	if(trace)

 		trace("tls finished\n");

 	if(fprint(c->ctl, "opened") < 0)

 		goto Err;

-	tlsSecOk(c->sec);

 	return c;

 Err:

 	msgClear(&m);

 	tlsConnectionFree(c);

-	return 0;

+	return nil;

 }

 static int

@@ -855,6 +826,7 @@

 isDHE(int tlsid)

 {

 	switch(tlsid){

+	case TLS_DHE_RSA_WITH_AES_128_GCM_SHA256:

 	case TLS_DHE_RSA_WITH_AES_128_CBC_SHA256:

  	case TLS_DHE_RSA_WITH_AES_128_CBC_SHA:

  	case TLS_DHE_RSA_WITH_AES_256_CBC_SHA:

@@ -876,6 +848,9 @@

 	case GOOGLE_ECDHE_ECDSA_WITH_CHACHA20_POLY1305:

 	case GOOGLE_ECDHE_RSA_WITH_CHACHA20_POLY1305:

+	case TLS_ECDHE_ECDSA_WITH_AES_128_GCM_SHA256:

+	case TLS_ECDHE_RSA_WITH_AES_128_GCM_SHA256:

+

 	case TLS_ECDHE_ECDSA_WITH_AES_128_CBC_SHA256:

 	case TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA256:

 	case TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA:

@@ -898,8 +873,7 @@

 }

 static Bytes*

-tlsSecDHEc(TlsSec *sec, uchar *srandom, int vers, 

-	Bytes *p, Bytes *g, Bytes *Ys)

+tlsSecDHEc(TlsSec *sec, Bytes *p, Bytes *g, Bytes *Ys)

 {

 	mpint *G, *P, *Y, *K;

 	Bytes *epm;

@@ -908,10 +882,6 @@

 	if(p == nil || g == nil || Ys == nil)

 		return nil;

-	memmove(sec->srandom, srandom, RandomSize);

-	if(setVers(sec, vers) < 0)

-		return nil;

-

 	epm = nil;

 	P = bytestomp(p);

 	G = bytestomp(g);

@@ -939,7 +909,7 @@

 }

 static Bytes*

-tlsSecECDHEc(TlsSec *sec, uchar *srandom, int vers, int curve, Bytes *Ys)

+tlsSecECDHEc(TlsSec *sec, int curve, Bytes *Ys)

 {

 	Namedcurve *nc, *enc;

 	Bytes *epm;

@@ -958,10 +928,6 @@

 	if(nc == enc)

 		return nil;

-		

-	memmove(sec->srandom, srandom, RandomSize);

-	if(setVers(sec, vers) < 0)

-		return nil;

 	ecdominit(&dom, nc->init);

 	pub = ecdecodepub(&dom, Ys->data, Ys->len);

@@ -1011,7 +977,7 @@

 	char *err;

 	if(par == nil || par->len <= 0)

-		return "no dh parameters";

+		return "no DH parameters";

 	if(sig == nil || sig->len <= 0){

 		if(c->sec->psklen > 0)

@@ -1023,8 +989,8 @@

 		return "no certificate";

 	blob = newbytes(2*RandomSize + par->len);

-	memmove(blob->data+0*RandomSize, c->crandom, RandomSize);

-	memmove(blob->data+1*RandomSize, c->srandom, RandomSize);

+	memmove(blob->data+0*RandomSize, c->sec->crandom, RandomSize);

+	memmove(blob->data+1*RandomSize, c->sec->srandom, RandomSize);

 	memmove(blob->data+2*RandomSize, par->data, par->len);

 	if(c->version < TLS12Version){

 		digestlen = MD5dlen + SHA1dlen;

@@ -1069,7 +1035,6 @@

 static TlsConnection *

 tlsClient2(int ctl, int hand,

-	uchar *csid, int ncsid, 

 	uchar *cert, int certlen,

 	char *pskid, uchar *psk, int psklen,

 	uchar *ext, int extlen,

@@ -1077,45 +1042,51 @@

 {

 	TlsConnection *c;

 	Msg m;

-	uchar kd[MaxKeyData];

-	char *secrets;

-	int creq, dhx, rv, cipher;

+	int creq, dhx, cipher;

 	Bytes *epm;

 	if(!initCiphers())

 		return nil;

+

 	epm = nil;

+	memset(&m, 0, sizeof(m));

 	c = emalloc(sizeof(TlsConnection));

-	c->version = ProtocolVersion;

 	c->ctl = ctl;

 	c->hand = hand;

 	c->trace = trace;

-	c->isClient = 1;

-	c->clientVersion = c->version;

 	c->cert = nil;

-	c->sec = tlsSecInitc(c->clientVersion, c->crandom);

-	if(c->sec == nil)

-		goto Err;

-

+	c->version = ProtocolVersion;

+	tlsSecInitc(c->sec, c->version);

 	if(psklen > 0){

 		c->sec->psk = psk;

 		c->sec->psklen = psklen;

 	}

+	if(certlen > 0){

+		/* client certificate */

+		c->sec->rsapub = X509toRSApub(cert, certlen, nil, 0);

+		if(c->sec->rsapub == nil){

+			tlsError(c, EInternalError, "invalid X509/rsa certificate");

+			goto Err;

+		}

+		c->sec->rpc = factotum_rsa_open(c->sec->rsapub);

+		if(c->sec->rpc == nil){

+			tlsError(c, EInternalError, "factotum_rsa_open: %r");

+			goto Err;

+		}

+	}

 	/* client hello */

-	memset(&m, 0, sizeof(m));

 	m.tag = HClientHello;

-	m.u.clientHello.version = c->clientVersion;

-	memmove(m.u.clientHello.random, c->crandom, RandomSize);

-	m.u.clientHello.sid = makebytes(csid, ncsid);

+	m.u.clientHello.version = c->version;

+	memmove(m.u.clientHello.random, c->sec->crandom, RandomSize);

+	m.u.clientHello.sid = makebytes(nil, 0);

 	m.u.clientHello.ciphers = makeciphers(psklen > 0);

 	m.u.clientHello.compressors = makebytes(compressors,sizeof(compressors));

 	m.u.clientHello.extensions = makebytes(ext, extlen);

 	if(!msgSend(c, &m, AFlush))

 		goto Err;

-	msgClear(&m);

 	/* server hello */

 	if(!msgRecv(c, &m))

@@ -1128,12 +1099,9 @@

 		tlsError(c, EIllegalParameter, "incompatible version: %r");

 		goto Err;

 	}

-	memmove(c->srandom, m.u.serverHello.random, RandomSize);

-	c->sid = makebytes(m.u.serverHello.sid->data, m.u.serverHello.sid->len);

-	if(c->sid->len != 0 && c->sid->len != SidSize) {

-		tlsError(c, EIllegalParameter, "invalid server session identifier");

-		goto Err;

-	}

+	tlsSecVers(c->sec, c->version);

+	memmove(c->sec->srandom, m.u.serverHello.random, RandomSize);

+

 	cipher = m.u.serverHello.cipher;

 	if((psklen > 0) != isPSK(cipher) || !setAlgs(c, cipher)) {

 		tlsError(c, EIllegalParameter, "invalid cipher suite");

@@ -1143,7 +1111,6 @@

 		tlsError(c, EIllegalParameter, "invalid compression");

 		goto Err;

 	}

-	msgClear(&m);

 	dhx = isDHE(cipher) || isECDHE(cipher);

 	if(!msgRecv(c, &m))

@@ -1154,7 +1121,6 @@

 			goto Err;

 		}

 		c->cert = makebytes(m.u.certificate.certs[0]->data, m.u.certificate.certs[0]->len);

-		msgClear(&m);

 		if(!msgRecv(c, &m))

 			goto Err;

 	} else if(psklen == 0) {

@@ -1168,25 +1134,26 @@

 				m.u.serverKeyExchange.dh_signature,

 				m.u.serverKeyExchange.sigalg);

 			if(err != nil){

-				tlsError(c, EBadCertificate, "can't verify dh parameters: %s", err);

+				tlsError(c, EBadCertificate, "can't verify DH parameters: %s", err);

 				goto Err;

 			}

 			if(isECDHE(cipher))

-				epm = tlsSecECDHEc(c->sec, c->srandom, c->version,

+				epm = tlsSecECDHEc(c->sec,

 					m.u.serverKeyExchange.curve,

 					m.u.serverKeyExchange.dh_Ys);

 			else

-				epm = tlsSecDHEc(c->sec, c->srandom, c->version,

+				epm = tlsSecDHEc(c->sec,

 					m.u.serverKeyExchange.dh_p, 

 					m.u.serverKeyExchange.dh_g,

 					m.u.serverKeyExchange.dh_Ys);

-			if(epm == nil)

-				goto Badcert;

+			if(epm == nil){

+				tlsError(c, EHandshakeFailure, "bad DH parameters");

+				goto Err;

+			}

 		} else if(psklen == 0){

 			tlsError(c, EUnexpectedMessage, "got an server key exchange");

 			goto Err;

 		}

-		msgClear(&m);

 		if(!msgRecv(c, &m))

 			goto Err;

 	} else if(dhx){

@@ -1198,7 +1165,6 @@

 	creq = 0;

 	if(m.tag == HCertificateRequest) {

 		creq = 1;

-		msgClear(&m);

 		if(!msgRecv(c, &m))

 			goto Err;

 	}

@@ -1211,16 +1177,13 @@

 	if(!dhx){

 		if(c->cert != nil){

-			epm = tlsSecRSAc(c->sec, c->sid->data, c->sid->len, c->srandom,

-				c->cert->data, c->cert->len, c->version);

+			epm = tlsSecRSAc(c->sec, c->cert->data, c->cert->len);

 			if(epm == nil){

-			Badcert:

 				tlsError(c, EBadCertificate, "bad certificate: %r");

 				goto Err;

 			}

-		} else if(psklen > 0) {

-			if(tlsSecPSKc(c->sec, c->srandom, c->version) < 0)

-				goto Badcert;

+		} else if(psklen > 0){

+			tlsSecPSKc(c->sec);

 		} else {

 			tlsError(c, EInternalError, "no psk or certificate");

 			goto Err;

@@ -1227,28 +1190,22 @@

 		}

 	}

-	setSecrets(c->sec, kd, c->nsecret);

-	secrets = (char*)emalloc(2*c->nsecret);

-	enc64(secrets, 2*c->nsecret, kd, c->nsecret);

-	rv = fprint(c->ctl, "secret %s %s 1 %s", c->digest, c->enc, secrets);

-	memset(secrets, 0, 2*c->nsecret);

-	free(secrets);

-	memset(kd, 0, c->nsecret);

-	if(rv < 0){

-		tlsError(c, EHandshakeFailure, "can't set keys: %r");

+	if(trace)

+		trace("tls secrets\n");

+	if(setSecrets(c, 1) < 0){

+		tlsError(c, EHandshakeFailure, "can't set secrets: %r");

 		goto Err;

 	}

 	if(creq) {

-		if(cert != nil && certlen > 0){

+		m.tag = HCertificate;

+		if(certlen > 0){

 			m.u.certificate.ncert = 1;

 			m.u.certificate.certs = emalloc(m.u.certificate.ncert * sizeof(Bytes*));

 			m.u.certificate.certs[0] = makebytes(cert, certlen);

 		}		

-		m.tag = HCertificate;

 		if(!msgSend(c, &m, AFlush))

 			goto Err;

-		msgClear(&m);

 	}

 	/* client key exchange */

@@ -1263,26 +1220,14 @@

 	if(!msgSend(c, &m, AFlush))

 		goto Err;

-	msgClear(&m);

 	/* certificate verify */

-	if(creq && cert != nil && certlen > 0) {

+	if(creq && certlen > 0) {

 		mpint *signedMP, *paddedHashes;

 		HandshakeHash hsave;

 		uchar buf[512];

 		int buflen;

-		c->sec->rpc = factotum_rsa_open(cert, certlen);

-		if(c->sec->rpc == nil){

-			tlsError(c, EHandshakeFailure, "factotum_rsa_open: %r");

-			goto Err;

-		}

-		c->sec->rsapub = X509toRSApub(cert, certlen, nil, 0);

-		if(c->sec->rsapub == nil){

-			tlsError(c, EHandshakeFailure, "invalid X509/rsa certificate");

-			goto Err;

-		}

-

 		/* save the state for the Finish message */

 		hsave = c->handhash;

 		if(c->version >= TLS12Version){

@@ -1315,7 +1260,6 @@

 		m.tag = HCertificateVerify;

 		if(!msgSend(c, &m, AFlush))

 			goto Err;

-		msgClear(&m);

 	} 

 	/* change cipher spec */

@@ -1336,7 +1280,6 @@

 		tlsError(c, EInternalError, "can't flush after client Finished: %r");

 		goto Err;

 	}

-	msgClear(&m);

 	if(tlsSecFinished(c->sec, c->handhash, c->finished.verify, c->finished.n, 0) < 0){

 		tlsError(c, EInternalError, "can't set finished 0: %r");

@@ -1362,7 +1305,6 @@

 			trace("unable to do final open: %r\n");

 		goto Err;

 	}

-	tlsSecOk(c->sec);

 	return c;

 Err:

@@ -1369,7 +1311,7 @@

 	free(epm);

 	msgClear(&m);

 	tlsConnectionFree(c);

-	return 0;

+	return nil;

 }

@@ -1414,13 +1356,11 @@

 		// sid

 		n = m->u.clientHello.sid->len;

-		assert(n < 256);

 		p[0] = n;

 		memmove(p+1, m->u.clientHello.sid->data, n);

 		p += n+1;

 		n = m->u.clientHello.ciphers->len;

-		assert(n > 0 && n < 200);

 		put16(p, n*2);

 		p += 2;

 		for(i=0; i<n; i++) {

@@ -1429,7 +1369,6 @@

 		}

 		n = m->u.clientHello.compressors->len;

-		assert(n > 0);

 		p[0] = n;

 		memmove(p+1, m->u.clientHello.compressors->data, n);

 		p += n+1;

@@ -1453,7 +1392,6 @@

 		// sid

 		n = m->u.serverHello.sid->len;

-		assert(n < 256);

 		p[0] = n;

 		memmove(p+1, m->u.serverHello.sid->data, n);

 		p += n+1;

@@ -1529,7 +1467,7 @@

 	// go back and fill in size

 	n = p - c->sendp;

-	assert(p <= c->sendbuf + sizeof(c->sendbuf));

+	assert(n <= sizeof(c->sendbuf));

 	put24(c->sendp+1, n-4);

 	// remember hash of Handshake messages

@@ -1580,8 +1518,9 @@

 msgRecv(TlsConnection *c, Msg *m)

 {

 	uchar *p, *s;

-	int type, n, nn, i, nsid, nrandom, nciph;

+	int type, n, nn, i;

+	msgClear(m);

 	for(;;) {

 		p = tlsReadN(c, 4);

 		if(p == nil)

@@ -1606,6 +1545,8 @@

 		/* Cope with an SSL3 ClientHello expressed in SSL2 record format.

 			This is sent by some clients that we must interoperate

 			with, such as Java's JSSE and Microsoft's Internet Explorer. */

+		int nsid, nrandom, nciph;

+

 		p = tlsReadN(c, n);

 		if(p == nil)

 			return 0;

@@ -1664,14 +1605,12 @@

 		if(n < 2)

 			goto Short;

 		m->u.clientHello.version = get16(p);

-		p += 2;

-		n -= 2;

+		p += 2, n -= 2;

 		if(n < RandomSize)

 			goto Short;

 		memmove(m->u.clientHello.random, p, RandomSize);

-		p += RandomSize;

-		n -= RandomSize;

+		p += RandomSize, n -= RandomSize;

 		if(n < 1 || n < p[0]+1)

 			goto Short;

 		m->u.clientHello.sid = makebytes(p+1, p[0]);

@@ -1681,8 +1620,7 @@

 		if(n < 2)

 			goto Short;

 		nn = get16(p);

-		p += 2;

-		n -= 2;

+		p += 2, n -= 2;

 		if((nn & 1) || n < nn || nn < 2)

 			goto Short;

@@ -1689,15 +1627,13 @@

 		m->u.clientHello.ciphers = newints(nn >> 1);

 		for(i = 0; i < nn; i += 2)

 			m->u.clientHello.ciphers->data[i >> 1] = get16(&p[i]);

-		p += nn;

-		n -= nn;

+		p += nn, n -= nn;

 		if(n < 1 || n < p[0]+1 || p[0] == 0)

 			goto Short;

 		nn = p[0];

 		m->u.clientHello.compressors = makebytes(p+1, nn);

-		p += nn + 1;

-		n -= nn + 1;

+		p += nn + 1, n -= nn + 1;

 		if(n < 2)

 			break;

@@ -1711,14 +1647,12 @@

 		if(n < 2)

 			goto Short;

 		m->u.serverHello.version = get16(p);

-		p += 2;

-		n -= 2;

+		p += 2, n -= 2;

 		if(n < RandomSize)

 			goto Short;

 		memmove(m->u.serverHello.random, p, RandomSize);

-		p += RandomSize;

-		n -= RandomSize;

+		p += RandomSize, n -= RandomSize;

 		if(n < 1 || n < p[0]+1)

 			goto Short;

@@ -1730,8 +1664,7 @@

 			goto Short;

 		m->u.serverHello.cipher = get16(p);

 		m->u.serverHello.compressor = p[2];

-		p += 3;

-		n -= 3;

+		p += 3, n -= 3;

 		if(n < 2)

 			break;

@@ -1745,8 +1678,7 @@

 		if(n < 3)

 			goto Short;

 		nn = get24(p);

-		p += 3;

-		n -= 3;

+		p += 3, n -= 3;

 		if(nn == 0 && n > 0)

 			goto Short;

 		/* certs */

@@ -1755,15 +1687,13 @@

 			if(n < 3)

 				goto Short;

 			nn = get24(p);

-			p += 3;

-			n -= 3;

+			p += 3, n -= 3;

 			if(nn > n)

 				goto Short;

 			m->u.certificate.ncert = i+1;

 			m->u.certificate.certs = erealloc(m->u.certificate.certs, (i+1)*sizeof(Bytes*));

 			m->u.certificate.certs[i] = makebytes(p, nn);

-			p += nn;

-			n -= nn;

+			p += nn, n -= nn;

 			i++;

 		}

 		break;

@@ -1771,33 +1701,28 @@

 		if(n < 1)

 			goto Short;

 		nn = p[0];

-		p += 1;

-		n -= 1;

+		p++, n--;

 		if(nn > n)

 			goto Short;

 		m->u.certificateRequest.types = makebytes(p, nn);

-		p += nn;

-		n -= nn;

+		p += nn, n -= nn;

 		if(c->version >= TLS12Version){

 			if(n < 2)

 				goto Short;

 			nn = get16(p);

-			p += 2;

-			n -= 2;

+			p += 2, n -= 2;

 			if(nn & 1)

 				goto Short;

 			m->u.certificateRequest.sigalgs = newints(nn>>1);

 			for(i = 0; i < nn; i += 2)

 				m->u.certificateRequest.sigalgs->data[i >> 1] = get16(&p[i]);

-			p += nn;

-			n -= nn;

+			p += nn, n -= nn;

 		}

 		if(n < 2)

 			goto Short;

 		nn = get16(p);

-		p += 2;

-		n -= 2;

+		p += 2, n -= 2;

 		/* nn == 0 can happen; yahoo's servers do it */

 		if(nn != n)

 			goto Short;

@@ -1807,8 +1732,7 @@

 			if(n < 2)

 				goto Short;

 			nn = get16(p);

-			p += 2;

-			n -= 2;

+			p += 2, n -= 2;

 			if(nn < 1 || nn > n)

 				goto Short;

 			m->u.certificateRequest.nca = i+1;

@@ -1815,8 +1739,7 @@

 			m->u.certificateRequest.cas = erealloc(

 				m->u.certificateRequest.cas, (i+1)*sizeof(Bytes*));

 			m->u.certificateRequest.cas[i] = makebytes(p, nn);

-			p += nn;

-			n -= nn;

+			p += nn, n -= nn;

 			i++;

 		}

 		break;

@@ -1921,8 +1844,7 @@

 			if(n < 2)

 				goto Short;

 			nn = get16(p);

-			p += 2;

-			n -= 2;

+			p += 2, n -= 2;

 		}

 		if(n < nn)

 			goto Short;

@@ -1961,8 +1883,6 @@

 	int i;

 	switch(m->tag) {

-	default:

-		sysfatal("msgClear: unknown message type: %d", m->tag);

 	case HHelloRequest:

 		break;

 	case HClientHello:

@@ -2167,7 +2087,7 @@

 static int

 setVersion(TlsConnection *c, int version)

 {

-	if(c->verset || version > MaxProtoVersion || version < MinProtoVersion)

+	if(version > MaxProtoVersion || version < MinProtoVersion)

 		return -1;

 	if(version > c->version)

 		version = c->version;

@@ -2178,7 +2098,6 @@

 		c->version = version;

 		c->finished.n = TLSFinishedLen;

 	}

-	c->verset = 1;

 	return fprint(c->ctl, "version 0x%x", version);

 }

@@ -2194,8 +2113,10 @@

 static void

 tlsConnectionFree(TlsConnection *c)

 {

-	tlsSecClose(c->sec);

-	freebytes(c->sid);

+	if(c == nil)

+		return;

+	factotum_rsa_close(c->sec->rpc);

+	rsapubfree(c->sec->rsapub);

 	freebytes(c->cert);

 	memset(c, 0, sizeof(*c));

 	free(c);

@@ -2229,6 +2150,7 @@

 	int i, j, c;

 	for(i = 0; i < cv->len; i++) {

+		c = cv->data[i];

 		if(isDHE(c) || isECDHE(c) || isPSK(c) != ispsk)

 			continue;	/* TODO: not implemented for server */

 		for(j = 0; j < nelem(cipherAlgs); j++)

@@ -2341,15 +2263,14 @@

 //================= security functions ========================

-// given X.509 certificate, set up connection to factotum

-//	for using corresponding private key

+// given a public key, set up connection to factotum

+// for using corresponding private key

 static AuthRpc*

-factotum_rsa_open(uchar *cert, int certlen)

+factotum_rsa_open(RSApub *rsapub)

 {

 	int afd;

 	char *s;

-	mpint *pub = nil;

-	RSApub *rsapub;

+	mpint *n;

 	AuthRpc *rpc;

 	// start talking to factotum

@@ -2360,28 +2281,20 @@

 		return nil;

 	}

 	s = "proto=rsa service=tls role=client";

-	if(auth_rpc(rpc, "start", s, strlen(s)) != ARok){

-		factotum_rsa_close(rpc);

-		return nil;

-	}

-

-	// roll factotum keyring around to match certificate

-	rsapub = X509toRSApub(cert, certlen, nil, 0);

-	while(1){

-		if(auth_rpc(rpc, "read", nil, 0) != ARok){

-			factotum_rsa_close(rpc);

-			rpc = nil;

-			goto done;

+	if(auth_rpc(rpc, "start", s, strlen(s)) == ARok){

+		// roll factotum keyring around to match public key

+		n = mpnew(0);

+		while(auth_rpc(rpc, "read", nil, 0) == ARok){

+			if(strtomp(rpc->arg, nil, 16, n) != nil

+			&& mpcmp(n, rsapub->n) == 0){

+				mpfree(n);

+				return rpc;

+			}

 		}

-		pub = strtomp(rpc->arg, nil, 16, nil);

-		assert(pub != nil);

-		if(mpcmp(pub,rsapub->n) == 0)

-			break;

+		mpfree(n);

 	}

-done:

-	mpfree(pub);

-	rsapubfree(rsapub);

-	return rpc;

+	factotum_rsa_close(rpc);

+	return nil;

 }

 static mpint*

@@ -2517,121 +2430,168 @@

 	p_sha256(buf, nbuf, key, nkey, (uchar*)label, strlen(label), seed, nseed0+nseed1);

 }

-/*

- * for setting server session id's

- */

-static Lock	sidLock;

-static long	maxSid = 1;

+static void

+sslPRF(uchar *buf, int nbuf, uchar *key, int nkey, char *label, uchar *seed0, int nseed0, uchar *seed1, int nseed1)

+{

+	uchar sha1dig[SHA1dlen], md5dig[MD5dlen], tmp[26];

+	DigestState *s;

+	int i, n, len;

-/* the keys are verified to have the same public components

- * and to function correctly with pkcs 1 encryption and decryption. */

-static TlsSec*

-tlsSecInits(int cvers, uchar *csid, int ncsid, uchar *crandom, uchar *ssid, int *nssid, uchar *srandom)

+	USED(label);

+	len = 1;

+	while(nbuf > 0){

+		if(len > 26)

+			return;

+		for(i = 0; i < len; i++)

+			tmp[i] = 'A' - 1 + len;

+		s = sha1(tmp, len, nil, nil);

+		s = sha1(key, nkey, nil, s);

+		s = sha1(seed0, nseed0, nil, s);

+		sha1(seed1, nseed1, sha1dig, s);

+		s = md5(key, nkey, nil, nil);

+		md5(sha1dig, SHA1dlen, md5dig, s);

+		n = MD5dlen;

+		if(n > nbuf)

+			n = nbuf;

+		memmove(buf, md5dig, n);

+		buf += n;

+		nbuf -= n;

+		len++;

+	}

+}

+

+static void

+sslSetFinished(TlsSec *sec, HandshakeHash hsh, uchar *finished, int isclient)

 {

-	TlsSec *sec = emalloc(sizeof(*sec));

+	DigestState *s;

+	uchar h0[MD5dlen], h1[SHA1dlen], pad[48];

+	char *label;

-	USED(csid); USED(ncsid);  // ignore csid for now

+	if(isclient)

+		label = "CLNT";

+	else

+		label = "SRVR";

-	memmove(sec->crandom, crandom, RandomSize);

+	md5((uchar*)label, 4, nil, &hsh.md5);

+	md5(sec->sec, MasterSecretSize, nil, &hsh.md5);

+	memset(pad, 0x36, 48);

+	md5(pad, 48, nil, &hsh.md5);

+	md5(nil, 0, h0, &hsh.md5);

+	memset(pad, 0x5C, 48);

+	s = md5(sec->sec, MasterSecretSize, nil, nil);

+	s = md5(pad, 48, nil, s);

+	md5(h0, MD5dlen, finished, s);

+

+	sha1((uchar*)label, 4, nil, &hsh.sha1);

+	sha1(sec->sec, MasterSecretSize, nil, &hsh.sha1);

+	memset(pad, 0x36, 40);

+	sha1(pad, 40, nil, &hsh.sha1);

+	sha1(nil, 0, h1, &hsh.sha1);

+	memset(pad, 0x5C, 40);

+	s = sha1(sec->sec, MasterSecretSize, nil, nil);

+	s = sha1(pad, 40, nil, s);

+	sha1(h1, SHA1dlen, finished + MD5dlen, s);

+}

+

+// fill "finished" arg with md5(args)^sha1(args)

+static void

+tls10SetFinished(TlsSec *sec, HandshakeHash hsh, uchar *finished, int isclient)

+{

+	uchar h0[MD5dlen], h1[SHA1dlen];

+	char *label;

+

+	// get current hash value, but allow further messages to be hashed in

+	md5(nil, 0, h0, &hsh.md5);

+	sha1(nil, 0, h1, &hsh.sha1);

+

+	if(isclient)

+		label = "client finished";

+	else

+		label = "server finished";

+	tls10PRF(finished, TLSFinishedLen, sec->sec, MasterSecretSize, label, h0, MD5dlen, h1, SHA1dlen);

+}

+

+static void

+tls12SetFinished(TlsSec *sec, HandshakeHash hsh, uchar *finished, int isclient)

+{

+	uchar seed[SHA2_256dlen];

+	char *label;

+

+	// get current hash value, but allow further messages to be hashed in

+	sha2_256(nil, 0, seed, &hsh.sha2_256);

+

+	if(isclient)

+		label = "client finished";

+	else

+		label = "server finished";

+	p_sha256(finished, TLSFinishedLen, sec->sec, MasterSecretSize, (uchar*)label, strlen(label), seed, SHA2_256dlen);

+}

+

+/* the keys are verified to have the same public components

+ * and to function correctly with pkcs 1 encryption and decryption. */

+static void

+tlsSecInits(TlsSec *sec, int cvers, uchar *crandom)

+{

+	memset(sec, 0, sizeof(*sec));

 	sec->clientVers = cvers;

+	memmove(sec->crandom, crandom, RandomSize);

-	put32(sec->srandom, time(0));

+	put32(sec->srandom, time(nil));

 	genrandom(sec->srandom+4, RandomSize-4);

-	memmove(srandom, sec->srandom, RandomSize);

-

-	/*

-	 * make up a unique sid: use our pid, and and incrementing id

-	 * can signal no sid by setting nssid to 0.

-	 */

-	memset(ssid, 0, SidSize);

-	put32(ssid, getpid());

-	lock(&sidLock);

-	put32(ssid+4, maxSid++);

-	unlock(&sidLock);

-	*nssid = SidSize;

-	return sec;

 }

 static int

-tlsSecRSAs(TlsSec *sec, int vers, Bytes *epm)

+tlsSecRSAs(TlsSec *sec, Bytes *epm)

 {

 	Bytes *pm;

-	if(setVers(sec, vers) < 0)

-		goto Err;

 	if(epm == nil){

 		werrstr("no encrypted premaster secret");

-		goto Err;

+		return -1;

 	}

 	// if the client messed up, just continue as if everything is ok,

 	// to prevent attacks to check for correctly formatted messages.

-	// Hence the fprint(2,) can't be replaced by tlsError(), which sends an Alert msg to the client.

 	pm = pkcs1_decrypt(sec, epm);

-	if(sec->ok < 0 || pm == nil || pm->len != MasterSecretSize || get16(pm->data) != sec->clientVers){

-		fprint(2, "tlsSecRSAs failed ok=%d pm=%p pmvers=%x cvers=%x nepm=%d\n",

-			sec->ok, pm, pm != nil ? get16(pm->data) : -1, sec->clientVers, epm->len);

-		sec->ok = -1;

+	if(pm == nil || pm->len != MasterSecretSize || get16(pm->data) != sec->clientVers){

 		freebytes(pm);

 		pm = newbytes(MasterSecretSize);

-		genrandom(pm->data, MasterSecretSize);

+		genrandom(pm->data, pm->len);

 	}

 	setMasterSecret(sec, pm);

 	return 0;

-Err:

-	sec->ok = -1;

-	return -1;

 }

-static int

-tlsSecPSKs(TlsSec *sec, int vers)

+static void

+tlsSecPSKs(TlsSec *sec)

 {

-	if(setVers(sec, vers) < 0){

-		sec->ok = -1;

-		return -1;

-	}

 	setMasterSecret(sec, newbytes(sec->psklen));

-	return 0;

 }

-static TlsSec*

-tlsSecInitc(int cvers, uchar *crandom)

+static void

+tlsSecInitc(TlsSec *sec, int cvers)

 {

-	TlsSec *sec = emalloc(sizeof(*sec));

+	memset(sec, 0, sizeof(*sec));

 	sec->clientVers = cvers;

-	put32(sec->crandom, time(0));

+	put32(sec->crandom, time(nil));

 	genrandom(sec->crandom+4, RandomSize-4);

-	memmove(crandom, sec->crandom, RandomSize);

-	return sec;

 }

-static int

-tlsSecPSKc(TlsSec *sec, uchar *srandom, int vers)

+static void

+tlsSecPSKc(TlsSec *sec)

 {

-	memmove(sec->srandom, srandom, RandomSize);

-	if(setVers(sec, vers) < 0){

-		sec->ok = -1;

-		return -1;

-	}

 	setMasterSecret(sec, newbytes(sec->psklen));

-	return 0;

 }

 static Bytes*

-tlsSecRSAc(TlsSec *sec, uchar *sid, int nsid, uchar *srandom, uchar *cert, int ncert, int vers)

+tlsSecRSAc(TlsSec *sec, uchar *cert, int ncert)

 {

 	RSApub *pub;

 	Bytes *pm, *epm;

-	USED(sid);

-	USED(nsid);

-	

-	memmove(sec->srandom, srandom, RandomSize);

-	if(setVers(sec, vers) < 0)

-		goto Err;

 	pub = X509toRSApub(cert, ncert, nil, 0);

 	if(pub == nil){

 		werrstr("invalid x509/rsa certificate");

-		goto Err;

+		return nil;

 	}

 	pm = newbytes(MasterSecretSize);

 	put16(pm->data, sec->clientVers);

@@ -2639,11 +2599,7 @@

 	epm = pkcs1_encrypt(pm, pub, 2);

 	setMasterSecret(sec, pm);

 	rsapubfree(pub);

-	if(epm != nil)

-		return epm;

-Err:

-	sec->ok = -1;

-	return nil;

+	return epm;

 }

 static int

@@ -2650,7 +2606,6 @@

 tlsSecFinished(TlsSec *sec, HandshakeHash hsh, uchar *fin, int nfin, int isclient)

 {

 	if(sec->nfin != nfin){

-		sec->ok = -1;

 		werrstr("invalid finished exchange");

 		return -1;

 	}

@@ -2658,29 +2613,12 @@

 	hsh.sha1.malloced = 0;

 	hsh.sha2_256.malloced = 0;

 	(*sec->setFinished)(sec, hsh, fin, isclient);

-	return 1;

+	return 0;

 }

 static void

-tlsSecOk(TlsSec *sec)

+tlsSecVers(TlsSec *sec, int v)

 {

-	if(sec->ok == 0)

-		sec->ok = 1;

-}

-

-static void

-tlsSecClose(TlsSec *sec)

-{

-	if(sec == nil)

-		return;

-	factotum_rsa_close(sec->rpc);

-	free(sec->server);

-	free(sec);

-}

-

-static int

-setVers(TlsSec *sec, int v)

-{

 	if(v == SSL3Version){

 		sec->setFinished = sslSetFinished;

 		sec->nfin = SSL3FinishedLen;

@@ -2694,22 +2632,36 @@

 		sec->nfin = TLSFinishedLen;

 		sec->prf = tls12PRF;

 	}

-	sec->vers = v;

-	return 0;

 }

-/*

- * generate secret keys from the master secret.

- *

- * different crypto selections will require different amounts

- * of key expansion and use of key expansion data,

- * but it's all generated using the same function.

- */

-static void

-setSecrets(TlsSec *sec, uchar *kd, int nkd)

+static int

+setSecrets(TlsConnection *c, int isclient)

 {

-	(*sec->prf)(kd, nkd, sec->sec, MasterSecretSize, "key expansion",

-			sec->srandom, RandomSize, sec->crandom, RandomSize);

+	uchar kd[MaxKeyData];

+	char *secrets;

+	int rv;

+

+	assert(c->nsecret <= sizeof(kd));

+	secrets = emalloc(2*c->nsecret);

+

+	/*

+	 * generate secret keys from the master secret.

+	 *

+	 * different cipher selections will require different amounts

+	 * of key expansion and use of key expansion data,

+	 * but it's all generated using the same function.

+	 */

+	(*c->sec->prf)(kd, c->nsecret, c->sec->sec, MasterSecretSize, "key expansion",

+			c->sec->srandom, RandomSize, c->sec->crandom, RandomSize);

+

+	enc64(secrets, 2*c->nsecret, kd, c->nsecret);

+	memset(kd, 0, c->nsecret);

+

+	rv = fprint(c->ctl, "secret %s %s %d %s", c->digest, c->enc, isclient, secrets);

+	memset(secrets, 0, 2*c->nsecret);

+	free(secrets);

+

+	return rv;

 }

 /*

@@ -2740,103 +2692,6 @@

 	memset(pm->data, 0, pm->len);	

 	freebytes(pm);

-}

-

-static void

-sslSetFinished(TlsSec *sec, HandshakeHash hsh, uchar *finished, int isClient)

-{

-	DigestState *s;

-	uchar h0[MD5dlen], h1[SHA1dlen], pad[48];

-	char *label;

-

-	if(isClient)

-		label = "CLNT";

-	else

-		label = "SRVR";

-

-	md5((uchar*)label, 4, nil, &hsh.md5);

-	md5(sec->sec, MasterSecretSize, nil, &hsh.md5);

-	memset(pad, 0x36, 48);

-	md5(pad, 48, nil, &hsh.md5);

-	md5(nil, 0, h0, &hsh.md5);

-	memset(pad, 0x5C, 48);

-	s = md5(sec->sec, MasterSecretSize, nil, nil);

-	s = md5(pad, 48, nil, s);

-	md5(h0, MD5dlen, finished, s);

-

-	sha1((uchar*)label, 4, nil, &hsh.sha1);

-	sha1(sec->sec, MasterSecretSize, nil, &hsh.sha1);

-	memset(pad, 0x36, 40);

-	sha1(pad, 40, nil, &hsh.sha1);

-	sha1(nil, 0, h1, &hsh.sha1);

-	memset(pad, 0x5C, 40);

-	s = sha1(sec->sec, MasterSecretSize, nil, nil);

-	s = sha1(pad, 40, nil, s);

-	sha1(h1, SHA1dlen, finished + MD5dlen, s);

-}

-

-// fill "finished" arg with md5(args)^sha1(args)

-static void

-tls10SetFinished(TlsSec *sec, HandshakeHash hsh, uchar *finished, int isClient)

-{

-	uchar h0[MD5dlen], h1[SHA1dlen];

-	char *label;

-

-	// get current hash value, but allow further messages to be hashed in

-	md5(nil, 0, h0, &hsh.md5);

-	sha1(nil, 0, h1, &hsh.sha1);

-

-	if(isClient)

-		label = "client finished";

-	else

-		label = "server finished";

-	tls10PRF(finished, TLSFinishedLen, sec->sec, MasterSecretSize, label, h0, MD5dlen, h1, SHA1dlen);

-}

-

-static void

-tls12SetFinished(TlsSec *sec, HandshakeHash hsh, uchar *finished, int isClient)

-{

-	uchar seed[SHA2_256dlen];

-	char *label;

-

-	// get current hash value, but allow further messages to be hashed in

-	sha2_256(nil, 0, seed, &hsh.sha2_256);

-

-	if(isClient)

-		label = "client finished";

-	else

-		label = "server finished";

-	p_sha256(finished, TLSFinishedLen, sec->sec, MasterSecretSize, (uchar*)label, strlen(label), seed, SHA2_256dlen);

-}

-

-static void

-sslPRF(uchar *buf, int nbuf, uchar *key, int nkey, char *label, uchar *seed0, int nseed0, uchar *seed1, int nseed1)

-{

-	uchar sha1dig[SHA1dlen], md5dig[MD5dlen], tmp[26];

-	DigestState *s;

-	int i, n, len;

-

-	USED(label);

-	len = 1;

-	while(nbuf > 0){

-		if(len > 26)

-			return;

-		for(i = 0; i < len; i++)

-			tmp[i] = 'A' - 1 + len;

-		s = sha1(tmp, len, nil, nil);

-		s = sha1(key, nkey, nil, s);

-		s = sha1(seed0, nseed0, nil, s);

-		sha1(seed1, nseed1, sha1dig, s);

-		s = md5(key, nkey, nil, nil);

-		md5(sha1dig, SHA1dlen, md5dig, s);

-		n = MD5dlen;

-		if(n > nbuf)

-			n = nbuf;

-		memmove(buf, md5dig, n);

-		buf += n;

-		nbuf -= n;

-		len++;

-	}

 }

 static mpint*

--- a/libsec/tsmemcmp.c

+++ b/libsec/tsmemcmp.c

@@ -1,5 +1,4 @@

-#include <u.h>

-#include <libc.h>

+#include "os.h"

 #include <libsec.h>

 /*

--- a/libsec/x509.c

+++ b/libsec/x509.c

@@ -478,6 +478,7 @@

 			pval->u.setval = vl;

 		}

 		break;

+

 	case UTF8String:

 	case NumericString:

 	case PrintableString:

@@ -491,13 +492,64 @@

 	case GeneralString:

 	case UniversalString:

 	case BMPString:

-		/* TODO: figure out when character set conversion is necessary */

 		err = octet_decode(&p, pend, length, isconstr, &va);

 		if(err == ASN_OK) {

-			pval->tag = VString;

-			pval->u.stringval = (char*)emalloc(va->len+1);

-			memmove(pval->u.stringval, va->data, va->len);

-			pval->u.stringval[va->len] = 0;

+			uchar *s;

+			char *d;

+			Rune r;

+			int n;

+

+			switch(kind){

+			case UniversalString:

+				n = va->len / 4;

+				d = emalloc(n*UTFmax+1);

+				pval->u.stringval = d;

+				s = va->data;

+				while(n > 0){

+					r = s[0]<<24 | s[1]<<16 | s[2]<<8 | s[3];

+					if(r == 0)

+						break;

+					n--;

+					s += 4;

+					d += runetochar(d, &r);

+				}

+				*d = 0;

+				break;

+			case BMPString:

+				n = va->len / 2;

+				d = emalloc(n*UTFmax+1);

+				pval->u.stringval = d;

+				s = va->data;

+				while(n > 0){

+					r = s[0]<<8 | s[1];

+					if(r == 0)

+						break;

+					n--;

+					s += 2;

+					d += runetochar(d, &r);

+				}

+				*d = 0;

+				break;

+			default:

+				n = va->len;

+				d = emalloc(n+1);

+				pval->u.stringval = d;

+				s = va->data;

+				while(n > 0){

+					if((*d = *s) == 0)

+						break;

+					n--;

+					s++;

+					d++;

+				}

+				*d = 0;

+				break;

+			}

+			if(n != 0){

+				err = ASN_EINVAL;

+				free(pval->u.stringval);

+			} else 

+				pval->tag = VString;

 			free(va);

 		}

 		break;

@@ -1908,16 +1960,19 @@

 	Elist *el;

 	RSApub* key;

-	key = rsapuballoc();

+	key = nil;

 	if(decode(a->data, a->len, &e) != ASN_OK)

 		goto errret;

 	if(!is_seq(&e, &el) || elistlen(el) != 2)

 		goto errret;

+

+	key = rsapuballoc();

 	if((key->n = asn1mpint(&el->hd)) == nil)

 		goto errret;

 	el = el->tl;

 	if((key->ek = asn1mpint(&el->hd)) == nil)

 		goto errret;

+

 	freevalfields(&e.val);

 	return key;

 errret:

@@ -1946,14 +2001,27 @@

 	Elist *el;

 	RSApriv* key;

-	key = rsaprivalloc();

+	key = nil;

 	if(decode(a->data, a->len, &e) != ASN_OK)

 		goto errret;

-	if(!is_seq(&e, &el) || elistlen(el) != 9)

+	if(!is_seq(&e, &el))

 		goto errret;

+

 	if(!is_int(&el->hd, &version) || version != 0)

 		goto errret;

+	if(elistlen(el) != 9){

+		if(elistlen(el) == 3

+		&& parse_alg(&el->tl->hd) == ALG_rsaEncryption

+		&& is_octetstring(&el->tl->tl->hd, &a)){

+			key = decode_rsaprivkey(a);

+			if(key != nil)

+				goto done;

+		}

+		goto errret;

+	}

+

+	key = rsaprivalloc();

 	el = el->tl;

 	if((key->pub.n = asn1mpint(&el->hd)) == nil)

 		goto errret;

@@ -1986,6 +2054,7 @@

 	if((key->c2 = asn1mpint(&el->hd)) == nil)

 		goto errret;

+done:

 	freevalfields(&e.val);

 	return key;

 errret:

@@ -2309,6 +2378,9 @@

 	Bytes *b;

 	CertX509 *c;

 	RSApub *pub;

+

+	if(name != nil)

+		memset(name, 0, nname);

 	b = makebytes(cert, ncert);

 	c = decode_cert(b);

-- 

⑨