/* * Copyright 1995-2022 The OpenSSL Project Authors. All Rights Reserved. * * Licensed under the OpenSSL license (the "License"). You may not use * this file except in compliance with the License. You can obtain a copy * in the file LICENSE in the source distribution or at * https://www.openssl.org/source/license.html */ #include "internal/cryptlib.h" #include "internal/constant_time.h" #include "bn_local.h" #include #ifdef _WIN32 # include # ifndef alloca # define alloca _alloca # endif #elif defined(__GNUC__) # ifndef alloca # define alloca(s) __builtin_alloca((s)) # endif #elif defined(__sun) # include #endif #include "rsaz_exp.h" #undef SPARC_T4_MONT #if defined(OPENSSL_BN_ASM_MONT) && (defined(__sparc__) || defined(__sparc)) # include "sparc_arch.h" extern unsigned int OPENSSL_sparcv9cap_P[]; # define SPARC_T4_MONT #endif /* maximum precomputation table size for *variable* sliding windows */ #define TABLE_SIZE 32 /* this one works - simple but works */ int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx) { int i, bits, ret = 0; BIGNUM *v, *rr; if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0 || BN_get_flags(a, BN_FLG_CONSTTIME) != 0) { /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ BNerr(BN_F_BN_EXP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; } BN_CTX_start(ctx); rr = ((r == a) || (r == p)) ? BN_CTX_get(ctx) : r; v = BN_CTX_get(ctx); if (rr == NULL || v == NULL) goto err; if (BN_copy(v, a) == NULL) goto err; bits = BN_num_bits(p); if (BN_is_odd(p)) { if (BN_copy(rr, a) == NULL) goto err; } else { if (!BN_one(rr)) goto err; } for (i = 1; i < bits; i++) { if (!BN_sqr(v, v, ctx)) goto err; if (BN_is_bit_set(p, i)) { if (!BN_mul(rr, rr, v, ctx)) goto err; } } if (r != rr && BN_copy(r, rr) == NULL) goto err; ret = 1; err: BN_CTX_end(ctx); bn_check_top(r); return ret; } int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m, BN_CTX *ctx) { int ret; bn_check_top(a); bn_check_top(p); bn_check_top(m); /*- * For even modulus m = 2^k*m_odd, it might make sense to compute * a^p mod m_odd and a^p mod 2^k separately (with Montgomery * exponentiation for the odd part), using appropriate exponent * reductions, and combine the results using the CRT. * * For now, we use Montgomery only if the modulus is odd; otherwise, * exponentiation using the reciprocal-based quick remaindering * algorithm is used. * * (Timing obtained with expspeed.c [computations a^p mod m * where a, p, m are of the same length: 256, 512, 1024, 2048, * 4096, 8192 bits], compared to the running time of the * standard algorithm: * * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration] * 55 .. 77 % [UltraSparc processor, but * debug-solaris-sparcv8-gcc conf.] * * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration] * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc] * * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont * at 2048 and more bits, but at 512 and 1024 bits, it was * slower even than the standard algorithm! * * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations] * should be obtained when the new Montgomery reduction code * has been integrated into OpenSSL.) */ #define MONT_MUL_MOD #define MONT_EXP_WORD #define RECP_MUL_MOD #ifdef MONT_MUL_MOD if (BN_is_odd(m)) { # ifdef MONT_EXP_WORD if (a->top == 1 && !a->neg && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0) && (BN_get_flags(a, BN_FLG_CONSTTIME) == 0) && (BN_get_flags(m, BN_FLG_CONSTTIME) == 0)) { BN_ULONG A = a->d[0]; ret = BN_mod_exp_mont_word(r, A, p, m, ctx, NULL); } else # endif ret = BN_mod_exp_mont(r, a, p, m, ctx, NULL); } else #endif #ifdef RECP_MUL_MOD { ret = BN_mod_exp_recp(r, a, p, m, ctx); } #else { ret = BN_mod_exp_simple(r, a, p, m, ctx); } #endif bn_check_top(r); return ret; } int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m, BN_CTX *ctx) { int i, j, bits, ret = 0, wstart, wend, window, wvalue; int start = 1; BIGNUM *aa; /* Table of variables obtained from 'ctx' */ BIGNUM *val[TABLE_SIZE]; BN_RECP_CTX recp; if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0 || BN_get_flags(a, BN_FLG_CONSTTIME) != 0 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) { /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ BNerr(BN_F_BN_MOD_EXP_RECP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; } bits = BN_num_bits(p); if (bits == 0) { /* x**0 mod 1, or x**0 mod -1 is still zero. */ if (BN_abs_is_word(m, 1)) { ret = 1; BN_zero(r); } else { ret = BN_one(r); } return ret; } BN_RECP_CTX_init(&recp); BN_CTX_start(ctx); aa = BN_CTX_get(ctx); val[0] = BN_CTX_get(ctx); if (val[0] == NULL) goto err; if (m->neg) { /* ignore sign of 'm' */ if (!BN_copy(aa, m)) goto err; aa->neg = 0; if (BN_RECP_CTX_set(&recp, aa, ctx) <= 0) goto err; } else { if (BN_RECP_CTX_set(&recp, m, ctx) <= 0) goto err; } if (!BN_nnmod(val[0], a, m, ctx)) goto err; /* 1 */ if (BN_is_zero(val[0])) { BN_zero(r); ret = 1; goto err; } window = BN_window_bits_for_exponent_size(bits); if (window > 1) { if (!BN_mod_mul_reciprocal(aa, val[0], val[0], &recp, ctx)) goto err; /* 2 */ j = 1 << (window - 1); for (i = 1; i < j; i++) { if (((val[i] = BN_CTX_get(ctx)) == NULL) || !BN_mod_mul_reciprocal(val[i], val[i - 1], aa, &recp, ctx)) goto err; } } start = 1; /* This is used to avoid multiplication etc * when there is only the value '1' in the * buffer. */ wvalue = 0; /* The 'value' of the window */ wstart = bits - 1; /* The top bit of the window */ wend = 0; /* The bottom bit of the window */ if (!BN_one(r)) goto err; for (;;) { if (BN_is_bit_set(p, wstart) == 0) { if (!start) if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx)) goto err; if (wstart == 0) break; wstart--; continue; } /* * We now have wstart on a 'set' bit, we now need to work out how bit * a window to do. To do this we need to scan forward until the last * set bit before the end of the window */ j = wstart; wvalue = 1; wend = 0; for (i = 1; i < window; i++) { if (wstart - i < 0) break; if (BN_is_bit_set(p, wstart - i)) { wvalue <<= (i - wend); wvalue |= 1; wend = i; } } /* wend is the size of the current window */ j = wend + 1; /* add the 'bytes above' */ if (!start) for (i = 0; i < j; i++) { if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx)) goto err; } /* wvalue will be an odd number < 2^window */ if (!BN_mod_mul_reciprocal(r, r, val[wvalue >> 1], &recp, ctx)) goto err; /* move the 'window' down further */ wstart -= wend + 1; wvalue = 0; start = 0; if (wstart < 0) break; } ret = 1; err: BN_CTX_end(ctx); BN_RECP_CTX_free(&recp); bn_check_top(r); return ret; } int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont) { int i, j, bits, ret = 0, wstart, wend, window, wvalue; int start = 1; BIGNUM *d, *r; const BIGNUM *aa; /* Table of variables obtained from 'ctx' */ BIGNUM *val[TABLE_SIZE]; BN_MONT_CTX *mont = NULL; if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0 || BN_get_flags(a, BN_FLG_CONSTTIME) != 0 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) { return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont); } bn_check_top(a); bn_check_top(p); bn_check_top(m); if (!BN_is_odd(m)) { BNerr(BN_F_BN_MOD_EXP_MONT, BN_R_CALLED_WITH_EVEN_MODULUS); return 0; } bits = BN_num_bits(p); if (bits == 0) { /* x**0 mod 1, or x**0 mod -1 is still zero. */ if (BN_abs_is_word(m, 1)) { ret = 1; BN_zero(rr); } else { ret = BN_one(rr); } return ret; } BN_CTX_start(ctx); d = BN_CTX_get(ctx); r = BN_CTX_get(ctx); val[0] = BN_CTX_get(ctx); if (val[0] == NULL) goto err; /* * If this is not done, things will break in the montgomery part */ if (in_mont != NULL) mont = in_mont; else { if ((mont = BN_MONT_CTX_new()) == NULL) goto err; if (!BN_MONT_CTX_set(mont, m, ctx)) goto err; } if (a->neg || BN_ucmp(a, m) >= 0) { if (!BN_nnmod(val[0], a, m, ctx)) goto err; aa = val[0]; } else aa = a; if (!bn_to_mont_fixed_top(val[0], aa, mont, ctx)) goto err; /* 1 */ window = BN_window_bits_for_exponent_size(bits); if (window > 1) { if (!bn_mul_mont_fixed_top(d, val[0], val[0], mont, ctx)) goto err; /* 2 */ j = 1 << (window - 1); for (i = 1; i < j; i++) { if (((val[i] = BN_CTX_get(ctx)) == NULL) || !bn_mul_mont_fixed_top(val[i], val[i - 1], d, mont, ctx)) goto err; } } start = 1; /* This is used to avoid multiplication etc * when there is only the value '1' in the * buffer. */ wvalue = 0; /* The 'value' of the window */ wstart = bits - 1; /* The top bit of the window */ wend = 0; /* The bottom bit of the window */ #if 1 /* by Shay Gueron's suggestion */ j = m->top; /* borrow j */ if (m->d[j - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) { if (bn_wexpand(r, j) == NULL) goto err; /* 2^(top*BN_BITS2) - m */ r->d[0] = (0 - m->d[0]) & BN_MASK2; for (i = 1; i < j; i++) r->d[i] = (~m->d[i]) & BN_MASK2; r->top = j; r->flags |= BN_FLG_FIXED_TOP; } else #endif if (!bn_to_mont_fixed_top(r, BN_value_one(), mont, ctx)) goto err; for (;;) { if (BN_is_bit_set(p, wstart) == 0) { if (!start) { if (!bn_mul_mont_fixed_top(r, r, r, mont, ctx)) goto err; } if (wstart == 0) break; wstart--; continue; } /* * We now have wstart on a 'set' bit, we now need to work out how bit * a window to do. To do this we need to scan forward until the last * set bit before the end of the window */ j = wstart; wvalue = 1; wend = 0; for (i = 1; i < window; i++) { if (wstart - i < 0) break; if (BN_is_bit_set(p, wstart - i)) { wvalue <<= (i - wend); wvalue |= 1; wend = i; } } /* wend is the size of the current window */ j = wend + 1; /* add the 'bytes above' */ if (!start) for (i = 0; i < j; i++) { if (!bn_mul_mont_fixed_top(r, r, r, mont, ctx)) goto err; } /* wvalue will be an odd number < 2^window */ if (!bn_mul_mont_fixed_top(r, r, val[wvalue >> 1], mont, ctx)) goto err; /* move the 'window' down further */ wstart -= wend + 1; wvalue = 0; start = 0; if (wstart < 0) break; } /* * Done with zero-padded intermediate BIGNUMs. Final BN_from_montgomery * removes padding [if any] and makes return value suitable for public * API consumer. */ #if defined(SPARC_T4_MONT) if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) { j = mont->N.top; /* borrow j */ val[0]->d[0] = 1; /* borrow val[0] */ for (i = 1; i < j; i++) val[0]->d[i] = 0; val[0]->top = j; if (!BN_mod_mul_montgomery(rr, r, val[0], mont, ctx)) goto err; } else #endif if (!BN_from_montgomery(rr, r, mont, ctx)) goto err; ret = 1; err: if (in_mont == NULL) BN_MONT_CTX_free(mont); BN_CTX_end(ctx); bn_check_top(rr); return ret; } static BN_ULONG bn_get_bits(const BIGNUM *a, int bitpos) { BN_ULONG ret = 0; int wordpos; wordpos = bitpos / BN_BITS2; bitpos %= BN_BITS2; if (wordpos >= 0 && wordpos < a->top) { ret = a->d[wordpos] & BN_MASK2; if (bitpos) { ret >>= bitpos; if (++wordpos < a->top) ret |= a->d[wordpos] << (BN_BITS2 - bitpos); } } return ret & BN_MASK2; } /* * BN_mod_exp_mont_consttime() stores the precomputed powers in a specific * layout so that accessing any of these table values shows the same access * pattern as far as cache lines are concerned. The following functions are * used to transfer a BIGNUM from/to that table. */ static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top, unsigned char *buf, int idx, int window) { int i, j; int width = 1 << window; BN_ULONG *table = (BN_ULONG *)buf; if (top > b->top) top = b->top; /* this works because 'buf' is explicitly * zeroed */ for (i = 0, j = idx; i < top; i++, j += width) { table[j] = b->d[i]; } return 1; } static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top, unsigned char *buf, int idx, int window) { int i, j; int width = 1 << window; /* * We declare table 'volatile' in order to discourage compiler * from reordering loads from the table. Concern is that if * reordered in specific manner loads might give away the * information we are trying to conceal. Some would argue that * compiler can reorder them anyway, but it can as well be * argued that doing so would be violation of standard... */ volatile BN_ULONG *table = (volatile BN_ULONG *)buf; if (bn_wexpand(b, top) == NULL) return 0; if (window <= 3) { for (i = 0; i < top; i++, table += width) { BN_ULONG acc = 0; for (j = 0; j < width; j++) { acc |= table[j] & ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1)); } b->d[i] = acc; } } else { int xstride = 1 << (window - 2); BN_ULONG y0, y1, y2, y3; i = idx >> (window - 2); /* equivalent of idx / xstride */ idx &= xstride - 1; /* equivalent of idx % xstride */ y0 = (BN_ULONG)0 - (constant_time_eq_int(i,0)&1); y1 = (BN_ULONG)0 - (constant_time_eq_int(i,1)&1); y2 = (BN_ULONG)0 - (constant_time_eq_int(i,2)&1); y3 = (BN_ULONG)0 - (constant_time_eq_int(i,3)&1); for (i = 0; i < top; i++, table += width) { BN_ULONG acc = 0; for (j = 0; j < xstride; j++) { acc |= ( (table[j + 0 * xstride] & y0) | (table[j + 1 * xstride] & y1) | (table[j + 2 * xstride] & y2) | (table[j + 3 * xstride] & y3) ) & ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1)); } b->d[i] = acc; } } b->top = top; b->flags |= BN_FLG_FIXED_TOP; return 1; } /* * Given a pointer value, compute the next address that is a cache line * multiple. */ #define MOD_EXP_CTIME_ALIGN(x_) \ ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK)))) /* * This variant of BN_mod_exp_mont() uses fixed windows and the special * precomputation memory layout to limit data-dependency to a minimum to * protect secret exponents (cf. the hyper-threading timing attacks pointed * out by Colin Percival, * http://www.daemonology.net/hyperthreading-considered-harmful/) */ int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont) { int i, bits, ret = 0, window, wvalue, wmask, window0; int top; BN_MONT_CTX *mont = NULL; int numPowers; unsigned char *powerbufFree = NULL; int powerbufLen = 0; unsigned char *powerbuf = NULL; BIGNUM tmp, am; #if defined(SPARC_T4_MONT) unsigned int t4 = 0; #endif bn_check_top(a); bn_check_top(p); bn_check_top(m); if (!BN_is_odd(m)) { BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME, BN_R_CALLED_WITH_EVEN_MODULUS); return 0; } top = m->top; /* * Use all bits stored in |p|, rather than |BN_num_bits|, so we do not leak * whether the top bits are zero. */ bits = p->top * BN_BITS2; if (bits == 0) { /* x**0 mod 1, or x**0 mod -1 is still zero. */ if (BN_abs_is_word(m, 1)) { ret = 1; BN_zero(rr); } else { ret = BN_one(rr); } return ret; } BN_CTX_start(ctx); /* * Allocate a montgomery context if it was not supplied by the caller. If * this is not done, things will break in the montgomery part. */ if (in_mont != NULL) mont = in_mont; else { if ((mont = BN_MONT_CTX_new()) == NULL) goto err; if (!BN_MONT_CTX_set(mont, m, ctx)) goto err; } if (a->neg || BN_ucmp(a, m) >= 0) { BIGNUM *reduced = BN_CTX_get(ctx); if (reduced == NULL || !BN_nnmod(reduced, a, m, ctx)) { goto err; } a = reduced; } #ifdef RSAZ_ENABLED /* * If the size of the operands allow it, perform the optimized * RSAZ exponentiation. For further information see * crypto/bn/rsaz_exp.c and accompanying assembly modules. */ if ((16 == a->top) && (16 == p->top) && (BN_num_bits(m) == 1024) && rsaz_avx2_eligible()) { if (NULL == bn_wexpand(rr, 16)) goto err; RSAZ_1024_mod_exp_avx2(rr->d, a->d, p->d, m->d, mont->RR.d, mont->n0[0]); rr->top = 16; rr->neg = 0; bn_correct_top(rr); ret = 1; goto err; } else if ((8 == a->top) && (8 == p->top) && (BN_num_bits(m) == 512)) { if (NULL == bn_wexpand(rr, 8)) goto err; RSAZ_512_mod_exp(rr->d, a->d, p->d, m->d, mont->n0[0], mont->RR.d); rr->top = 8; rr->neg = 0; bn_correct_top(rr); ret = 1; goto err; } #endif /* Get the window size to use with size of p. */ window = BN_window_bits_for_ctime_exponent_size(bits); #if defined(SPARC_T4_MONT) if (window >= 5 && (top & 15) == 0 && top <= 64 && (OPENSSL_sparcv9cap_P[1] & (CFR_MONTMUL | CFR_MONTSQR)) == (CFR_MONTMUL | CFR_MONTSQR) && (t4 = OPENSSL_sparcv9cap_P[0])) window = 5; else #endif #if defined(OPENSSL_BN_ASM_MONT5) if (window >= 5) { window = 5; /* ~5% improvement for RSA2048 sign, and even * for RSA4096 */ /* reserve space for mont->N.d[] copy */ powerbufLen += top * sizeof(mont->N.d[0]); } #endif (void)0; /* * Allocate a buffer large enough to hold all of the pre-computed powers * of am, am itself and tmp. */ numPowers = 1 << window; powerbufLen += sizeof(m->d[0]) * (top * numPowers + ((2 * top) > numPowers ? (2 * top) : numPowers)); #ifdef alloca if (powerbufLen < 3072) powerbufFree = alloca(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH); else #endif if ((powerbufFree = OPENSSL_malloc(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH)) == NULL) goto err; powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree); memset(powerbuf, 0, powerbufLen); #ifdef alloca if (powerbufLen < 3072) powerbufFree = NULL; #endif /* lay down tmp and am right after powers table */ tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers); am.d = tmp.d + top; tmp.top = am.top = 0; tmp.dmax = am.dmax = top; tmp.neg = am.neg = 0; tmp.flags = am.flags = BN_FLG_STATIC_DATA; /* prepare a^0 in Montgomery domain */ #if 1 /* by Shay Gueron's suggestion */ if (m->d[top - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) { /* 2^(top*BN_BITS2) - m */ tmp.d[0] = (0 - m->d[0]) & BN_MASK2; for (i = 1; i < top; i++) tmp.d[i] = (~m->d[i]) & BN_MASK2; tmp.top = top; } else #endif if (!bn_to_mont_fixed_top(&tmp, BN_value_one(), mont, ctx)) goto err; /* prepare a^1 in Montgomery domain */ if (!bn_to_mont_fixed_top(&am, a, mont, ctx)) goto err; #if defined(SPARC_T4_MONT) if (t4) { typedef int (*bn_pwr5_mont_f) (BN_ULONG *tp, const BN_ULONG *np, const BN_ULONG *n0, const void *table, int power, int bits); int bn_pwr5_mont_t4_8(BN_ULONG *tp, const BN_ULONG *np, const BN_ULONG *n0, const void *table, int power, int bits); int bn_pwr5_mont_t4_16(BN_ULONG *tp, const BN_ULONG *np, const BN_ULONG *n0, const void *table, int power, int bits); int bn_pwr5_mont_t4_24(BN_ULONG *tp, const BN_ULONG *np, const BN_ULONG *n0, const void *table, int power, int bits); int bn_pwr5_mont_t4_32(BN_ULONG *tp, const BN_ULONG *np, const BN_ULONG *n0, const void *table, int power, int bits); static const bn_pwr5_mont_f pwr5_funcs[4] = { bn_pwr5_mont_t4_8, bn_pwr5_mont_t4_16, bn_pwr5_mont_t4_24, bn_pwr5_mont_t4_32 }; bn_pwr5_mont_f pwr5_worker = pwr5_funcs[top / 16 - 1]; typedef int (*bn_mul_mont_f) (BN_ULONG *rp, const BN_ULONG *ap, const void *bp, const BN_ULONG *np, const BN_ULONG *n0); int bn_mul_mont_t4_8(BN_ULONG *rp, const BN_ULONG *ap, const void *bp, const BN_ULONG *np, const BN_ULONG *n0); int bn_mul_mont_t4_16(BN_ULONG *rp, const BN_ULONG *ap, const void *bp, const BN_ULONG *np, const BN_ULONG *n0); int bn_mul_mont_t4_24(BN_ULONG *rp, const BN_ULONG *ap, const void *bp, const BN_ULONG *np, const BN_ULONG *n0); int bn_mul_mont_t4_32(BN_ULONG *rp, const BN_ULONG *ap, const void *bp, const BN_ULONG *np, const BN_ULONG *n0); static const bn_mul_mont_f mul_funcs[4] = { bn_mul_mont_t4_8, bn_mul_mont_t4_16, bn_mul_mont_t4_24, bn_mul_mont_t4_32 }; bn_mul_mont_f mul_worker = mul_funcs[top / 16 - 1]; void bn_mul_mont_vis3(BN_ULONG *rp, const BN_ULONG *ap, const void *bp, const BN_ULONG *np, const BN_ULONG *n0, int num); void bn_mul_mont_t4(BN_ULONG *rp, const BN_ULONG *ap, const void *bp, const BN_ULONG *np, const BN_ULONG *n0, int num); void bn_mul_mont_gather5_t4(BN_ULONG *rp, const BN_ULONG *ap, const void *table, const BN_ULONG *np, const BN_ULONG *n0, int num, int power); void bn_flip_n_scatter5_t4(const BN_ULONG *inp, size_t num, void *table, size_t power); void bn_gather5_t4(BN_ULONG *out, size_t num, void *table, size_t power); void bn_flip_t4(BN_ULONG *dst, BN_ULONG *src, size_t num); BN_ULONG *np = mont->N.d, *n0 = mont->n0; int stride = 5 * (6 - (top / 16 - 1)); /* multiple of 5, but less * than 32 */ /* * BN_to_montgomery can contaminate words above .top [in * BN_DEBUG[_DEBUG] build]... */ for (i = am.top; i < top; i++) am.d[i] = 0; for (i = tmp.top; i < top; i++) tmp.d[i] = 0; bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 0); bn_flip_n_scatter5_t4(am.d, top, powerbuf, 1); if (!(*mul_worker) (tmp.d, am.d, am.d, np, n0) && !(*mul_worker) (tmp.d, am.d, am.d, np, n0)) bn_mul_mont_vis3(tmp.d, am.d, am.d, np, n0, top); bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 2); for (i = 3; i < 32; i++) { /* Calculate a^i = a^(i-1) * a */ if (!(*mul_worker) (tmp.d, tmp.d, am.d, np, n0) && !(*mul_worker) (tmp.d, tmp.d, am.d, np, n0)) bn_mul_mont_vis3(tmp.d, tmp.d, am.d, np, n0, top); bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, i); } /* switch to 64-bit domain */ np = alloca(top * sizeof(BN_ULONG)); top /= 2; bn_flip_t4(np, mont->N.d, top); /* * The exponent may not have a whole number of fixed-size windows. * To simplify the main loop, the initial window has between 1 and * full-window-size bits such that what remains is always a whole * number of windows */ window0 = (bits - 1) % 5 + 1; wmask = (1 << window0) - 1; bits -= window0; wvalue = bn_get_bits(p, bits) & wmask; bn_gather5_t4(tmp.d, top, powerbuf, wvalue); /* * Scan the exponent one window at a time starting from the most * significant bits. */ while (bits > 0) { if (bits < stride) stride = bits; bits -= stride; wvalue = bn_get_bits(p, bits); if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride)) continue; /* retry once and fall back */ if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride)) continue; bits += stride - 5; wvalue >>= stride - 5; wvalue &= 31; bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top); bn_mul_mont_gather5_t4(tmp.d, tmp.d, powerbuf, np, n0, top, wvalue); } bn_flip_t4(tmp.d, tmp.d, top); top *= 2; /* back to 32-bit domain */ tmp.top = top; bn_correct_top(&tmp); OPENSSL_cleanse(np, top * sizeof(BN_ULONG)); } else #endif #if defined(OPENSSL_BN_ASM_MONT5) if (window == 5 && top > 1) { /* * This optimization uses ideas from https://eprint.iacr.org/2011/239, * specifically optimization of cache-timing attack countermeasures, * pre-computation optimization, and Almost Montgomery Multiplication. * * The paper discusses a 4-bit window to optimize 512-bit modular * exponentiation, used in RSA-1024 with CRT, but RSA-1024 is no longer * important. * * |bn_mul_mont_gather5| and |bn_power5| implement the "almost" * reduction variant, so the values here may not be fully reduced. * They are bounded by R (i.e. they fit in |top| words), not |m|. * Additionally, we pass these "almost" reduced inputs into * |bn_mul_mont|, which implements the normal reduction variant. * Given those inputs, |bn_mul_mont| may not give reduced * output, but it will still produce "almost" reduced output. */ void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap, const void *table, const BN_ULONG *np, const BN_ULONG *n0, int num, int power); void bn_scatter5(const BN_ULONG *inp, size_t num, void *table, size_t power); void bn_gather5(BN_ULONG *out, size_t num, void *table, size_t power); void bn_power5(BN_ULONG *rp, const BN_ULONG *ap, const void *table, const BN_ULONG *np, const BN_ULONG *n0, int num, int power); int bn_get_bits5(const BN_ULONG *ap, int off); BN_ULONG *n0 = mont->n0, *np; /* * BN_to_montgomery can contaminate words above .top [in * BN_DEBUG[_DEBUG] build]... */ for (i = am.top; i < top; i++) am.d[i] = 0; for (i = tmp.top; i < top; i++) tmp.d[i] = 0; /* * copy mont->N.d[] to improve cache locality */ for (np = am.d + top, i = 0; i < top; i++) np[i] = mont->N.d[i]; bn_scatter5(tmp.d, top, powerbuf, 0); bn_scatter5(am.d, am.top, powerbuf, 1); bn_mul_mont(tmp.d, am.d, am.d, np, n0, top); bn_scatter5(tmp.d, top, powerbuf, 2); # if 0 for (i = 3; i < 32; i++) { /* Calculate a^i = a^(i-1) * a */ bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); bn_scatter5(tmp.d, top, powerbuf, i); } # else /* same as above, but uses squaring for 1/2 of operations */ for (i = 4; i < 32; i *= 2) { bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); bn_scatter5(tmp.d, top, powerbuf, i); } for (i = 3; i < 8; i += 2) { int j; bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); bn_scatter5(tmp.d, top, powerbuf, i); for (j = 2 * i; j < 32; j *= 2) { bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); bn_scatter5(tmp.d, top, powerbuf, j); } } for (; i < 16; i += 2) { bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); bn_scatter5(tmp.d, top, powerbuf, i); bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); bn_scatter5(tmp.d, top, powerbuf, 2 * i); } for (; i < 32; i += 2) { bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1); bn_scatter5(tmp.d, top, powerbuf, i); } # endif /* * The exponent may not have a whole number of fixed-size windows. * To simplify the main loop, the initial window has between 1 and * full-window-size bits such that what remains is always a whole * number of windows */ window0 = (bits - 1) % 5 + 1; wmask = (1 << window0) - 1; bits -= window0; wvalue = bn_get_bits(p, bits) & wmask; bn_gather5(tmp.d, top, powerbuf, wvalue); /* * Scan the exponent one window at a time starting from the most * significant bits. */ if (top & 7) { while (bits > 0) { bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top); bn_mul_mont_gather5(tmp.d, tmp.d, powerbuf, np, n0, top, bn_get_bits5(p->d, bits -= 5)); } } else { while (bits > 0) { bn_power5(tmp.d, tmp.d, powerbuf, np, n0, top, bn_get_bits5(p->d, bits -= 5)); } } tmp.top = top; /* * The result is now in |tmp| in Montgomery form, but it may not be * fully reduced. This is within bounds for |BN_from_montgomery| * (tmp < R <= m*R) so it will, when converting from Montgomery form, * produce a fully reduced result. * * This differs from Figure 2 of the paper, which uses AMM(h, 1) to * convert from Montgomery form with unreduced output, followed by an * extra reduction step. In the paper's terminology, we replace * steps 9 and 10 with MM(h, 1). */ } else #endif { if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, window)) goto err; if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, window)) goto err; /* * If the window size is greater than 1, then calculate * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even * powers could instead be computed as (a^(i/2))^2 to use the slight * performance advantage of sqr over mul). */ if (window > 1) { if (!bn_mul_mont_fixed_top(&tmp, &am, &am, mont, ctx)) goto err; if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2, window)) goto err; for (i = 3; i < numPowers; i++) { /* Calculate a^i = a^(i-1) * a */ if (!bn_mul_mont_fixed_top(&tmp, &am, &tmp, mont, ctx)) goto err; if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i, window)) goto err; } } /* * The exponent may not have a whole number of fixed-size windows. * To simplify the main loop, the initial window has between 1 and * full-window-size bits such that what remains is always a whole * number of windows */ window0 = (bits - 1) % window + 1; wmask = (1 << window0) - 1; bits -= window0; wvalue = bn_get_bits(p, bits) & wmask; if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp, top, powerbuf, wvalue, window)) goto err; wmask = (1 << window) - 1; /* * Scan the exponent one window at a time starting from the most * significant bits. */ while (bits > 0) { /* Square the result window-size times */ for (i = 0; i < window; i++) if (!bn_mul_mont_fixed_top(&tmp, &tmp, &tmp, mont, ctx)) goto err; /* * Get a window's worth of bits from the exponent * This avoids calling BN_is_bit_set for each bit, which * is not only slower but also makes each bit vulnerable to * EM (and likely other) side-channel attacks like One&Done * (for details see "One&Done: A Single-Decryption EM-Based * Attack on OpenSSL's Constant-Time Blinded RSA" by M. Alam, * H. Khan, M. Dey, N. Sinha, R. Callan, A. Zajic, and * M. Prvulovic, in USENIX Security'18) */ bits -= window; wvalue = bn_get_bits(p, bits) & wmask; /* * Fetch the appropriate pre-computed value from the pre-buf */ if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue, window)) goto err; /* Multiply the result into the intermediate result */ if (!bn_mul_mont_fixed_top(&tmp, &tmp, &am, mont, ctx)) goto err; } } /* * Done with zero-padded intermediate BIGNUMs. Final BN_from_montgomery * removes padding [if any] and makes return value suitable for public * API consumer. */ #if defined(SPARC_T4_MONT) if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) { am.d[0] = 1; /* borrow am */ for (i = 1; i < top; i++) am.d[i] = 0; if (!BN_mod_mul_montgomery(rr, &tmp, &am, mont, ctx)) goto err; } else #endif if (!BN_from_montgomery(rr, &tmp, mont, ctx)) goto err; ret = 1; err: if (in_mont == NULL) BN_MONT_CTX_free(mont); if (powerbuf != NULL) { OPENSSL_cleanse(powerbuf, powerbufLen); OPENSSL_free(powerbufFree); } BN_CTX_end(ctx); return ret; } int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p, const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont) { BN_MONT_CTX *mont = NULL; int b, bits, ret = 0; int r_is_one; BN_ULONG w, next_w; BIGNUM *r, *t; BIGNUM *swap_tmp; #define BN_MOD_MUL_WORD(r, w, m) \ (BN_mul_word(r, (w)) && \ (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \ (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1)))) /* * BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is * probably more overhead than always using BN_mod (which uses BN_copy if * a similar test returns true). */ /* * We can use BN_mod and do not need BN_nnmod because our accumulator is * never negative (the result of BN_mod does not depend on the sign of * the modulus). */ #define BN_TO_MONTGOMERY_WORD(r, w, mont) \ (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx)) if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) { /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ BNerr(BN_F_BN_MOD_EXP_MONT_WORD, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; } bn_check_top(p); bn_check_top(m); if (!BN_is_odd(m)) { BNerr(BN_F_BN_MOD_EXP_MONT_WORD, BN_R_CALLED_WITH_EVEN_MODULUS); return 0; } if (m->top == 1) a %= m->d[0]; /* make sure that 'a' is reduced */ bits = BN_num_bits(p); if (bits == 0) { /* x**0 mod 1, or x**0 mod -1 is still zero. */ if (BN_abs_is_word(m, 1)) { ret = 1; BN_zero(rr); } else { ret = BN_one(rr); } return ret; } if (a == 0) { BN_zero(rr); ret = 1; return ret; } BN_CTX_start(ctx); r = BN_CTX_get(ctx); t = BN_CTX_get(ctx); if (t == NULL) goto err; if (in_mont != NULL) mont = in_mont; else { if ((mont = BN_MONT_CTX_new()) == NULL) goto err; if (!BN_MONT_CTX_set(mont, m, ctx)) goto err; } r_is_one = 1; /* except for Montgomery factor */ /* bits-1 >= 0 */ /* The result is accumulated in the product r*w. */ w = a; /* bit 'bits-1' of 'p' is always set */ for (b = bits - 2; b >= 0; b--) { /* First, square r*w. */ next_w = w * w; if ((next_w / w) != w) { /* overflow */ if (r_is_one) { if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err; r_is_one = 0; } else { if (!BN_MOD_MUL_WORD(r, w, m)) goto err; } next_w = 1; } w = next_w; if (!r_is_one) { if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) goto err; } /* Second, multiply r*w by 'a' if exponent bit is set. */ if (BN_is_bit_set(p, b)) { next_w = w * a; if ((next_w / a) != w) { /* overflow */ if (r_is_one) { if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err; r_is_one = 0; } else { if (!BN_MOD_MUL_WORD(r, w, m)) goto err; } next_w = a; } w = next_w; } } /* Finally, set r:=r*w. */ if (w != 1) { if (r_is_one) { if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err; r_is_one = 0; } else { if (!BN_MOD_MUL_WORD(r, w, m)) goto err; } } if (r_is_one) { /* can happen only if a == 1 */ if (!BN_one(rr)) goto err; } else { if (!BN_from_montgomery(rr, r, mont, ctx)) goto err; } ret = 1; err: if (in_mont == NULL) BN_MONT_CTX_free(mont); BN_CTX_end(ctx); bn_check_top(rr); return ret; } /* The old fallback, simple version :-) */ int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m, BN_CTX *ctx) { int i, j, bits, ret = 0, wstart, wend, window, wvalue; int start = 1; BIGNUM *d; /* Table of variables obtained from 'ctx' */ BIGNUM *val[TABLE_SIZE]; if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0 || BN_get_flags(a, BN_FLG_CONSTTIME) != 0 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) { /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ BNerr(BN_F_BN_MOD_EXP_SIMPLE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; } bits = BN_num_bits(p); if (bits == 0) { /* x**0 mod 1, or x**0 mod -1 is still zero. */ if (BN_abs_is_word(m, 1)) { ret = 1; BN_zero(r); } else { ret = BN_one(r); } return ret; } BN_CTX_start(ctx); d = BN_CTX_get(ctx); val[0] = BN_CTX_get(ctx); if (val[0] == NULL) goto err; if (!BN_nnmod(val[0], a, m, ctx)) goto err; /* 1 */ if (BN_is_zero(val[0])) { BN_zero(r); ret = 1; goto err; } window = BN_window_bits_for_exponent_size(bits); if (window > 1) { if (!BN_mod_mul(d, val[0], val[0], m, ctx)) goto err; /* 2 */ j = 1 << (window - 1); for (i = 1; i < j; i++) { if (((val[i] = BN_CTX_get(ctx)) == NULL) || !BN_mod_mul(val[i], val[i - 1], d, m, ctx)) goto err; } } start = 1; /* This is used to avoid multiplication etc * when there is only the value '1' in the * buffer. */ wvalue = 0; /* The 'value' of the window */ wstart = bits - 1; /* The top bit of the window */ wend = 0; /* The bottom bit of the window */ if (!BN_one(r)) goto err; for (;;) { if (BN_is_bit_set(p, wstart) == 0) { if (!start) if (!BN_mod_mul(r, r, r, m, ctx)) goto err; if (wstart == 0) break; wstart--; continue; } /* * We now have wstart on a 'set' bit, we now need to work out how bit * a window to do. To do this we need to scan forward until the last * set bit before the end of the window */ j = wstart; wvalue = 1; wend = 0; for (i = 1; i < window; i++) { if (wstart - i < 0) break; if (BN_is_bit_set(p, wstart - i)) { wvalue <<= (i - wend); wvalue |= 1; wend = i; } } /* wend is the size of the current window */ j = wend + 1; /* add the 'bytes above' */ if (!start) for (i = 0; i < j; i++) { if (!BN_mod_mul(r, r, r, m, ctx)) goto err; } /* wvalue will be an odd number < 2^window */ if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx)) goto err; /* move the 'window' down further */ wstart -= wend + 1; wvalue = 0; start = 0; if (wstart < 0) break; } ret = 1; err: BN_CTX_end(ctx); bn_check_top(r); return ret; }