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-rw-r--r--schnorr.c668
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diff --git a/schnorr.c b/schnorr.c
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--- a/schnorr.c
+++ /dev/null
@@ -1,668 +0,0 @@
-/* $OpenBSD: schnorr.c,v 1.9 2014/01/09 23:20:00 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 "includes.h"
-
-#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"
-#include "digest.h"
-
-#include "openbsd-compat/openssl-compat.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 "hash_alg". Returns signature as
- * bignum or NULL on error.
- */
-static BIGNUM *
-schnorr_hash(const BIGNUM *p, const BIGNUM *q, const BIGNUM *g,
- int hash_alg, 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), hash_alg,
- &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);
- free(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 "hash_alg".
- * '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,
- int hash_alg, 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;
- }
- if (BN_cmp(g_x, grp_p) >= 0) {
- error("%s: g_x > g", __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, hash_alg, 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, SSH_DIGEST_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 "hash_alg".
- * 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,
- int hash_alg, const BIGNUM *g_x, const u_char *id, u_int idlen,
- const BIGNUM *r, const BIGNUM *e)
-{
- int success = -1;
- BIGNUM *h = NULL, *g_xh = NULL, *g_r = NULL, *gx_q = NULL;
- BIGNUM *expected = NULL;
- 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;
- }
- if (BN_cmp(g_x, grp_p) >= 0) {
- error("%s: g_x >= p", __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 ||
- (gx_q = 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__));
-
- /* gx_q = (g^x)^q must === 1 mod p */
- if (BN_mod_exp(gx_q, g_x, grp_q, grp_p, bn_ctx) == -1) {
- error("%s: BN_mod_exp (g_x^q mod p)", __func__);
- goto out;
- }
- if (BN_cmp(gx_q, BN_value_one()) != 0) {
- error("%s: Invalid signature (g^x)^q != 1 mod p", __func__);
- goto out;
- }
-
- SCHNORR_DEBUG_BN((g_xh, "%s: g_xh = ", __func__));
- /* h = H(g || g^v || g^x || id) */
- if ((h = schnorr_hash(grp_p, grp_q, grp_g, hash_alg, 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);
- if (gx_q != NULL)
- BN_clear_free(gx_q);
- if (g_xh != NULL)
- BN_clear_free(g_xh);
- if (g_r != NULL)
- BN_clear_free(g_r);
- if (expected != NULL)
- 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, SSH_DIGEST_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;
-}
-
-/* XXX convert all callers of this to use ssh_digest_memory() directly */
-/*
- * 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, int hash_alg,
- u_char **digestp, u_int *lenp)
-{
- u_char digest[SSH_DIGEST_MAX_LENGTH];
- u_int digest_len = ssh_digest_bytes(hash_alg);
-
- if (digest_len == 0) {
- error("%s: invalid hash", __func__);
- return -1;
- }
- if (ssh_digest_memory(hash_alg, buf, len, digest, digest_len) != 0) {
- error("%s: digest_memory failed", __func__);
- return -1;
- }
- *digestp = xmalloc(digest_len);
- *lenp = digest_len;
- memcpy(*digestp, digest, *lenp);
- bzero(digest, sizeof(digest));
- digest_len = 0;
- return 0;
-}
-
-/* print formatted string followed by bignum */
-void
-debug3_bn(const BIGNUM *n, const char *fmt, ...)
-{
- char *out, *h;
- va_list args;
- int ret;
-
- out = NULL;
- va_start(args, fmt);
- ret = vasprintf(&out, fmt, args);
- va_end(args);
- if (ret == -1 || 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;
- int ret;
-
- out = NULL;
- va_start(args, fmt);
- ret = vasprintf(&out, fmt, args);
- va_end(args);
- if (ret == -1 || 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 = xcalloc(1, 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));
- free(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__);
- free(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
-