rsaz_exp_x2.c
/*
* Copyright 2020-2023 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 <openssl/opensslconf.h>
#include <openssl/crypto.h>
#include "rsaz_exp.h"
#ifndef RSAZ_ENABLED
NON_EMPTY_TRANSLATION_UNIT
#else
# include <assert.h>
# include <string.h>
# 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 ossl_rsaz_amm52x20_x1_256(BN_ULONG *res, const BN_ULONG *base,
const BN_ULONG *exp, const BN_ULONG *m,
BN_ULONG k0);
static 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 ossl_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 ossl_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 ossl_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 = ossl_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);
/* bn_reduce_once_in_place expects number of BN_ULONG, not bit size */
factor_size /= sizeof(BN_ULONG) * 8;
bn_reduce_once_in_place(res1, /*carry=*/0, m1, storage, factor_size);
bn_reduce_once_in_place(res2, /*carry=*/0, m2, storage, factor_size);
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).
*/
static 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 ossl_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) \
ossl_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 */
{
const int rem = BITSIZE_MODULUS % EXP_WIN_SIZE;
BN_ULONG table_idx_mask = EXP_WIN_MASK;
int exp_bit_no = BITSIZE_MODULUS - rem;
int exp_chunk_no = exp_bit_no / 64;
int exp_chunk_shift = exp_bit_no % 64;
BN_ULONG red_table_idx_0, red_table_idx_1;
/*
* If rem == 0, then
* exp_bit_no = modulus_bitsize - exp_win_size
* However, this isn't possible because rem is { 1024, 1536, 2048 } % 5
* which is { 4, 1, 3 } respectively.
*
* If this assertion ever fails the fix above is easy.
*/
OPENSSL_assert(rem != 0);
/* Process 1-st exp window - just init result */
red_table_idx_0 = expz[0][exp_chunk_no];
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;
ossl_extract_multiplier_2x20_win5(red_Y[0], (const BN_ULONG*)red_table,
(int)red_table_idx_0, 0);
ossl_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;
ossl_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;
ossl_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) {
uint64_t digit;
memcpy(&digit, in_str, sizeof(digit));
out[0] = digit & DIGIT_MASK;
in_str += 6;
memcpy(&digit, in_str, sizeof(digit));
out[1] = (digit >> 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 digit;
digit = in[0];
memcpy(out_str, &digit, sizeof(digit));
out_str += 6;
digit = digit >> 48 | in[1] << 4;
memcpy(out_str, &digit, sizeof(digit));
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
