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Make the rest of RSA CRT constant-time.

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Alas, the existence of RSA keys with q > p is obnoxious, but we can
canonicalize it away. To my knowledge, the remaining leaks in RSA are:

- Key generation. This is kind of hopelessly non-constant-time but
  perhaps deserves a more careful ponder. Though hopefully it does not
  come in at a measurable point for practical purposes.

- Private key serialization. RSAPrivateKey inherently leaks the
  magnitudes of d, dmp1, dmq1, and iqmp. This is unavoidable but
  hopefully does not come in at a measurable point for practical
  purposes.

- If p and q have different word widths, we currently fall back to the
  variable-time BN_mod rather than Montgomery reduction at the start of
  CRT. I can think of ways to apply Montgomery reduction, but it's
  probably better to deny CRT to such keys, if not reject them outright.

- bn_mul_fixed and bn_sqr_fixed which affect the Montgomery
  multiplication bn_mul_mont-less configurations, as well as the final
  CRT multiplication. We should fix this.

Bug: 233
Change-Id: I8c2ecf8f8ec104e9f26299b66ac8cbb0cad04616
Reviewed-on: https://boringssl-review.googlesource.com/25263
Commit-Queue: David Benjamin <davidben@google.com>
CQ-Verified: CQ bot account: commit-bot@chromium.org <commit-bot@chromium.org>
Reviewed-by: Adam Langley <agl@google.com>
This commit is contained in:
David Benjamin 2018-01-24 17:22:17 -05:00 committed by CQ bot account: commit-bot@chromium.org
parent 150ad30d28
commit be837402a9
3 changed files with 100 additions and 97 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

17
crypto/fipsmodule/rsa/rsa.c
View File

@ -132,17 +132,18 @@ void RSA_free(RSA *rsa) {
CRYPTO_free_ex_data(g_rsa_ex_data_class_bss_get(), rsa, &rsa->ex_data);
BN_clear_free(rsa->n);
BN_clear_free(rsa->e);
BN_clear_free(rsa->d);
BN_clear_free(rsa->p);
BN_clear_free(rsa->q);
BN_clear_free(rsa->dmp1);
BN_clear_free(rsa->dmq1);
BN_clear_free(rsa->iqmp);
BN_free(rsa->n);
BN_free(rsa->e);
BN_free(rsa->d);
BN_free(rsa->p);
BN_free(rsa->q);
BN_free(rsa->dmp1);
BN_free(rsa->dmq1);
BN_free(rsa->iqmp);
BN_MONT_CTX_free(rsa->mont_n);
BN_MONT_CTX_free(rsa->mont_p);
BN_MONT_CTX_free(rsa->mont_q);
BN_free(rsa->inv_small_mod_large_mont);
for (u = 0; u < rsa->num_blindings; u++) {
BN_BLINDING_free(rsa->blindings[u]);
}

173
crypto/fipsmodule/rsa/rsa_impl.c
View File

@ -165,16 +165,50 @@ static int freeze_private_key(RSA *rsa, BN_CTX *ctx) {
}
}
// CRT components are only publicly bounded by their corresponding moduli's
// bit lengths.
if ((rsa->dmp1 != NULL &&
!bn_resize_words(rsa->dmp1, rsa->p->width)) ||
(rsa->dmq1 != NULL &&
!bn_resize_words(rsa->dmq1, rsa->q->width)) ||
(rsa->iqmp != NULL &&
!bn_resize_words(rsa->iqmp, rsa->p->width))) {
if (rsa->dmp1 != NULL && rsa->dmq1 != NULL) {
// Key generation relies on this function to compute |iqmp|.
if (rsa->iqmp == NULL) {
BIGNUM *iqmp = BN_new();
if (iqmp == NULL ||
!bn_mod_inverse_secret_prime(iqmp, rsa->q, rsa->p, ctx,
rsa->mont_p)) {
BN_free(iqmp);
goto err;
}
rsa->iqmp = iqmp;
}
// CRT components are only publicly bounded by their corresponding
// moduli's bit lengths.
if (!bn_resize_words(rsa->dmp1, rsa->p->width) ||
!bn_resize_words(rsa->dmq1, rsa->q->width) ||
!bn_resize_words(rsa->iqmp, rsa->p->width)) {
goto err;
}
// Compute |inv_small_mod_large_mont|. Note that it is always modulo the
// larger prime, independent of what is stored in |rsa->iqmp|.
if (rsa->inv_small_mod_large_mont == NULL) {
BIGNUM *inv_small_mod_large_mont = BN_new();
int ok;
if (BN_less_than_consttime(rsa->p, rsa->q)) {
ok = inv_small_mod_large_mont != NULL &&
bn_mod_inverse_secret_prime(inv_small_mod_large_mont, rsa->p,
rsa->q, ctx, rsa->mont_q) &&
BN_to_montgomery(inv_small_mod_large_mont,
inv_small_mod_large_mont, rsa->mont_q, ctx);
} else {
ok = inv_small_mod_large_mont != NULL &&
BN_to_montgomery(inv_small_mod_large_mont, rsa->iqmp,
rsa->mont_p, ctx);
}
if (!ok) {
BN_free(inv_small_mod_large_mont);
goto err;
}
rsa->inv_small_mod_large_mont = inv_small_mod_large_mont;
}
}
}
rsa->flags |= RSA_FLAG_PRIVATE_KEY_FROZEN;
@ -757,16 +791,14 @@ static int mod_exp(BIGNUM *r0, const BIGNUM *I, RSA *rsa, BN_CTX *ctx) {
assert(rsa->dmq1 != NULL);
assert(rsa->iqmp != NULL);
BIGNUM *r1, *m1, *vrfy;
BIGNUM *r1, *m1;
int ret = 0;
BN_CTX_start(ctx);
r1 = BN_CTX_get(ctx);
m1 = BN_CTX_get(ctx);
vrfy = BN_CTX_get(ctx);
if (r1 == NULL ||
m1 == NULL ||
vrfy == NULL) {
m1 == NULL) {
goto err;
}
@ -774,77 +806,47 @@ static int mod_exp(BIGNUM *r0, const BIGNUM *I, RSA *rsa, BN_CTX *ctx) {
goto err;
}
// Implementing RSA with CRT in constant-time is sensitive to which prime is
// larger. Canonicalize fields so that |p| is the larger prime.
const BIGNUM *p = rsa->p, *q = rsa->q, *dmp1 = rsa->dmp1, *dmq1 = rsa->dmq1;
const BN_MONT_CTX *mont_p = rsa->mont_p, *mont_q = rsa->mont_q;
if (BN_less_than_consttime(rsa->p, rsa->q)) {
p = rsa->q;
q = rsa->p;
mont_p = rsa->mont_q;
mont_q = rsa->mont_p;
dmp1 = rsa->dmq1;
dmq1 = rsa->dmp1;
}
// This is a pre-condition for |mod_montgomery|. It was already checked by the
// caller.
assert(BN_ucmp(I, rsa->n) < 0);
// compute I mod q
if (!mod_montgomery(r1, I, rsa->q, rsa->mont_q, rsa->p, ctx)) {
goto err;
}
// compute r1^dmq1 mod q
if (!BN_mod_exp_mont_consttime(m1, r1, rsa->dmq1, rsa->q, ctx, rsa->mont_q)) {
goto err;
}
// compute I mod p
if (!mod_montgomery(r1, I, rsa->p, rsa->mont_p, rsa->q, ctx)) {
goto err;
}
// compute r1^dmp1 mod p
if (!BN_mod_exp_mont_consttime(r0, r1, rsa->dmp1, rsa->p, ctx, rsa->mont_p)) {
goto err;
}
// TODO(davidben): The code below is not constant-time:
//
// 1. Finish adding support for non-minimal |BIGNUM|s.
//
// 2. Canonicalize keys on p > q in |freeze_private_key|. (p > q for keys we
// generate, but not ones we import.) This removes the p < q case below.
//
// 3. Use |bn_mod_sub_quick_ctx| to compute r0 - m1 (mod p).
//
// 4. When computing mont_*, additionally compute iqmp_mont, iqmp in
// Montgomery form. The |BN_mul| and |BN_mod| pair can then be replaced
// with |BN_mod_mul_montgomery|.
if (!BN_sub(r0, r0, m1)) {
goto err;
}
// This will help stop the size of r0 increasing, which does
// affect the multiply if it optimised for a power of 2 size
if (BN_is_negative(r0)) {
if (!BN_add(r0, r0, rsa->p)) {
goto err;
}
}
if (!BN_mul(r1, r0, rsa->iqmp, ctx)) {
goto err;
}
if (!BN_mod(r0, r1, rsa->p, ctx)) {
goto err;
}
// If p < q it is occasionally possible for the correction of
// adding 'p' if r0 is negative above to leave the result still
// negative. This can break the private key operations: the following
// second correction should *always* correct this rare occurrence.
// This will *never* happen with OpenSSL generated keys because
// they ensure p > q [steve]
if (BN_is_negative(r0)) {
if (!BN_add(r0, r0, rsa->p)) {
goto err;
}
}
if (!BN_mul(r1, r0, rsa->q, ctx)) {
goto err;
}
if (!BN_add(r0, r1, m1)) {
if (// |m1| is the result modulo |q|.
!mod_montgomery(r1, I, q, mont_q, p, ctx) ||
!BN_mod_exp_mont_consttime(m1, r1, dmq1, q, ctx, mont_q) ||
// |r0| is the result modulo |p|.
!mod_montgomery(r1, I, p, mont_p, q, ctx) ||
!BN_mod_exp_mont_consttime(r0, r1, dmp1, p, ctx, mont_p) ||
// Compute r0 = r0 - m1 mod p. |p| is the larger prime, so |m1| is already
// fully reduced mod |p|.
!bn_mod_sub_quick_ctx(r0, r0, m1, p, ctx) ||
// r0 = r0 * iqmp mod p. We use Montgomery multiplication to compute this
// in constant time. |inv_small_mod_large_mont| is in Montgomery form and
// r0 is not, so the result is taken out of Montgomery form.
!BN_mod_mul_montgomery(r0, r0, rsa->inv_small_mod_large_mont, mont_p,
ctx) ||
// r0 = r0 * q + m1 gives the final result. Reducing modulo q gives m1, so
// it is correct mod p. Reducing modulo p gives (r0-m1)*iqmp*q + m1 = r0,
// so it is correct mod q. Finally, the result is bounded by [m1, n + m1),
// and the result is at least |m1|, so this must be the unique answer in
// [0, n).
!bn_mul_fixed(r0, r0, q, ctx) ||
!bn_uadd_fixed(r0, r0, m1) ||
// The result should be bounded by |rsa->n|, but fixed-width operations
// bound the width slightly higher, so fix it.
!bn_resize_words(r0, rsa->n->width)) {
goto err;
}
@ -1033,8 +1035,7 @@ int RSA_generate_key_ex(RSA *rsa, int bits, BIGNUM *e_value, BN_GENCB *cb) {
!ensure_bignum(&rsa->p) ||
!ensure_bignum(&rsa->q) ||
!ensure_bignum(&rsa->dmp1) ||
!ensure_bignum(&rsa->dmq1) ||
!ensure_bignum(&rsa->iqmp)) {
!ensure_bignum(&rsa->dmq1)) {
goto bn_err;
}
@ -1118,13 +1119,9 @@ int RSA_generate_key_ex(RSA *rsa, int bits, BIGNUM *e_value, BN_GENCB *cb) {
goto err;
}
// Calculate inverse of q mod p. Note that although RSA key generation is far
// from constant-time, |bn_mod_inverse_secret_prime| uses the same modular
// exponentation logic as in RSA private key operations and, if the RSAZ-1024
// code is enabled, will be optimized for common RSA prime sizes.
if (!freeze_private_key(rsa, ctx) ||
!bn_mod_inverse_secret_prime(rsa->iqmp, rsa->q, rsa->p, ctx,
rsa->mont_p)) {
// Call |freeze_private_key| to compute the inverse of q mod p, by way of
// |rsa->mont_p|.
if (!freeze_private_key(rsa, ctx)) {
goto bn_err;
}

5
include/openssl/rsa.h
View File

@ -662,6 +662,11 @@ struct rsa_st {
BN_MONT_CTX *mont_p;
BN_MONT_CTX *mont_q;
// inv_small_mod_large_mont is q^-1 mod p in Montgomery form, using |mont_p|,
// if |p| >= |q|. Otherwise, it is p^-1 mod q in Montgomery form, using
// |mont_q|.
BIGNUM *inv_small_mod_large_mont;
// num_blindings contains the size of the |blindings| and |blindings_inuse|
// arrays. This member and the |blindings_inuse| array are protected by
// |lock|.