Move some RSA keygen support code into separate files. This was all new code. There was a request to make this available under ISC. Change-Id: Ibabbe6fbf593c2a781aac47a4de7ac378604dbcf Reviewed-on: https://boringssl-review.googlesource.com/28267 Reviewed-by: Adam Langley <agl@google.com>
diff --git a/crypto/fipsmodule/bcm.c b/crypto/fipsmodule/bcm.c index 51ac7d5..e456d3a 100644 --- a/crypto/fipsmodule/bcm.c +++ b/crypto/fipsmodule/bcm.c
@@ -36,8 +36,10 @@ #include "bn/cmp.c" #include "bn/ctx.c" #include "bn/div.c" +#include "bn/div_extra.c" #include "bn/exponentiation.c" #include "bn/gcd.c" +#include "bn/gcd_extra.c" #include "bn/generic.c" #include "bn/jacobi.c" #include "bn/montgomery.c"
diff --git a/crypto/fipsmodule/bn/div_extra.c b/crypto/fipsmodule/bn/div_extra.c new file mode 100644 index 0000000..7f03f28 --- /dev/null +++ b/crypto/fipsmodule/bn/div_extra.c
@@ -0,0 +1,87 @@ +/* Copyright (c) 2018, Google Inc. + * + * Permission to use, copy, modify, and/or 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. */ + +#include <openssl/bn.h> + +#include <assert.h> + +#include "internal.h" + + +// The following functions use a Barrett reduction variant to avoid leaking the +// numerator. See http://ridiculousfish.com/blog/posts/labor-of-division-episode-i.html +// +// We use 32-bit numerator and 16-bit divisor for simplicity. This allows +// computing |m| and |q| without architecture-specific code. + +// mod_u16 returns |n| mod |d|. |p| and |m| are the "magic numbers" for |d| (see +// reference). For proof of correctness in Coq, see +// https://github.com/davidben/fiat-crypto/blob/barrett/src/Arithmetic/BarrettReduction/RidiculousFish.v +// Note the Coq version of |mod_u16| additionally includes the computation of +// |p| and |m| from |bn_mod_u16_consttime| below. +static uint16_t mod_u16(uint32_t n, uint16_t d, uint32_t p, uint32_t m) { + // Compute floor(n/d) per steps 3 through 5. + uint32_t q = ((uint64_t)m * n) >> 32; + // Note there is a typo in the reference. We right-shift by one, not two. + uint32_t t = ((n - q) >> 1) + q; + t = t >> (p - 1); + + // Multiply and subtract to get the remainder. + n -= d * t; + assert(n < d); + return n; +} + +// shift_and_add_mod_u16 returns |r| * 2^32 + |a| mod |d|. |p| and |m| are the +// "magic numbers" for |d| (see reference). +static uint16_t shift_and_add_mod_u16(uint16_t r, uint32_t a, uint16_t d, + uint32_t p, uint32_t m) { + // Incorporate |a| in two 16-bit chunks. + uint32_t t = r; + t <<= 16; + t |= a >> 16; + t = mod_u16(t, d, p, m); + + t <<= 16; + t |= a & 0xffff; + t = mod_u16(t, d, p, m); + return t; +} + +uint16_t bn_mod_u16_consttime(const BIGNUM *bn, uint16_t d) { + if (d <= 1) { + return 0; + } + + // Compute the "magic numbers" for |d|. See steps 1 and 2. + // This computes p = ceil(log_2(d)). + uint32_t p = BN_num_bits_word(d - 1); + // This operation is not constant-time, but |p| and |d| are public values. + // Note that |p| is at most 16, so the computation fits in |uint64_t|. + assert(p <= 16); + uint32_t m = ((UINT64_C(1) << (32 + p)) + d - 1) / d; + + uint16_t ret = 0; + for (int i = bn->width - 1; i >= 0; i--) { +#if BN_BITS2 == 32 + ret = shift_and_add_mod_u16(ret, bn->d[i], d, p, m); +#elif BN_BITS2 == 64 + ret = shift_and_add_mod_u16(ret, bn->d[i] >> 32, d, p, m); + ret = shift_and_add_mod_u16(ret, bn->d[i] & 0xffffffff, d, p, m); +#else +#error "Unknown BN_ULONG size" +#endif + } + return ret; +}
diff --git a/crypto/fipsmodule/bn/gcd.c b/crypto/fipsmodule/bn/gcd.c index 7868b40..bd0fa6f 100644 --- a/crypto/fipsmodule/bn/gcd.c +++ b/crypto/fipsmodule/bn/gcd.c
@@ -108,316 +108,11 @@ #include <openssl/bn.h> -#include <assert.h> - #include <openssl/err.h> #include "internal.h" -static BN_ULONG word_is_odd_mask(BN_ULONG a) { return (BN_ULONG)0 - (a & 1); } - -static void maybe_rshift1_words(BN_ULONG *a, BN_ULONG mask, BN_ULONG *tmp, - size_t num) { - bn_rshift1_words(tmp, a, num); - bn_select_words(a, mask, tmp, a, num); -} - -static void maybe_rshift1_words_carry(BN_ULONG *a, BN_ULONG carry, - BN_ULONG mask, BN_ULONG *tmp, - size_t num) { - maybe_rshift1_words(a, mask, tmp, num); - if (num != 0) { - carry &= mask; - a[num - 1] |= carry << (BN_BITS2-1); - } -} - -static BN_ULONG maybe_add_words(BN_ULONG *a, BN_ULONG mask, const BN_ULONG *b, - BN_ULONG *tmp, size_t num) { - BN_ULONG carry = bn_add_words(tmp, a, b, num); - bn_select_words(a, mask, tmp, a, num); - return carry & mask; -} - -static int bn_gcd_consttime(BIGNUM *r, unsigned *out_shift, const BIGNUM *x, - const BIGNUM *y, BN_CTX *ctx) { - size_t width = x->width > y->width ? x->width : y->width; - if (width == 0) { - *out_shift = 0; - BN_zero(r); - return 1; - } - - // This is a constant-time implementation of Stein's algorithm (binary GCD). - int ret = 0; - BN_CTX_start(ctx); - BIGNUM *u = BN_CTX_get(ctx); - BIGNUM *v = BN_CTX_get(ctx); - BIGNUM *tmp = BN_CTX_get(ctx); - if (u == NULL || v == NULL || tmp == NULL || - !BN_copy(u, x) || - !BN_copy(v, y) || - !bn_resize_words(u, width) || - !bn_resize_words(v, width) || - !bn_resize_words(tmp, width)) { - goto err; - } - - // Each loop iteration halves at least one of |u| and |v|. Thus we need at - // most the combined bit width of inputs for at least one value to be zero. - unsigned x_bits = x->width * BN_BITS2, y_bits = y->width * BN_BITS2; - unsigned num_iters = x_bits + y_bits; - if (num_iters < x_bits) { - OPENSSL_PUT_ERROR(BN, BN_R_BIGNUM_TOO_LONG); - goto err; - } - - unsigned shift = 0; - for (unsigned i = 0; i < num_iters; i++) { - BN_ULONG both_odd = word_is_odd_mask(u->d[0]) & word_is_odd_mask(v->d[0]); - - // If both |u| and |v| are odd, subtract the smaller from the larger. - BN_ULONG u_less_than_v = - (BN_ULONG)0 - bn_sub_words(tmp->d, u->d, v->d, width); - bn_select_words(u->d, both_odd & ~u_less_than_v, tmp->d, u->d, width); - bn_sub_words(tmp->d, v->d, u->d, width); - bn_select_words(v->d, both_odd & u_less_than_v, tmp->d, v->d, width); - - // At least one of |u| and |v| is now even. - BN_ULONG u_is_odd = word_is_odd_mask(u->d[0]); - BN_ULONG v_is_odd = word_is_odd_mask(v->d[0]); - assert(!(u_is_odd & v_is_odd)); - - // If both are even, the final GCD gains a factor of two. - shift += 1 & (~u_is_odd & ~v_is_odd); - - // Halve any which are even. - maybe_rshift1_words(u->d, ~u_is_odd, tmp->d, width); - maybe_rshift1_words(v->d, ~v_is_odd, tmp->d, width); - } - - // One of |u| or |v| is zero at this point. The algorithm usually makes |u| - // zero, unless |y| was already zero on input. Fix this by combining the - // values. - assert(BN_is_zero(u) || BN_is_zero(v)); - for (size_t i = 0; i < width; i++) { - v->d[i] |= u->d[i]; - } - - *out_shift = shift; - ret = bn_set_words(r, v->d, width); - -err: - BN_CTX_end(ctx); - return ret; -} - -int BN_gcd(BIGNUM *r, const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx) { - unsigned shift; - return bn_gcd_consttime(r, &shift, x, y, ctx) && - BN_lshift(r, r, shift); -} - -int bn_is_relatively_prime(int *out_relatively_prime, const BIGNUM *x, - const BIGNUM *y, BN_CTX *ctx) { - int ret = 0; - BN_CTX_start(ctx); - unsigned shift; - BIGNUM *gcd = BN_CTX_get(ctx); - if (gcd == NULL || - !bn_gcd_consttime(gcd, &shift, x, y, ctx)) { - goto err; - } - - // Check that 2^|shift| * |gcd| is one. - if (gcd->width == 0) { - *out_relatively_prime = 0; - } else { - BN_ULONG mask = shift | (gcd->d[0] ^ 1); - for (int i = 1; i < gcd->width; i++) { - mask |= gcd->d[i]; - } - *out_relatively_prime = mask == 0; - } - ret = 1; - -err: - BN_CTX_end(ctx); - return ret; -} - -int bn_lcm_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) { - BN_CTX_start(ctx); - unsigned shift; - BIGNUM *gcd = BN_CTX_get(ctx); - int ret = gcd != NULL && - bn_mul_consttime(r, a, b, ctx) && - bn_gcd_consttime(gcd, &shift, a, b, ctx) && - bn_div_consttime(r, NULL, r, gcd, ctx) && - bn_rshift_secret_shift(r, r, shift, ctx); - BN_CTX_end(ctx); - return ret; -} - -int bn_mod_inverse_consttime(BIGNUM *r, int *out_no_inverse, const BIGNUM *a, - const BIGNUM *n, BN_CTX *ctx) { - *out_no_inverse = 0; - if (BN_is_negative(a) || BN_ucmp(a, n) >= 0) { - OPENSSL_PUT_ERROR(BN, BN_R_INPUT_NOT_REDUCED); - return 0; - } - if (BN_is_zero(a)) { - if (BN_is_one(n)) { - BN_zero(r); - return 1; - } - *out_no_inverse = 1; - OPENSSL_PUT_ERROR(BN, BN_R_NO_INVERSE); - return 0; - } - - // This is a constant-time implementation of the extended binary GCD - // algorithm. It is adapted from the Handbook of Applied Cryptography, section - // 14.4.3, algorithm 14.51, and modified to bound coefficients and avoid - // negative numbers. - // - // For more details and proof of correctness, see - // https://github.com/mit-plv/fiat-crypto/pull/333. In particular, see |step| - // and |mod_inverse_consttime| for the algorithm in Gallina and see - // |mod_inverse_consttime_spec| for the correctness result. - - if (!BN_is_odd(a) && !BN_is_odd(n)) { - *out_no_inverse = 1; - OPENSSL_PUT_ERROR(BN, BN_R_NO_INVERSE); - return 0; - } - - // This function exists to compute the RSA private exponent, where |a| is one - // word. We'll thus use |a_width| when available. - size_t n_width = n->width, a_width = a->width; - if (a_width > n_width) { - a_width = n_width; - } - - int ret = 0; - BN_CTX_start(ctx); - BIGNUM *u = BN_CTX_get(ctx); - BIGNUM *v = BN_CTX_get(ctx); - BIGNUM *A = BN_CTX_get(ctx); - BIGNUM *B = BN_CTX_get(ctx); - BIGNUM *C = BN_CTX_get(ctx); - BIGNUM *D = BN_CTX_get(ctx); - BIGNUM *tmp = BN_CTX_get(ctx); - BIGNUM *tmp2 = BN_CTX_get(ctx); - if (u == NULL || v == NULL || A == NULL || B == NULL || C == NULL || - D == NULL || tmp == NULL || tmp2 == NULL || - !BN_copy(u, a) || - !BN_copy(v, n) || - !BN_one(A) || - !BN_one(D) || - // For convenience, size |u| and |v| equivalently. - !bn_resize_words(u, n_width) || - !bn_resize_words(v, n_width) || - // |A| and |C| are bounded by |m|. - !bn_resize_words(A, n_width) || - !bn_resize_words(C, n_width) || - // |B| and |D| are bounded by |a|. - !bn_resize_words(B, a_width) || - !bn_resize_words(D, a_width) || - // |tmp| and |tmp2| may be used at either size. - !bn_resize_words(tmp, n_width) || - !bn_resize_words(tmp2, n_width)) { - goto err; - } - - // Each loop iteration halves at least one of |u| and |v|. Thus we need at - // most the combined bit width of inputs for at least one value to be zero. - unsigned a_bits = a_width * BN_BITS2, n_bits = n_width * BN_BITS2; - unsigned num_iters = a_bits + n_bits; - if (num_iters < a_bits) { - OPENSSL_PUT_ERROR(BN, BN_R_BIGNUM_TOO_LONG); - goto err; - } - - // Before and after each loop iteration, the following hold: - // - // u = A*a - B*n - // v = D*n - C*a - // 0 < u <= a - // 0 <= v <= n - // 0 <= A < n - // 0 <= B <= a - // 0 <= C < n - // 0 <= D <= a - // - // After each loop iteration, u and v only get smaller, and at least one of - // them shrinks by at least a factor of two. - for (unsigned i = 0; i < num_iters; i++) { - BN_ULONG both_odd = word_is_odd_mask(u->d[0]) & word_is_odd_mask(v->d[0]); - - // If both |u| and |v| are odd, subtract the smaller from the larger. - BN_ULONG v_less_than_u = - (BN_ULONG)0 - bn_sub_words(tmp->d, v->d, u->d, n_width); - bn_select_words(v->d, both_odd & ~v_less_than_u, tmp->d, v->d, n_width); - bn_sub_words(tmp->d, u->d, v->d, n_width); - bn_select_words(u->d, both_odd & v_less_than_u, tmp->d, u->d, n_width); - - // If we updated one of the values, update the corresponding coefficient. - BN_ULONG carry = bn_add_words(tmp->d, A->d, C->d, n_width); - carry -= bn_sub_words(tmp2->d, tmp->d, n->d, n_width); - bn_select_words(tmp->d, carry, tmp->d, tmp2->d, n_width); - bn_select_words(A->d, both_odd & v_less_than_u, tmp->d, A->d, n_width); - bn_select_words(C->d, both_odd & ~v_less_than_u, tmp->d, C->d, n_width); - - bn_add_words(tmp->d, B->d, D->d, a_width); - bn_sub_words(tmp2->d, tmp->d, a->d, a_width); - bn_select_words(tmp->d, carry, tmp->d, tmp2->d, a_width); - bn_select_words(B->d, both_odd & v_less_than_u, tmp->d, B->d, a_width); - bn_select_words(D->d, both_odd & ~v_less_than_u, tmp->d, D->d, a_width); - - // Our loop invariants hold at this point. Additionally, exactly one of |u| - // and |v| is now even. - BN_ULONG u_is_even = ~word_is_odd_mask(u->d[0]); - BN_ULONG v_is_even = ~word_is_odd_mask(v->d[0]); - assert(u_is_even != v_is_even); - - // Halve the even one and adjust the corresponding coefficient. - maybe_rshift1_words(u->d, u_is_even, tmp->d, n_width); - BN_ULONG A_or_B_is_odd = - word_is_odd_mask(A->d[0]) | word_is_odd_mask(B->d[0]); - BN_ULONG A_carry = - maybe_add_words(A->d, A_or_B_is_odd & u_is_even, n->d, tmp->d, n_width); - BN_ULONG B_carry = - maybe_add_words(B->d, A_or_B_is_odd & u_is_even, a->d, tmp->d, a_width); - maybe_rshift1_words_carry(A->d, A_carry, u_is_even, tmp->d, n_width); - maybe_rshift1_words_carry(B->d, B_carry, u_is_even, tmp->d, a_width); - - maybe_rshift1_words(v->d, v_is_even, tmp->d, n_width); - BN_ULONG C_or_D_is_odd = - word_is_odd_mask(C->d[0]) | word_is_odd_mask(D->d[0]); - BN_ULONG C_carry = - maybe_add_words(C->d, C_or_D_is_odd & v_is_even, n->d, tmp->d, n_width); - BN_ULONG D_carry = - maybe_add_words(D->d, C_or_D_is_odd & v_is_even, a->d, tmp->d, a_width); - maybe_rshift1_words_carry(C->d, C_carry, v_is_even, tmp->d, n_width); - maybe_rshift1_words_carry(D->d, D_carry, v_is_even, tmp->d, a_width); - } - - assert(BN_is_zero(v)); - if (!BN_is_one(u)) { - *out_no_inverse = 1; - OPENSSL_PUT_ERROR(BN, BN_R_NO_INVERSE); - goto err; - } - - ret = BN_copy(r, A) != NULL; - -err: - BN_CTX_end(ctx); - return ret; -} - int BN_mod_inverse_odd(BIGNUM *out, int *out_no_inverse, const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx) { *out_no_inverse = 0;
diff --git a/crypto/fipsmodule/bn/gcd_extra.c b/crypto/fipsmodule/bn/gcd_extra.c new file mode 100644 index 0000000..30540e3 --- /dev/null +++ b/crypto/fipsmodule/bn/gcd_extra.c
@@ -0,0 +1,325 @@ +/* Copyright (c) 2018, Google Inc. + * + * Permission to use, copy, modify, and/or 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. */ + +#include <openssl/bn.h> + +#include <assert.h> + +#include <openssl/err.h> + +#include "internal.h" + + +static BN_ULONG word_is_odd_mask(BN_ULONG a) { return (BN_ULONG)0 - (a & 1); } + +static void maybe_rshift1_words(BN_ULONG *a, BN_ULONG mask, BN_ULONG *tmp, + size_t num) { + bn_rshift1_words(tmp, a, num); + bn_select_words(a, mask, tmp, a, num); +} + +static void maybe_rshift1_words_carry(BN_ULONG *a, BN_ULONG carry, + BN_ULONG mask, BN_ULONG *tmp, + size_t num) { + maybe_rshift1_words(a, mask, tmp, num); + if (num != 0) { + carry &= mask; + a[num - 1] |= carry << (BN_BITS2-1); + } +} + +static BN_ULONG maybe_add_words(BN_ULONG *a, BN_ULONG mask, const BN_ULONG *b, + BN_ULONG *tmp, size_t num) { + BN_ULONG carry = bn_add_words(tmp, a, b, num); + bn_select_words(a, mask, tmp, a, num); + return carry & mask; +} + +static int bn_gcd_consttime(BIGNUM *r, unsigned *out_shift, const BIGNUM *x, + const BIGNUM *y, BN_CTX *ctx) { + size_t width = x->width > y->width ? x->width : y->width; + if (width == 0) { + *out_shift = 0; + BN_zero(r); + return 1; + } + + // This is a constant-time implementation of Stein's algorithm (binary GCD). + int ret = 0; + BN_CTX_start(ctx); + BIGNUM *u = BN_CTX_get(ctx); + BIGNUM *v = BN_CTX_get(ctx); + BIGNUM *tmp = BN_CTX_get(ctx); + if (u == NULL || v == NULL || tmp == NULL || + !BN_copy(u, x) || + !BN_copy(v, y) || + !bn_resize_words(u, width) || + !bn_resize_words(v, width) || + !bn_resize_words(tmp, width)) { + goto err; + } + + // Each loop iteration halves at least one of |u| and |v|. Thus we need at + // most the combined bit width of inputs for at least one value to be zero. + unsigned x_bits = x->width * BN_BITS2, y_bits = y->width * BN_BITS2; + unsigned num_iters = x_bits + y_bits; + if (num_iters < x_bits) { + OPENSSL_PUT_ERROR(BN, BN_R_BIGNUM_TOO_LONG); + goto err; + } + + unsigned shift = 0; + for (unsigned i = 0; i < num_iters; i++) { + BN_ULONG both_odd = word_is_odd_mask(u->d[0]) & word_is_odd_mask(v->d[0]); + + // If both |u| and |v| are odd, subtract the smaller from the larger. + BN_ULONG u_less_than_v = + (BN_ULONG)0 - bn_sub_words(tmp->d, u->d, v->d, width); + bn_select_words(u->d, both_odd & ~u_less_than_v, tmp->d, u->d, width); + bn_sub_words(tmp->d, v->d, u->d, width); + bn_select_words(v->d, both_odd & u_less_than_v, tmp->d, v->d, width); + + // At least one of |u| and |v| is now even. + BN_ULONG u_is_odd = word_is_odd_mask(u->d[0]); + BN_ULONG v_is_odd = word_is_odd_mask(v->d[0]); + assert(!(u_is_odd & v_is_odd)); + + // If both are even, the final GCD gains a factor of two. + shift += 1 & (~u_is_odd & ~v_is_odd); + + // Halve any which are even. + maybe_rshift1_words(u->d, ~u_is_odd, tmp->d, width); + maybe_rshift1_words(v->d, ~v_is_odd, tmp->d, width); + } + + // One of |u| or |v| is zero at this point. The algorithm usually makes |u| + // zero, unless |y| was already zero on input. Fix this by combining the + // values. + assert(BN_is_zero(u) || BN_is_zero(v)); + for (size_t i = 0; i < width; i++) { + v->d[i] |= u->d[i]; + } + + *out_shift = shift; + ret = bn_set_words(r, v->d, width); + +err: + BN_CTX_end(ctx); + return ret; +} + +int BN_gcd(BIGNUM *r, const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx) { + unsigned shift; + return bn_gcd_consttime(r, &shift, x, y, ctx) && + BN_lshift(r, r, shift); +} + +int bn_is_relatively_prime(int *out_relatively_prime, const BIGNUM *x, + const BIGNUM *y, BN_CTX *ctx) { + int ret = 0; + BN_CTX_start(ctx); + unsigned shift; + BIGNUM *gcd = BN_CTX_get(ctx); + if (gcd == NULL || + !bn_gcd_consttime(gcd, &shift, x, y, ctx)) { + goto err; + } + + // Check that 2^|shift| * |gcd| is one. + if (gcd->width == 0) { + *out_relatively_prime = 0; + } else { + BN_ULONG mask = shift | (gcd->d[0] ^ 1); + for (int i = 1; i < gcd->width; i++) { + mask |= gcd->d[i]; + } + *out_relatively_prime = mask == 0; + } + ret = 1; + +err: + BN_CTX_end(ctx); + return ret; +} + +int bn_lcm_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) { + BN_CTX_start(ctx); + unsigned shift; + BIGNUM *gcd = BN_CTX_get(ctx); + int ret = gcd != NULL && + bn_mul_consttime(r, a, b, ctx) && + bn_gcd_consttime(gcd, &shift, a, b, ctx) && + bn_div_consttime(r, NULL, r, gcd, ctx) && + bn_rshift_secret_shift(r, r, shift, ctx); + BN_CTX_end(ctx); + return ret; +} + +int bn_mod_inverse_consttime(BIGNUM *r, int *out_no_inverse, const BIGNUM *a, + const BIGNUM *n, BN_CTX *ctx) { + *out_no_inverse = 0; + if (BN_is_negative(a) || BN_ucmp(a, n) >= 0) { + OPENSSL_PUT_ERROR(BN, BN_R_INPUT_NOT_REDUCED); + return 0; + } + if (BN_is_zero(a)) { + if (BN_is_one(n)) { + BN_zero(r); + return 1; + } + *out_no_inverse = 1; + OPENSSL_PUT_ERROR(BN, BN_R_NO_INVERSE); + return 0; + } + + // This is a constant-time implementation of the extended binary GCD + // algorithm. It is adapted from the Handbook of Applied Cryptography, section + // 14.4.3, algorithm 14.51, and modified to bound coefficients and avoid + // negative numbers. + // + // For more details and proof of correctness, see + // https://github.com/mit-plv/fiat-crypto/pull/333. In particular, see |step| + // and |mod_inverse_consttime| for the algorithm in Gallina and see + // |mod_inverse_consttime_spec| for the correctness result. + + if (!BN_is_odd(a) && !BN_is_odd(n)) { + *out_no_inverse = 1; + OPENSSL_PUT_ERROR(BN, BN_R_NO_INVERSE); + return 0; + } + + // This function exists to compute the RSA private exponent, where |a| is one + // word. We'll thus use |a_width| when available. + size_t n_width = n->width, a_width = a->width; + if (a_width > n_width) { + a_width = n_width; + } + + int ret = 0; + BN_CTX_start(ctx); + BIGNUM *u = BN_CTX_get(ctx); + BIGNUM *v = BN_CTX_get(ctx); + BIGNUM *A = BN_CTX_get(ctx); + BIGNUM *B = BN_CTX_get(ctx); + BIGNUM *C = BN_CTX_get(ctx); + BIGNUM *D = BN_CTX_get(ctx); + BIGNUM *tmp = BN_CTX_get(ctx); + BIGNUM *tmp2 = BN_CTX_get(ctx); + if (u == NULL || v == NULL || A == NULL || B == NULL || C == NULL || + D == NULL || tmp == NULL || tmp2 == NULL || + !BN_copy(u, a) || + !BN_copy(v, n) || + !BN_one(A) || + !BN_one(D) || + // For convenience, size |u| and |v| equivalently. + !bn_resize_words(u, n_width) || + !bn_resize_words(v, n_width) || + // |A| and |C| are bounded by |m|. + !bn_resize_words(A, n_width) || + !bn_resize_words(C, n_width) || + // |B| and |D| are bounded by |a|. + !bn_resize_words(B, a_width) || + !bn_resize_words(D, a_width) || + // |tmp| and |tmp2| may be used at either size. + !bn_resize_words(tmp, n_width) || + !bn_resize_words(tmp2, n_width)) { + goto err; + } + + // Each loop iteration halves at least one of |u| and |v|. Thus we need at + // most the combined bit width of inputs for at least one value to be zero. + unsigned a_bits = a_width * BN_BITS2, n_bits = n_width * BN_BITS2; + unsigned num_iters = a_bits + n_bits; + if (num_iters < a_bits) { + OPENSSL_PUT_ERROR(BN, BN_R_BIGNUM_TOO_LONG); + goto err; + } + + // Before and after each loop iteration, the following hold: + // + // u = A*a - B*n + // v = D*n - C*a + // 0 < u <= a + // 0 <= v <= n + // 0 <= A < n + // 0 <= B <= a + // 0 <= C < n + // 0 <= D <= a + // + // After each loop iteration, u and v only get smaller, and at least one of + // them shrinks by at least a factor of two. + for (unsigned i = 0; i < num_iters; i++) { + BN_ULONG both_odd = word_is_odd_mask(u->d[0]) & word_is_odd_mask(v->d[0]); + + // If both |u| and |v| are odd, subtract the smaller from the larger. + BN_ULONG v_less_than_u = + (BN_ULONG)0 - bn_sub_words(tmp->d, v->d, u->d, n_width); + bn_select_words(v->d, both_odd & ~v_less_than_u, tmp->d, v->d, n_width); + bn_sub_words(tmp->d, u->d, v->d, n_width); + bn_select_words(u->d, both_odd & v_less_than_u, tmp->d, u->d, n_width); + + // If we updated one of the values, update the corresponding coefficient. + BN_ULONG carry = bn_add_words(tmp->d, A->d, C->d, n_width); + carry -= bn_sub_words(tmp2->d, tmp->d, n->d, n_width); + bn_select_words(tmp->d, carry, tmp->d, tmp2->d, n_width); + bn_select_words(A->d, both_odd & v_less_than_u, tmp->d, A->d, n_width); + bn_select_words(C->d, both_odd & ~v_less_than_u, tmp->d, C->d, n_width); + + bn_add_words(tmp->d, B->d, D->d, a_width); + bn_sub_words(tmp2->d, tmp->d, a->d, a_width); + bn_select_words(tmp->d, carry, tmp->d, tmp2->d, a_width); + bn_select_words(B->d, both_odd & v_less_than_u, tmp->d, B->d, a_width); + bn_select_words(D->d, both_odd & ~v_less_than_u, tmp->d, D->d, a_width); + + // Our loop invariants hold at this point. Additionally, exactly one of |u| + // and |v| is now even. + BN_ULONG u_is_even = ~word_is_odd_mask(u->d[0]); + BN_ULONG v_is_even = ~word_is_odd_mask(v->d[0]); + assert(u_is_even != v_is_even); + + // Halve the even one and adjust the corresponding coefficient. + maybe_rshift1_words(u->d, u_is_even, tmp->d, n_width); + BN_ULONG A_or_B_is_odd = + word_is_odd_mask(A->d[0]) | word_is_odd_mask(B->d[0]); + BN_ULONG A_carry = + maybe_add_words(A->d, A_or_B_is_odd & u_is_even, n->d, tmp->d, n_width); + BN_ULONG B_carry = + maybe_add_words(B->d, A_or_B_is_odd & u_is_even, a->d, tmp->d, a_width); + maybe_rshift1_words_carry(A->d, A_carry, u_is_even, tmp->d, n_width); + maybe_rshift1_words_carry(B->d, B_carry, u_is_even, tmp->d, a_width); + + maybe_rshift1_words(v->d, v_is_even, tmp->d, n_width); + BN_ULONG C_or_D_is_odd = + word_is_odd_mask(C->d[0]) | word_is_odd_mask(D->d[0]); + BN_ULONG C_carry = + maybe_add_words(C->d, C_or_D_is_odd & v_is_even, n->d, tmp->d, n_width); + BN_ULONG D_carry = + maybe_add_words(D->d, C_or_D_is_odd & v_is_even, a->d, tmp->d, a_width); + maybe_rshift1_words_carry(C->d, C_carry, v_is_even, tmp->d, n_width); + maybe_rshift1_words_carry(D->d, D_carry, v_is_even, tmp->d, a_width); + } + + assert(BN_is_zero(v)); + if (!BN_is_one(u)) { + *out_no_inverse = 1; + OPENSSL_PUT_ERROR(BN, BN_R_NO_INVERSE); + goto err; + } + + ret = BN_copy(r, A) != NULL; + +err: + BN_CTX_end(ctx); + return ret; +}
diff --git a/crypto/fipsmodule/bn/prime.c b/crypto/fipsmodule/bn/prime.c index 80b33c2..903d6b1 100644 --- a/crypto/fipsmodule/bn/prime.c +++ b/crypto/fipsmodule/bn/prime.c
@@ -532,73 +532,6 @@ return found; } -// The following functions use a Barrett reduction variant to avoid leaking the -// numerator. See http://ridiculousfish.com/blog/posts/labor-of-division-episode-i.html -// -// We use 32-bit numerator and 16-bit divisor for simplicity. This allows -// computing |m| and |q| without architecture-specific code. - -// mod_u16 returns |n| mod |d|. |p| and |m| are the "magic numbers" for |d| (see -// reference). For proof of correctness in Coq, see -// https://github.com/davidben/fiat-crypto/blob/barrett/src/Arithmetic/BarrettReduction/RidiculousFish.v -// Note the Coq version of |mod_u16| additionally includes the computation of -// |p| and |m| from |bn_mod_u16_consttime| below. -static uint16_t mod_u16(uint32_t n, uint16_t d, uint32_t p, uint32_t m) { - // Compute floor(n/d) per steps 3 through 5. - uint32_t q = ((uint64_t)m * n) >> 32; - // Note there is a typo in the reference. We right-shift by one, not two. - uint32_t t = ((n - q) >> 1) + q; - t = t >> (p - 1); - - // Multiply and subtract to get the remainder. - n -= d * t; - assert(n < d); - return n; -} - -// shift_and_add_mod_u16 returns |r| * 2^32 + |a| mod |d|. |p| and |m| are the -// "magic numbers" for |d| (see reference). -static uint16_t shift_and_add_mod_u16(uint16_t r, uint32_t a, uint16_t d, - uint32_t p, uint32_t m) { - // Incorporate |a| in two 16-bit chunks. - uint32_t t = r; - t <<= 16; - t |= a >> 16; - t = mod_u16(t, d, p, m); - - t <<= 16; - t |= a & 0xffff; - t = mod_u16(t, d, p, m); - return t; -} - -uint16_t bn_mod_u16_consttime(const BIGNUM *bn, uint16_t d) { - if (d <= 1) { - return 0; - } - - // Compute the "magic numbers" for |d|. See steps 1 and 2. - // This computes p = ceil(log_2(d)). - uint32_t p = BN_num_bits_word(d - 1); - // This operation is not constant-time, but |p| and |d| are public values. - // Note that |p| is at most 16, so the computation fits in |uint64_t|. - assert(p <= 16); - uint32_t m = ((UINT64_C(1) << (32 + p)) + d - 1) / d; - - uint16_t ret = 0; - for (int i = bn->width - 1; i >= 0; i--) { -#if BN_BITS2 == 32 - ret = shift_and_add_mod_u16(ret, bn->d[i], d, p, m); -#elif BN_BITS2 == 64 - ret = shift_and_add_mod_u16(ret, bn->d[i] >> 32, d, p, m); - ret = shift_and_add_mod_u16(ret, bn->d[i] & 0xffffffff, d, p, m); -#else -#error "Unknown BN_ULONG size" -#endif - } - return ret; -} - static int bn_trial_division(uint16_t *out, const BIGNUM *bn) { const size_t num_primes = num_trial_division_primes(bn); for (size_t i = 1; i < num_primes; i++) {