OpenBSD-4.6/usr.bin/ssh/schnorr.c
/* $OpenBSD: schnorr.c,v 1.3 2009/03/05 07:18:19 djm Exp $ */
/*
* Copyright (c) 2008 Damien Miller. All rights reserved.
*
* Permission to use, copy, modify, and distribute this software for any
* purpose with or without fee is hereby granted, provided that the above
* copyright notice and this permission notice appear in all copies.
*
* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
*/
/*
* Implementation of Schnorr signatures / zero-knowledge proofs, based on
* description in:
*
* F. Hao, P. Ryan, "Password Authenticated Key Exchange by Juggling",
* 16th Workshop on Security Protocols, Cambridge, April 2008
*
* http://grouper.ieee.org/groups/1363/Research/contributions/hao-ryan-2008.pdf
*/
#include <sys/types.h>
#include <string.h>
#include <stdarg.h>
#include <stdio.h>
#include <openssl/evp.h>
#include <openssl/bn.h>
#include "xmalloc.h"
#include "buffer.h"
#include "log.h"
#include "schnorr.h"
/* #define SCHNORR_DEBUG */ /* Privacy-violating debugging */
/* #define SCHNORR_MAIN */ /* Include main() selftest */
#ifndef SCHNORR_DEBUG
# define SCHNORR_DEBUG_BN(a)
# define SCHNORR_DEBUG_BUF(a)
#else
# define SCHNORR_DEBUG_BN(a) debug3_bn a
# define SCHNORR_DEBUG_BUF(a) debug3_buf a
#endif /* SCHNORR_DEBUG */
/*
* Calculate hash component of Schnorr signature H(g || g^v || g^x || id)
* using the hash function defined by "evp_md". Returns signature as
* bignum or NULL on error.
*/
static BIGNUM *
schnorr_hash(const BIGNUM *p, const BIGNUM *q, const BIGNUM *g,
const EVP_MD *evp_md, const BIGNUM *g_v, const BIGNUM *g_x,
const u_char *id, u_int idlen)
{
u_char *digest;
u_int digest_len;
BIGNUM *h;
Buffer b;
int success = -1;
if ((h = BN_new()) == NULL) {
error("%s: BN_new", __func__);
return NULL;
}
buffer_init(&b);
/* h = H(g || p || q || g^v || g^x || id) */
buffer_put_bignum2(&b, g);
buffer_put_bignum2(&b, p);
buffer_put_bignum2(&b, q);
buffer_put_bignum2(&b, g_v);
buffer_put_bignum2(&b, g_x);
buffer_put_string(&b, id, idlen);
SCHNORR_DEBUG_BUF((buffer_ptr(&b), buffer_len(&b),
"%s: hashblob", __func__));
if (hash_buffer(buffer_ptr(&b), buffer_len(&b), evp_md,
&digest, &digest_len) != 0) {
error("%s: hash_buffer", __func__);
goto out;
}
if (BN_bin2bn(digest, (int)digest_len, h) == NULL) {
error("%s: BN_bin2bn", __func__);
goto out;
}
success = 0;
SCHNORR_DEBUG_BN((h, "%s: h = ", __func__));
out:
buffer_free(&b);
bzero(digest, digest_len);
xfree(digest);
digest_len = 0;
if (success == 0)
return h;
BN_clear_free(h);
return NULL;
}
/*
* Generate Schnorr signature to prove knowledge of private value 'x' used
* in public exponent g^x, under group defined by 'grp_p', 'grp_q' and 'grp_g'
* using the hash function "evp_md".
* 'idlen' bytes from 'id' will be included in the signature hash as an anti-
* replay salt.
*
* On success, 0 is returned. The signature values are returned as *e_p
* (g^v mod p) and *r_p (v - xh mod q). The caller must free these values.
* On failure, -1 is returned.
*/
int
schnorr_sign(const BIGNUM *grp_p, const BIGNUM *grp_q, const BIGNUM *grp_g,
const EVP_MD *evp_md, const BIGNUM *x, const BIGNUM *g_x,
const u_char *id, u_int idlen, BIGNUM **r_p, BIGNUM **e_p)
{
int success = -1;
BIGNUM *h, *tmp, *v, *g_v, *r;
BN_CTX *bn_ctx;
SCHNORR_DEBUG_BN((x, "%s: x = ", __func__));
SCHNORR_DEBUG_BN((g_x, "%s: g_x = ", __func__));
/* Avoid degenerate cases: g^0 yields a spoofable signature */
if (BN_cmp(g_x, BN_value_one()) <= 0) {
error("%s: g_x < 1", __func__);
return -1;
}
h = g_v = r = tmp = v = NULL;
if ((bn_ctx = BN_CTX_new()) == NULL) {
error("%s: BN_CTX_new", __func__);
goto out;
}
if ((g_v = BN_new()) == NULL ||
(r = BN_new()) == NULL ||
(tmp = BN_new()) == NULL) {
error("%s: BN_new", __func__);
goto out;
}
/*
* v must be a random element of Zq, so 1 <= v < q
* we also exclude v = 1, since g^1 looks dangerous
*/
if ((v = bn_rand_range_gt_one(grp_p)) == NULL) {
error("%s: bn_rand_range2", __func__);
goto out;
}
SCHNORR_DEBUG_BN((v, "%s: v = ", __func__));
/* g_v = g^v mod p */
if (BN_mod_exp(g_v, grp_g, v, grp_p, bn_ctx) == -1) {
error("%s: BN_mod_exp (g^v mod p)", __func__);
goto out;
}
SCHNORR_DEBUG_BN((g_v, "%s: g_v = ", __func__));
/* h = H(g || g^v || g^x || id) */
if ((h = schnorr_hash(grp_p, grp_q, grp_g, evp_md, g_v, g_x,
id, idlen)) == NULL) {
error("%s: schnorr_hash failed", __func__);
goto out;
}
/* r = v - xh mod q */
if (BN_mod_mul(tmp, x, h, grp_q, bn_ctx) == -1) {
error("%s: BN_mod_mul (tmp = xv mod q)", __func__);
goto out;
}
if (BN_mod_sub(r, v, tmp, grp_q, bn_ctx) == -1) {
error("%s: BN_mod_mul (r = v - tmp)", __func__);
goto out;
}
SCHNORR_DEBUG_BN((g_v, "%s: e = ", __func__));
SCHNORR_DEBUG_BN((r, "%s: r = ", __func__));
*e_p = g_v;
*r_p = r;
success = 0;
out:
BN_CTX_free(bn_ctx);
if (h != NULL)
BN_clear_free(h);
if (v != NULL)
BN_clear_free(v);
BN_clear_free(tmp);
return success;
}
/*
* Generate Schnorr signature to prove knowledge of private value 'x' used
* in public exponent g^x, under group defined by 'grp_p', 'grp_q' and 'grp_g'
* using a SHA256 hash.
* 'idlen' bytes from 'id' will be included in the signature hash as an anti-
* replay salt.
* On success, 0 is returned and *siglen bytes of signature are returned in
* *sig (caller to free). Returns -1 on failure.
*/
int
schnorr_sign_buf(const BIGNUM *grp_p, const BIGNUM *grp_q, const BIGNUM *grp_g,
const BIGNUM *x, const BIGNUM *g_x, const u_char *id, u_int idlen,
u_char **sig, u_int *siglen)
{
Buffer b;
BIGNUM *r, *e;
if (schnorr_sign(grp_p, grp_q, grp_g, EVP_sha256(),
x, g_x, id, idlen, &r, &e) != 0)
return -1;
/* Signature is (e, r) */
buffer_init(&b);
/* XXX sigtype-hash as string? */
buffer_put_bignum2(&b, e);
buffer_put_bignum2(&b, r);
*siglen = buffer_len(&b);
*sig = xmalloc(*siglen);
memcpy(*sig, buffer_ptr(&b), *siglen);
SCHNORR_DEBUG_BUF((buffer_ptr(&b), buffer_len(&b),
"%s: sigblob", __func__));
buffer_free(&b);
BN_clear_free(r);
BN_clear_free(e);
return 0;
}
/*
* Verify Schnorr signature { r (v - xh mod q), e (g^v mod p) } against
* public exponent g_x (g^x) under group defined by 'grp_p', 'grp_q' and
* 'grp_g' using hash "evp_md".
* Signature hash will be salted with 'idlen' bytes from 'id'.
* Returns -1 on failure, 0 on incorrect signature or 1 on matching signature.
*/
int
schnorr_verify(const BIGNUM *grp_p, const BIGNUM *grp_q, const BIGNUM *grp_g,
const EVP_MD *evp_md, const BIGNUM *g_x, const u_char *id, u_int idlen,
const BIGNUM *r, const BIGNUM *e)
{
int success = -1;
BIGNUM *h, *g_xh, *g_r, *expected;
BN_CTX *bn_ctx;
SCHNORR_DEBUG_BN((g_x, "%s: g_x = ", __func__));
/* Avoid degenerate cases: g^0 yields a spoofable signature */
if (BN_cmp(g_x, BN_value_one()) <= 0) {
error("%s: g_x < 1", __func__);
return -1;
}
h = g_xh = g_r = expected = NULL;
if ((bn_ctx = BN_CTX_new()) == NULL) {
error("%s: BN_CTX_new", __func__);
goto out;
}
if ((g_xh = BN_new()) == NULL ||
(g_r = BN_new()) == NULL ||
(expected = BN_new()) == NULL) {
error("%s: BN_new", __func__);
goto out;
}
SCHNORR_DEBUG_BN((e, "%s: e = ", __func__));
SCHNORR_DEBUG_BN((r, "%s: r = ", __func__));
/* h = H(g || g^v || g^x || id) */
if ((h = schnorr_hash(grp_p, grp_q, grp_g, evp_md, e, g_x,
id, idlen)) == NULL) {
error("%s: schnorr_hash failed", __func__);
goto out;
}
/* g_xh = (g^x)^h */
if (BN_mod_exp(g_xh, g_x, h, grp_p, bn_ctx) == -1) {
error("%s: BN_mod_exp (g_x^h mod p)", __func__);
goto out;
}
SCHNORR_DEBUG_BN((g_xh, "%s: g_xh = ", __func__));
/* g_r = g^r */
if (BN_mod_exp(g_r, grp_g, r, grp_p, bn_ctx) == -1) {
error("%s: BN_mod_exp (g_x^h mod p)", __func__);
goto out;
}
SCHNORR_DEBUG_BN((g_r, "%s: g_r = ", __func__));
/* expected = g^r * g_xh */
if (BN_mod_mul(expected, g_r, g_xh, grp_p, bn_ctx) == -1) {
error("%s: BN_mod_mul (expected = g_r mod p)", __func__);
goto out;
}
SCHNORR_DEBUG_BN((expected, "%s: expected = ", __func__));
/* Check e == expected */
success = BN_cmp(expected, e) == 0;
out:
BN_CTX_free(bn_ctx);
if (h != NULL)
BN_clear_free(h);
BN_clear_free(g_xh);
BN_clear_free(g_r);
BN_clear_free(expected);
return success;
}
/*
* Verify Schnorr signature 'sig' of length 'siglen' against public exponent
* g_x (g^x) under group defined by 'grp_p', 'grp_q' and 'grp_g' using a
* SHA256 hash.
* Signature hash will be salted with 'idlen' bytes from 'id'.
* Returns -1 on failure, 0 on incorrect signature or 1 on matching signature.
*/
int
schnorr_verify_buf(const BIGNUM *grp_p, const BIGNUM *grp_q,
const BIGNUM *grp_g,
const BIGNUM *g_x, const u_char *id, u_int idlen,
const u_char *sig, u_int siglen)
{
Buffer b;
int ret = -1;
u_int rlen;
BIGNUM *r, *e;
e = r = NULL;
if ((e = BN_new()) == NULL ||
(r = BN_new()) == NULL) {
error("%s: BN_new", __func__);
goto out;
}
/* Extract g^v and r from signature blob */
buffer_init(&b);
buffer_append(&b, sig, siglen);
SCHNORR_DEBUG_BUF((buffer_ptr(&b), buffer_len(&b),
"%s: sigblob", __func__));
buffer_get_bignum2(&b, e);
buffer_get_bignum2(&b, r);
rlen = buffer_len(&b);
buffer_free(&b);
if (rlen != 0) {
error("%s: remaining bytes in signature %d", __func__, rlen);
goto out;
}
ret = schnorr_verify(grp_p, grp_q, grp_g, EVP_sha256(),
g_x, id, idlen, r, e);
out:
BN_clear_free(e);
BN_clear_free(r);
return ret;
}
/* Helper functions */
/*
* Generate uniformly distributed random number in range (1, high).
* Return number on success, NULL on failure.
*/
BIGNUM *
bn_rand_range_gt_one(const BIGNUM *high)
{
BIGNUM *r, *tmp;
int success = -1;
if ((tmp = BN_new()) == NULL) {
error("%s: BN_new", __func__);
return NULL;
}
if ((r = BN_new()) == NULL) {
error("%s: BN_new failed", __func__);
goto out;
}
if (BN_set_word(tmp, 2) != 1) {
error("%s: BN_set_word(tmp, 2)", __func__);
goto out;
}
if (BN_sub(tmp, high, tmp) == -1) {
error("%s: BN_sub failed (tmp = high - 2)", __func__);
goto out;
}
if (BN_rand_range(r, tmp) == -1) {
error("%s: BN_rand_range failed", __func__);
goto out;
}
if (BN_set_word(tmp, 2) != 1) {
error("%s: BN_set_word(tmp, 2)", __func__);
goto out;
}
if (BN_add(r, r, tmp) == -1) {
error("%s: BN_add failed (r = r + 2)", __func__);
goto out;
}
success = 0;
out:
BN_clear_free(tmp);
if (success == 0)
return r;
BN_clear_free(r);
return NULL;
}
/*
* Hash contents of buffer 'b' with hash 'md'. Returns 0 on success,
* with digest via 'digestp' (caller to free) and length via 'lenp'.
* Returns -1 on failure.
*/
int
hash_buffer(const u_char *buf, u_int len, const EVP_MD *md,
u_char **digestp, u_int *lenp)
{
u_char digest[EVP_MAX_MD_SIZE];
u_int digest_len;
EVP_MD_CTX evp_md_ctx;
int success = -1;
EVP_MD_CTX_init(&evp_md_ctx);
if (EVP_DigestInit_ex(&evp_md_ctx, md, NULL) != 1) {
error("%s: EVP_DigestInit_ex", __func__);
goto out;
}
if (EVP_DigestUpdate(&evp_md_ctx, buf, len) != 1) {
error("%s: EVP_DigestUpdate", __func__);
goto out;
}
if (EVP_DigestFinal_ex(&evp_md_ctx, digest, &digest_len) != 1) {
error("%s: EVP_DigestFinal_ex", __func__);
goto out;
}
*digestp = xmalloc(digest_len);
*lenp = digest_len;
memcpy(*digestp, digest, *lenp);
success = 0;
out:
EVP_MD_CTX_cleanup(&evp_md_ctx);
bzero(digest, sizeof(digest));
digest_len = 0;
return success;
}
/* print formatted string followed by bignum */
void
debug3_bn(const BIGNUM *n, const char *fmt, ...)
{
char *out, *h;
va_list args;
out = NULL;
va_start(args, fmt);
vasprintf(&out, fmt, args);
va_end(args);
if (out == NULL)
fatal("%s: vasprintf failed", __func__);
if (n == NULL)
debug3("%s(null)", out);
else {
h = BN_bn2hex(n);
debug3("%s0x%s", out, h);
free(h);
}
free(out);
}
/* print formatted string followed by buffer contents in hex */
void
debug3_buf(const u_char *buf, u_int len, const char *fmt, ...)
{
char *out, h[65];
u_int i, j;
va_list args;
out = NULL;
va_start(args, fmt);
vasprintf(&out, fmt, args);
va_end(args);
if (out == NULL)
fatal("%s: vasprintf failed", __func__);
debug3("%s length %u%s", out, len, buf == NULL ? " (null)" : "");
free(out);
if (buf == NULL)
return;
*h = '\0';
for (i = j = 0; i < len; i++) {
snprintf(h + j, sizeof(h) - j, "%02x", buf[i]);
j += 2;
if (j >= sizeof(h) - 1 || i == len - 1) {
debug3(" %s", h);
*h = '\0';
j = 0;
}
}
}
/*
* Construct a MODP group from hex strings p (which must be a safe
* prime) and g, automatically calculating subgroup q as (p / 2)
*/
struct modp_group *
modp_group_from_g_and_safe_p(const char *grp_g, const char *grp_p)
{
struct modp_group *ret;
ret = xmalloc(sizeof(*ret));
ret->p = ret->q = ret->g = NULL;
if (BN_hex2bn(&ret->p, grp_p) == 0 ||
BN_hex2bn(&ret->g, grp_g) == 0)
fatal("%s: BN_hex2bn", __func__);
/* Subgroup order is p/2 (p is a safe prime) */
if ((ret->q = BN_new()) == NULL)
fatal("%s: BN_new", __func__);
if (BN_rshift1(ret->q, ret->p) != 1)
fatal("%s: BN_rshift1", __func__);
return ret;
}
void
modp_group_free(struct modp_group *grp)
{
if (grp->g != NULL)
BN_clear_free(grp->g);
if (grp->p != NULL)
BN_clear_free(grp->p);
if (grp->q != NULL)
BN_clear_free(grp->q);
bzero(grp, sizeof(*grp));
xfree(grp);
}
/* main() function for self-test */
#ifdef SCHNORR_MAIN
static void
schnorr_selftest_one(const BIGNUM *grp_p, const BIGNUM *grp_q,
const BIGNUM *grp_g, const BIGNUM *x)
{
BIGNUM *g_x;
u_char *sig;
u_int siglen;
BN_CTX *bn_ctx;
if ((bn_ctx = BN_CTX_new()) == NULL)
fatal("%s: BN_CTX_new", __func__);
if ((g_x = BN_new()) == NULL)
fatal("%s: BN_new", __func__);
if (BN_mod_exp(g_x, grp_g, x, grp_p, bn_ctx) == -1)
fatal("%s: g_x", __func__);
if (schnorr_sign_buf(grp_p, grp_q, grp_g, x, g_x, "junk", 4,
&sig, &siglen))
fatal("%s: schnorr_sign", __func__);
if (schnorr_verify_buf(grp_p, grp_q, grp_g, g_x, "junk", 4,
sig, siglen) != 1)
fatal("%s: verify fail", __func__);
if (schnorr_verify_buf(grp_p, grp_q, grp_g, g_x, "JUNK", 4,
sig, siglen) != 0)
fatal("%s: verify should have failed (bad ID)", __func__);
sig[4] ^= 1;
if (schnorr_verify_buf(grp_p, grp_q, grp_g, g_x, "junk", 4,
sig, siglen) != 0)
fatal("%s: verify should have failed (bit error)", __func__);
xfree(sig);
BN_free(g_x);
BN_CTX_free(bn_ctx);
}
static void
schnorr_selftest(void)
{
BIGNUM *x;
struct modp_group *grp;
u_int i;
char *hh;
grp = jpake_default_group();
if ((x = BN_new()) == NULL)
fatal("%s: BN_new", __func__);
SCHNORR_DEBUG_BN((grp->p, "%s: grp->p = ", __func__));
SCHNORR_DEBUG_BN((grp->q, "%s: grp->q = ", __func__));
SCHNORR_DEBUG_BN((grp->g, "%s: grp->g = ", __func__));
/* [1, 20) */
for (i = 1; i < 20; i++) {
printf("x = %u\n", i);
fflush(stdout);
if (BN_set_word(x, i) != 1)
fatal("%s: set x word", __func__);
schnorr_selftest_one(grp->p, grp->q, grp->g, x);
}
/* 100 x random [0, p) */
for (i = 0; i < 100; i++) {
if (BN_rand_range(x, grp->p) != 1)
fatal("%s: BN_rand_range", __func__);
hh = BN_bn2hex(x);
printf("x = (random) 0x%s\n", hh);
free(hh);
fflush(stdout);
schnorr_selftest_one(grp->p, grp->q, grp->g, x);
}
/* [q-20, q) */
if (BN_set_word(x, 20) != 1)
fatal("%s: BN_set_word (x = 20)", __func__);
if (BN_sub(x, grp->q, x) != 1)
fatal("%s: BN_sub (q - x)", __func__);
for (i = 0; i < 19; i++) {
hh = BN_bn2hex(x);
printf("x = (q - %d) 0x%s\n", 20 - i, hh);
free(hh);
fflush(stdout);
schnorr_selftest_one(grp->p, grp->q, grp->g, x);
if (BN_add(x, x, BN_value_one()) != 1)
fatal("%s: BN_add (x + 1)", __func__);
}
BN_free(x);
}
int
main(int argc, char **argv)
{
log_init(argv[0], SYSLOG_LEVEL_DEBUG3, SYSLOG_FACILITY_USER, 1);
schnorr_selftest();
return 0;
}
#endif