mirror of https://github.com/openssl/openssl.git
199 lines
8.2 KiB
C
199 lines
8.2 KiB
C
/*
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* Copyright 2024-2025 The OpenSSL Project Authors. All Rights Reserved.
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*
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* Licensed under the Apache License 2.0 (the "License"). You may not use
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* this file except in compliance with the License. You can obtain a copy
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* in the file LICENSE in the source distribution or at
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* https://www.openssl.org/source/license.html
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*/
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#include "ml_dsa_local.h"
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#include "ml_dsa_poly.h"
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/*
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* This file has multiple parts required for fast matrix multiplication,
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* 1) NTT (See https://eprint.iacr.org/2024/585.pdf)
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* NTT and NTT inverse transformations are Discrete Fourier Transforms in a
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* polynomial ring. Fast-Fourier Transformations can then be applied to make
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* multiplications n log(n). This uses the symmetry of the transformation to
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* reduce computations.
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*
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* 2) Montgomery multiplication
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* The multiplication of a.b mod q requires division by q which is a slow operation.
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*
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* When many multiplications mod q are required montgomery multiplication
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* can be used. This requires a number R > q such that R & q are coprime
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* (i.e. GCD(R, q) = 1), so that division happens using R instead of q.
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* If r is a power of 2 then this division can be done as a bit shift.
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*
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* Given that q = 2^23 - 2^13 + 1
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* We can chose a Montgomery multiplier of R = 2^32.
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*
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* To transform |a| into Montgomery form |m| we use
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* m = a mod q * ((2^32)*(2^32) mod q)
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* which is then Montgomery reduced, removing the excess factor of R = 2^32.
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*/
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/*
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* The table in FIPS 204 Appendix B uses the following formula
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* zeta[k]= 1753^bitrev(k) mod q for (k = 1..255) (The first value is not used).
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*
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* As this implementation uses montgomery form with a multiplier of 2^32.
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* The values need to be transformed i.e.
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*
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* zetasMontgomery[k] = reduce_montgomery(zeta[k] * (2^32 * 2^32 mod(q)))
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* reduce_montgomery() is defined below..
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*/
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static const uint32_t zetas_montgomery[256] = {
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4193792, 25847, 5771523, 7861508, 237124, 7602457, 7504169, 466468,
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1826347, 2353451, 8021166, 6288512, 3119733, 5495562, 3111497, 2680103,
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2725464, 1024112, 7300517, 3585928, 7830929, 7260833, 2619752, 6271868,
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6262231, 4520680, 6980856, 5102745, 1757237, 8360995, 4010497, 280005,
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2706023, 95776, 3077325, 3530437, 6718724, 4788269, 5842901, 3915439,
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4519302, 5336701, 3574422, 5512770, 3539968, 8079950, 2348700, 7841118,
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6681150, 6736599, 3505694, 4558682, 3507263, 6239768, 6779997, 3699596,
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811944, 531354, 954230, 3881043, 3900724, 5823537, 2071892, 5582638,
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4450022, 6851714, 4702672, 5339162, 6927966, 3475950, 2176455, 6795196,
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7122806, 1939314, 4296819, 7380215, 5190273, 5223087, 4747489, 126922,
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3412210, 7396998, 2147896, 2715295, 5412772, 4686924, 7969390, 5903370,
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7709315, 7151892, 8357436, 7072248, 7998430, 1349076, 1852771, 6949987,
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5037034, 264944, 508951, 3097992, 44288, 7280319, 904516, 3958618,
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4656075, 8371839, 1653064, 5130689, 2389356, 8169440, 759969, 7063561,
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189548, 4827145, 3159746, 6529015, 5971092, 8202977, 1315589, 1341330,
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1285669, 6795489, 7567685, 6940675, 5361315, 4499357, 4751448, 3839961,
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2091667, 3407706, 2316500, 3817976, 5037939, 2244091, 5933984, 4817955,
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266997, 2434439, 7144689, 3513181, 4860065, 4621053, 7183191, 5187039,
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900702, 1859098, 909542, 819034, 495491, 6767243, 8337157, 7857917,
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7725090, 5257975, 2031748, 3207046, 4823422, 7855319, 7611795, 4784579,
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342297, 286988, 5942594, 4108315, 3437287, 5038140, 1735879, 203044,
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2842341, 2691481, 5790267, 1265009, 4055324, 1247620, 2486353, 1595974,
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4613401, 1250494, 2635921, 4832145, 5386378, 1869119, 1903435, 7329447,
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7047359, 1237275, 5062207, 6950192, 7929317, 1312455, 3306115, 6417775,
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7100756, 1917081, 5834105, 7005614, 1500165, 777191, 2235880, 3406031,
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7838005, 5548557, 6709241, 6533464, 5796124, 4656147, 594136, 4603424,
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6366809, 2432395, 2454455, 8215696, 1957272, 3369112, 185531, 7173032,
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5196991, 162844, 1616392, 3014001, 810149, 1652634, 4686184, 6581310,
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5341501, 3523897, 3866901, 269760, 2213111, 7404533, 1717735, 472078,
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7953734, 1723600, 6577327, 1910376, 6712985, 7276084, 8119771, 4546524,
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5441381, 6144432, 7959518, 6094090, 183443, 7403526, 1612842, 4834730,
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7826001, 3919660, 8332111, 7018208, 3937738, 1400424, 7534263, 1976782
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};
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/*
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* @brief When multiplying 2 numbers mod q that are in montgomery form, the
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* product mod q needs to be multiplied by 2^-32 to be in montgomery form.
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* See FIPS 204, Algorithm 49, MontgomeryReduce()
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* Note it is slightly different due to the input range being positive
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*
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* @param a is the result of a multiply of 2 numbers in montgomery form,
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* in the range 0...(2^32)*q
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* @returns The Montgomery form of 'a' with multiplier 2^32 in the range 0..q-1
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* The result is congruent to x * 2^-32 mod q
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*/
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static uint32_t reduce_montgomery(uint64_t a)
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{
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uint64_t t = (uint32_t)a * (uint32_t)ML_DSA_Q_NEG_INV; /* a * -qinv */
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uint64_t b = a + t * ML_DSA_Q; /* a - t * q */
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uint32_t c = b >> 32; /* /2^32 = 0..2q */
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return reduce_once(c); /* 0..q */
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}
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/*
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* @brief Multiply two polynomials in the number theoretically transformed state.
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* See FIPS 204, Algorithm 45, MultiplyNTT()
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* This function has been modified to use montgomery multiplication
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*
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* @param lhs A polynomial multiplicand
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* @param rhs A polynomial multiplier
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* @param out The returned result of the polynomial multiply
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*/
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void ossl_ml_dsa_poly_ntt_mult(const POLY *lhs, const POLY *rhs, POLY *out)
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{
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int i;
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for (i = 0; i < ML_DSA_NUM_POLY_COEFFICIENTS; i++)
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out->coeff[i] =
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reduce_montgomery((uint64_t)lhs->coeff[i] * (uint64_t)rhs->coeff[i]);
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}
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/*
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* In place number theoretic transform of a given polynomial.
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*
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* See FIPS 204, Algorithm 41, NTT()
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* This function uses montgomery multiplication.
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*
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* @param p a polynomial that is used as the input, that is replaced with
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* the NTT of the polynomial
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*/
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void ossl_ml_dsa_poly_ntt(POLY *p)
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{
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int i, j, k;
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int step;
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int offset = ML_DSA_NUM_POLY_COEFFICIENTS;
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/* Step: 1, 2, 4, 8, ..., 128 */
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for (step = 1; step < ML_DSA_NUM_POLY_COEFFICIENTS; step <<= 1) {
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k = 0;
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offset >>= 1; /* Offset: 128, 64, 32, 16, ..., 1 */
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for (i = 0; i < step; i++) {
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const uint32_t z_step_root = zetas_montgomery[step + i];
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for (j = k; j < k + offset; j++) {
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uint32_t w_even = p->coeff[j];
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uint32_t t_odd =
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reduce_montgomery((uint64_t)z_step_root
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* (uint64_t)p->coeff[j + offset]);
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p->coeff[j] = reduce_once(w_even + t_odd);
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p->coeff[j + offset] = mod_sub(w_even, t_odd);
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}
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k += 2 * offset;
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}
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}
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}
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/*
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* @brief In place inverse number theoretic transform of a given polynomial.
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* See FIPS 204, Algorithm 42, NTT^-1()
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*
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* @param p a polynomial that is used as the input, that is overwritten with
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* the inverse of the NTT.
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*/
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void ossl_ml_dsa_poly_ntt_inverse(POLY *p)
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{
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/*
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* Step: 128, 64, 32, 16, ..., 1
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* Offset: 1, 2, 4, 8, ..., 128
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*/
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int i, j, k, offset, step = ML_DSA_NUM_POLY_COEFFICIENTS;
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/*
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* The multiplicative inverse of 256 mod q, in Montgomery form is
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* ((256^-1 mod q) * ((2^32 * 2^32) mod q)) mod q = (8347681 * 2365951) mod 8380417
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*/
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static const uint32_t inverse_degree_montgomery = 41978;
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for (offset = 1; offset < ML_DSA_NUM_POLY_COEFFICIENTS; offset <<= 1) {
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step >>= 1;
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k = 0;
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for (i = 0; i < step; i++) {
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const uint32_t step_root =
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ML_DSA_Q - zetas_montgomery[step + (step - 1 - i)];
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for (j = k; j < k + offset; j++) {
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uint32_t even = p->coeff[j];
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uint32_t odd = p->coeff[j + offset];
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p->coeff[j] = reduce_once(odd + even);
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p->coeff[j + offset] =
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reduce_montgomery((uint64_t)step_root
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* (uint64_t)(ML_DSA_Q + even - odd));
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}
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k += 2 * offset;
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}
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}
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for (i = 0; i < ML_DSA_NUM_POLY_COEFFICIENTS; i++)
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p->coeff[i] = reduce_montgomery((uint64_t)p->coeff[i] *
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(uint64_t)inverse_degree_montgomery);
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}
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