/* * Copyright 2020-2021 The OpenSSL Project Authors. All Rights Reserved. * Copyright (c) 2020, Intel Corporation. All Rights Reserved. * * Licensed under the Apache License 2.0 (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 * * * Originally written by Ilya Albrekht, Sergey Kirillov and Andrey Matyukov * Intel Corporation * */ #include #include "rsaz_exp.h" #ifndef RSAZ_ENABLED NON_EMPTY_TRANSLATION_UNIT #else # include # include # if defined(__GNUC__) # define ALIGN64 __attribute__((aligned(64))) # elif defined(_MSC_VER) # define ALIGN64 __declspec(align(64)) # else # define ALIGN64 # endif # define ALIGN_OF(ptr, boundary) \ ((unsigned char *)(ptr) + (boundary - (((size_t)(ptr)) & (boundary - 1)))) /* Internal radix */ # define DIGIT_SIZE (52) /* 52-bit mask */ # define DIGIT_MASK ((uint64_t)0xFFFFFFFFFFFFF) # define BITS2WORD8_SIZE(x) (((x) + 7) >> 3) # define BITS2WORD64_SIZE(x) (((x) + 63) >> 6) static ossl_inline uint64_t get_digit52(const uint8_t *in, int in_len); static ossl_inline void put_digit52(uint8_t *out, int out_len, uint64_t digit); static void to_words52(BN_ULONG *out, int out_len, const BN_ULONG *in, int in_bitsize); static void from_words52(BN_ULONG *bn_out, int out_bitsize, const BN_ULONG *in); static ossl_inline void set_bit(BN_ULONG *a, int idx); /* Number of |digit_size|-bit digits in |bitsize|-bit value */ static ossl_inline int number_of_digits(int bitsize, int digit_size) { return (bitsize + digit_size - 1) / digit_size; } typedef void (*AMM52)(BN_ULONG *res, const BN_ULONG *base, const BN_ULONG *exp, const BN_ULONG *m, BN_ULONG k0); typedef void (*EXP52_x2)(BN_ULONG *res, const BN_ULONG *base, const BN_ULONG *exp[2], const BN_ULONG *m, const BN_ULONG *rr, const BN_ULONG k0[2]); /* * For details of the methods declared below please refer to * crypto/bn/asm/rsaz-avx512.pl * * Naming notes: * amm = Almost Montgomery Multiplication * ams = Almost Montgomery Squaring * 52x20 - data represented as array of 20 digits in 52-bit radix * _x1_/_x2_ - 1 or 2 independent inputs/outputs * _256 suffix - uses 256-bit (AVX512VL) registers */ /*AMM = Almost Montgomery Multiplication. */ void RSAZ_amm52x20_x1_256(BN_ULONG *res, const BN_ULONG *base, const BN_ULONG *exp, const BN_ULONG *m, BN_ULONG k0); void RSAZ_exp52x20_x2_256(BN_ULONG *res, const BN_ULONG *base, const BN_ULONG *exp[2], const BN_ULONG *m, const BN_ULONG *rr, const BN_ULONG k0[2]); void RSAZ_amm52x20_x2_256(BN_ULONG *out, const BN_ULONG *a, const BN_ULONG *b, const BN_ULONG *m, const BN_ULONG k0[2]); void extract_multiplier_2x20_win5(BN_ULONG *red_Y, const BN_ULONG *red_table, int red_table_idx, int tbl_idx); /* * Dual Montgomery modular exponentiation using prime moduli of the * same bit size, optimized with AVX512 ISA. * * Input and output parameters for each exponentiation are independent and * denoted here by index |i|, i = 1..2. * * Input and output are all in regular 2^64 radix. * * Each moduli shall be |factor_size| bit size. * * NOTE: currently only 2x1024 case is supported. * * [out] res|i| - result of modular exponentiation: array of qword values * in regular (2^64) radix. Size of array shall be enough * to hold |factor_size| bits. * [in] base|i| - base * [in] exp|i| - exponent * [in] m|i| - moduli * [in] rr|i| - Montgomery parameter RR = R^2 mod m|i| * [in] k0_|i| - Montgomery parameter k0 = -1/m|i| mod 2^64 * [in] factor_size - moduli bit size * * \return 0 in case of failure, * 1 in case of success. */ int RSAZ_mod_exp_avx512_x2(BN_ULONG *res1, const BN_ULONG *base1, const BN_ULONG *exp1, const BN_ULONG *m1, const BN_ULONG *rr1, BN_ULONG k0_1, BN_ULONG *res2, const BN_ULONG *base2, const BN_ULONG *exp2, const BN_ULONG *m2, const BN_ULONG *rr2, BN_ULONG k0_2, int factor_size) { int ret = 0; /* * Number of word-size (BN_ULONG) digits to store exponent in redundant * representation. */ int exp_digits = number_of_digits(factor_size + 2, DIGIT_SIZE); int coeff_pow = 4 * (DIGIT_SIZE * exp_digits - factor_size); BN_ULONG *base1_red, *m1_red, *rr1_red; BN_ULONG *base2_red, *m2_red, *rr2_red; BN_ULONG *coeff_red; BN_ULONG *storage = NULL; BN_ULONG *storage_aligned = NULL; BN_ULONG storage_len_bytes = 7 * exp_digits * sizeof(BN_ULONG); /* AMM = Almost Montgomery Multiplication */ AMM52 amm = NULL; /* Dual (2-exps in parallel) exponentiation */ EXP52_x2 exp_x2 = NULL; const BN_ULONG *exp[2] = {0}; BN_ULONG k0[2] = {0}; /* Only 1024-bit factor size is supported now */ switch (factor_size) { case 1024: amm = RSAZ_amm52x20_x1_256; exp_x2 = RSAZ_exp52x20_x2_256; break; default: goto err; } storage = (BN_ULONG *)OPENSSL_malloc(storage_len_bytes + 64); if (storage == NULL) goto err; storage_aligned = (BN_ULONG *)ALIGN_OF(storage, 64); /* Memory layout for red(undant) representations */ base1_red = storage_aligned; base2_red = storage_aligned + 1 * exp_digits; m1_red = storage_aligned + 2 * exp_digits; m2_red = storage_aligned + 3 * exp_digits; rr1_red = storage_aligned + 4 * exp_digits; rr2_red = storage_aligned + 5 * exp_digits; coeff_red = storage_aligned + 6 * exp_digits; /* Convert base_i, m_i, rr_i, from regular to 52-bit radix */ to_words52(base1_red, exp_digits, base1, factor_size); to_words52(base2_red, exp_digits, base2, factor_size); to_words52(m1_red, exp_digits, m1, factor_size); to_words52(m2_red, exp_digits, m2, factor_size); to_words52(rr1_red, exp_digits, rr1, factor_size); to_words52(rr2_red, exp_digits, rr2, factor_size); /* * Compute target domain Montgomery converters RR' for each modulus * based on precomputed original domain's RR. * * RR -> RR' transformation steps: * (1) coeff = 2^k * (2) t = AMM(RR,RR) = RR^2 / R' mod m * (3) RR' = AMM(t, coeff) = RR^2 * 2^k / R'^2 mod m * where * k = 4 * (52 * digits52 - modlen) * R = 2^(64 * ceil(modlen/64)) mod m * RR = R^2 mod M * R' = 2^(52 * ceil(modlen/52)) mod m * * modlen = 1024: k = 64, RR = 2^2048 mod m, RR' = 2^2080 mod m */ memset(coeff_red, 0, exp_digits * sizeof(BN_ULONG)); /* (1) in reduced domain representation */ set_bit(coeff_red, 64 * (int)(coeff_pow / 52) + coeff_pow % 52); amm(rr1_red, rr1_red, rr1_red, m1_red, k0_1); /* (2) for m1 */ amm(rr1_red, rr1_red, coeff_red, m1_red, k0_1); /* (3) for m1 */ amm(rr2_red, rr2_red, rr2_red, m2_red, k0_2); /* (2) for m2 */ amm(rr2_red, rr2_red, coeff_red, m2_red, k0_2); /* (3) for m2 */ exp[0] = exp1; exp[1] = exp2; k0[0] = k0_1; k0[1] = k0_2; exp_x2(rr1_red, base1_red, exp, m1_red, rr1_red, k0); /* Convert rr_i back to regular radix */ from_words52(res1, factor_size, rr1_red); from_words52(res2, factor_size, rr2_red); ret = 1; err: if (storage != NULL) { OPENSSL_cleanse(storage, storage_len_bytes); OPENSSL_free(storage); } return ret; } /* * Dual 1024-bit w-ary modular exponentiation using prime moduli of the same * bit size using Almost Montgomery Multiplication, optimized with AVX512_IFMA * ISA. * * The parameter w (window size) = 5. * * [out] res - result of modular exponentiation: 2x20 qword * values in 2^52 radix. * [in] base - base (2x20 qword values in 2^52 radix) * [in] exp - array of 2 pointers to 16 qword values in 2^64 radix. * Exponent is not converted to redundant representation. * [in] m - moduli (2x20 qword values in 2^52 radix) * [in] rr - Montgomery parameter for 2 moduli: RR = 2^2080 mod m. * (2x20 qword values in 2^52 radix) * [in] k0 - Montgomery parameter for 2 moduli: k0 = -1/m mod 2^64 * * \return (void). */ void RSAZ_exp52x20_x2_256(BN_ULONG *out, /* [2][20] */ const BN_ULONG *base, /* [2][20] */ const BN_ULONG *exp[2], /* 2x16 */ const BN_ULONG *m, /* [2][20] */ const BN_ULONG *rr, /* [2][20] */ const BN_ULONG k0[2]) { # define BITSIZE_MODULUS (1024) # define EXP_WIN_SIZE (5) # define EXP_WIN_MASK ((1U << EXP_WIN_SIZE) - 1) /* * Number of digits (64-bit words) in redundant representation to handle * modulus bits */ # define RED_DIGITS (20) # define EXP_DIGITS (16) # define DAMM RSAZ_amm52x20_x2_256 /* * Squaring is done using multiplication now. That can be a subject of * optimization in future. */ # define DAMS(r,a,m,k0) \ RSAZ_amm52x20_x2_256((r),(a),(a),(m),(k0)) /* Allocate stack for red(undant) result Y and multiplier X */ ALIGN64 BN_ULONG red_Y[2][RED_DIGITS]; ALIGN64 BN_ULONG red_X[2][RED_DIGITS]; /* Allocate expanded exponent */ ALIGN64 BN_ULONG expz[2][EXP_DIGITS + 1]; /* Pre-computed table of base powers */ ALIGN64 BN_ULONG red_table[1U << EXP_WIN_SIZE][2][RED_DIGITS]; int idx; memset(red_Y, 0, sizeof(red_Y)); memset(red_table, 0, sizeof(red_table)); memset(red_X, 0, sizeof(red_X)); /* * Compute table of powers base^i, i = 0, ..., (2^EXP_WIN_SIZE) - 1 * table[0] = mont(x^0) = mont(1) * table[1] = mont(x^1) = mont(x) */ red_X[0][0] = 1; red_X[1][0] = 1; DAMM(red_table[0][0], (const BN_ULONG*)red_X, rr, m, k0); DAMM(red_table[1][0], base, rr, m, k0); for (idx = 1; idx < (int)((1U << EXP_WIN_SIZE) / 2); idx++) { DAMS(red_table[2 * idx + 0][0], red_table[1 * idx][0], m, k0); DAMM(red_table[2 * idx + 1][0], red_table[2 * idx][0], red_table[1][0], m, k0); } /* Copy and expand exponents */ memcpy(expz[0], exp[0], EXP_DIGITS * sizeof(BN_ULONG)); expz[0][EXP_DIGITS] = 0; memcpy(expz[1], exp[1], EXP_DIGITS * sizeof(BN_ULONG)); expz[1][EXP_DIGITS] = 0; /* Exponentiation */ { int rem = BITSIZE_MODULUS % EXP_WIN_SIZE; int delta = rem ? rem : EXP_WIN_SIZE; BN_ULONG table_idx_mask = EXP_WIN_MASK; int exp_bit_no = BITSIZE_MODULUS - delta; int exp_chunk_no = exp_bit_no / 64; int exp_chunk_shift = exp_bit_no % 64; /* Process 1-st exp window - just init result */ BN_ULONG red_table_idx_0 = expz[0][exp_chunk_no]; BN_ULONG red_table_idx_1 = expz[1][exp_chunk_no]; /* * The function operates with fixed moduli sizes divisible by 64, * thus table index here is always in supported range [0, EXP_WIN_SIZE). */ red_table_idx_0 >>= exp_chunk_shift; red_table_idx_1 >>= exp_chunk_shift; extract_multiplier_2x20_win5(red_Y[0], (const BN_ULONG*)red_table, (int)red_table_idx_0, 0); extract_multiplier_2x20_win5(red_Y[1], (const BN_ULONG*)red_table, (int)red_table_idx_1, 1); /* Process other exp windows */ for (exp_bit_no -= EXP_WIN_SIZE; exp_bit_no >= 0; exp_bit_no -= EXP_WIN_SIZE) { /* Extract pre-computed multiplier from the table */ { BN_ULONG T; exp_chunk_no = exp_bit_no / 64; exp_chunk_shift = exp_bit_no % 64; { red_table_idx_0 = expz[0][exp_chunk_no]; T = expz[0][exp_chunk_no + 1]; red_table_idx_0 >>= exp_chunk_shift; /* * Get additional bits from then next quadword * when 64-bit boundaries are crossed. */ if (exp_chunk_shift > 64 - EXP_WIN_SIZE) { T <<= (64 - exp_chunk_shift); red_table_idx_0 ^= T; } red_table_idx_0 &= table_idx_mask; extract_multiplier_2x20_win5(red_X[0], (const BN_ULONG*)red_table, (int)red_table_idx_0, 0); } { red_table_idx_1 = expz[1][exp_chunk_no]; T = expz[1][exp_chunk_no + 1]; red_table_idx_1 >>= exp_chunk_shift; /* * Get additional bits from then next quadword * when 64-bit boundaries are crossed. */ if (exp_chunk_shift > 64 - EXP_WIN_SIZE) { T <<= (64 - exp_chunk_shift); red_table_idx_1 ^= T; } red_table_idx_1 &= table_idx_mask; extract_multiplier_2x20_win5(red_X[1], (const BN_ULONG*)red_table, (int)red_table_idx_1, 1); } } /* Series of squaring */ DAMS((BN_ULONG*)red_Y, (const BN_ULONG*)red_Y, m, k0); DAMS((BN_ULONG*)red_Y, (const BN_ULONG*)red_Y, m, k0); DAMS((BN_ULONG*)red_Y, (const BN_ULONG*)red_Y, m, k0); DAMS((BN_ULONG*)red_Y, (const BN_ULONG*)red_Y, m, k0); DAMS((BN_ULONG*)red_Y, (const BN_ULONG*)red_Y, m, k0); DAMM((BN_ULONG*)red_Y, (const BN_ULONG*)red_Y, (const BN_ULONG*)red_X, m, k0); } } /* * * NB: After the last AMM of exponentiation in Montgomery domain, the result * may be 1025-bit, but the conversion out of Montgomery domain performs an * AMM(x,1) which guarantees that the final result is less than |m|, so no * conditional subtraction is needed here. See "Efficient Software * Implementations of Modular Exponentiation" (by Shay Gueron) paper for details. */ /* Convert result back in regular 2^52 domain */ memset(red_X, 0, sizeof(red_X)); red_X[0][0] = 1; red_X[1][0] = 1; DAMM(out, (const BN_ULONG*)red_Y, (const BN_ULONG*)red_X, m, k0); /* Clear exponents */ OPENSSL_cleanse(expz, sizeof(expz)); OPENSSL_cleanse(red_Y, sizeof(red_Y)); # undef DAMS # undef DAMM # undef EXP_DIGITS # undef RED_DIGITS # undef EXP_WIN_MASK # undef EXP_WIN_SIZE # undef BITSIZE_MODULUS } static ossl_inline uint64_t get_digit52(const uint8_t *in, int in_len) { uint64_t digit = 0; assert(in != NULL); for (; in_len > 0; in_len--) { digit <<= 8; digit += (uint64_t)(in[in_len - 1]); } return digit; } /* * Convert array of words in regular (base=2^64) representation to array of * words in redundant (base=2^52) one. */ static void to_words52(BN_ULONG *out, int out_len, const BN_ULONG *in, int in_bitsize) { uint8_t *in_str = NULL; assert(out != NULL); assert(in != NULL); /* Check destination buffer capacity */ assert(out_len >= number_of_digits(in_bitsize, DIGIT_SIZE)); in_str = (uint8_t *)in; for (; in_bitsize >= (2 * DIGIT_SIZE); in_bitsize -= (2 * DIGIT_SIZE), out += 2) { out[0] = (*(uint64_t *)in_str) & DIGIT_MASK; in_str += 6; out[1] = ((*(uint64_t *)in_str) >> 4) & DIGIT_MASK; in_str += 7; out_len -= 2; } if (in_bitsize > DIGIT_SIZE) { uint64_t digit = get_digit52(in_str, 7); out[0] = digit & DIGIT_MASK; in_str += 6; in_bitsize -= DIGIT_SIZE; digit = get_digit52(in_str, BITS2WORD8_SIZE(in_bitsize)); out[1] = digit >> 4; out += 2; out_len -= 2; } else if (in_bitsize > 0) { out[0] = get_digit52(in_str, BITS2WORD8_SIZE(in_bitsize)); out++; out_len--; } while (out_len > 0) { *out = 0; out_len--; out++; } } static ossl_inline void put_digit52(uint8_t *pStr, int strLen, uint64_t digit) { assert(pStr != NULL); for (; strLen > 0; strLen--) { *pStr++ = (uint8_t)(digit & 0xFF); digit >>= 8; } } /* * Convert array of words in redundant (base=2^52) representation to array of * words in regular (base=2^64) one. */ static void from_words52(BN_ULONG *out, int out_bitsize, const BN_ULONG *in) { int i; int out_len = BITS2WORD64_SIZE(out_bitsize); assert(out != NULL); assert(in != NULL); for (i = 0; i < out_len; i++) out[i] = 0; { uint8_t *out_str = (uint8_t *)out; for (; out_bitsize >= (2 * DIGIT_SIZE); out_bitsize -= (2 * DIGIT_SIZE), in += 2) { (*(uint64_t *)out_str) = in[0]; out_str += 6; (*(uint64_t *)out_str) ^= in[1] << 4; out_str += 7; } if (out_bitsize > DIGIT_SIZE) { put_digit52(out_str, 7, in[0]); out_str += 6; out_bitsize -= DIGIT_SIZE; put_digit52(out_str, BITS2WORD8_SIZE(out_bitsize), (in[1] << 4 | in[0] >> 48)); } else if (out_bitsize) { put_digit52(out_str, BITS2WORD8_SIZE(out_bitsize), in[0]); } } } /* * Set bit at index |idx| in the words array |a|. * It does not do any boundaries checks, make sure the index is valid before * calling the function. */ static ossl_inline void set_bit(BN_ULONG *a, int idx) { assert(a != NULL); { int i, j; i = idx / BN_BITS2; j = idx % BN_BITS2; a[i] |= (((BN_ULONG)1) << j); } } #endif