/*

 * Copyright 2024-2026 The OpenSSL Project Authors. 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

 */

#include "ml_dsa_local.h"

#include "ml_dsa_poly.h"

#include <openssl/crypto.h>

/* Assembly function declarations for AVX2 implementations */

#if !defined(OPENSSL_NO_ASM) && (defined(__x86_64) || defined(__x86_64__) || defined(_M_AMD64) || defined(_M_X64))

#define ML_DSA_NTT_ASM

int ml_dsa_ntt_avx2_capable(void);

void ml_dsa_poly_ntt_avx2(uint32_t *p_coeff, const uint32_t *p_zetas);

void ml_dsa_poly_ntt_inverse_avx2(uint32_t *p_coeff);

void ml_dsa_poly_ntt_mult_avx2(const uint32_t *a, const uint32_t *b, uint32_t *out);

#endif

/*

 * Function pointer types for NTT operations.

 * These allow selecting AVX2 or scalar implementations at initialization time.

 */

typedef void (*ml_dsa_poly_ntt_fn)(POLY *p);

typedef void (*ml_dsa_poly_ntt_inverse_fn)(POLY *p);

typedef void (*ml_dsa_poly_ntt_mult_fn)(const POLY *lhs, const POLY *rhs,

    POLY *out);

/* Forward declarations of scalar NTT functions */

static void poly_ntt_scalar(POLY *p);

static void poly_ntt_inverse_scalar(POLY *p);

static void poly_ntt_mult_scalar(const POLY *lhs, const POLY *rhs, POLY *out);

/*

 * NTT function pointers - initialized to scalar implementations by default.

 */

static ml_dsa_poly_ntt_fn poly_ntt_impl = poly_ntt_scalar;

static ml_dsa_poly_ntt_inverse_fn poly_ntt_inverse_impl = poly_ntt_inverse_scalar;

static ml_dsa_poly_ntt_mult_fn poly_ntt_mult_impl = poly_ntt_mult_scalar;

static CRYPTO_ONCE ml_dsa_ntt_once = CRYPTO_ONCE_STATIC_INIT;

/*

 * This file has multiple parts required for fast matrix multiplication,

 * 1) NTT (See https://eprint.iacr.org/2024/585.pdf)

 * NTT and NTT inverse transformations are Discrete Fourier Transforms in a

 * polynomial ring. Fast-Fourier Transformations can then be applied to make

 * multiplications n log(n). This uses the symmetry of the transformation to

 * reduce computations.

 *

 * 2) Montgomery multiplication

 * The multiplication of a.b mod q requires division by q which is a slow operation.

 *

 * When many multiplications mod q are required montgomery multiplication

 * can be used. This requires a number R > q such that R & q are coprime

 * (i.e. GCD(R, q) = 1), so that division happens using R instead of q.

 * If r is a power of 2 then this division can be done as a bit shift.

 *

 * Given that q = 2^23 - 2^13 + 1

 * We can chose a Montgomery multiplier of R = 2^32.

 *

 * To transform |a| into Montgomery form |m| we use

 *   m = a mod q * ((2^32)*(2^32) mod q)

 * which is then Montgomery reduced, removing the excess factor of R = 2^32.

 */

/*

 * The table in FIPS 204 Appendix B uses the following formula

 * zeta[k]= 1753^bitrev(k) mod q for (k = 1..255) (The first value is not used).

 *

 * As this implementation uses montgomery form with a multiplier of 2^32.

 * The values need to be transformed i.e.

 *

 * zetasMontgomery[k] = reduce_montgomery(zeta[k] * (2^32 * 2^32 mod(q)))

 * reduce_montgomery() is defined below..

 */

static const uint32_t zetas_montgomery[256] = {

    4193792, 25847, 5771523, 7861508, 237124, 7602457, 7504169, 466468,

    1826347, 2353451, 8021166, 6288512, 3119733, 5495562, 3111497, 2680103,

    2725464, 1024112, 7300517, 3585928, 7830929, 7260833, 2619752, 6271868,

    6262231, 4520680, 6980856, 5102745, 1757237, 8360995, 4010497, 280005,

    2706023, 95776, 3077325, 3530437, 6718724, 4788269, 5842901, 3915439,

    4519302, 5336701, 3574422, 5512770, 3539968, 8079950, 2348700, 7841118,

    6681150, 6736599, 3505694, 4558682, 3507263, 6239768, 6779997, 3699596,

    811944, 531354, 954230, 3881043, 3900724, 5823537, 2071892, 5582638,

    4450022, 6851714, 4702672, 5339162, 6927966, 3475950, 2176455, 6795196,

    7122806, 1939314, 4296819, 7380215, 5190273, 5223087, 4747489, 126922,

    3412210, 7396998, 2147896, 2715295, 5412772, 4686924, 7969390, 5903370,

    7709315, 7151892, 8357436, 7072248, 7998430, 1349076, 1852771, 6949987,

    5037034, 264944, 508951, 3097992, 44288, 7280319, 904516, 3958618,

    4656075, 8371839, 1653064, 5130689, 2389356, 8169440, 759969, 7063561,

    189548, 4827145, 3159746, 6529015, 5971092, 8202977, 1315589, 1341330,

    1285669, 6795489, 7567685, 6940675, 5361315, 4499357, 4751448, 3839961,

    2091667, 3407706, 2316500, 3817976, 5037939, 2244091, 5933984, 4817955,

    266997, 2434439, 7144689, 3513181, 4860065, 4621053, 7183191, 5187039,

    900702, 1859098, 909542, 819034, 495491, 6767243, 8337157, 7857917,

    7725090, 5257975, 2031748, 3207046, 4823422, 7855319, 7611795, 4784579,

    342297, 286988, 5942594, 4108315, 3437287, 5038140, 1735879, 203044,

    2842341, 2691481, 5790267, 1265009, 4055324, 1247620, 2486353, 1595974,

    4613401, 1250494, 2635921, 4832145, 5386378, 1869119, 1903435, 7329447,

    7047359, 1237275, 5062207, 6950192, 7929317, 1312455, 3306115, 6417775,

    7100756, 1917081, 5834105, 7005614, 1500165, 777191, 2235880, 3406031,

    7838005, 5548557, 6709241, 6533464, 5796124, 4656147, 594136, 4603424,

    6366809, 2432395, 2454455, 8215696, 1957272, 3369112, 185531, 7173032,

    5196991, 162844, 1616392, 3014001, 810149, 1652634, 4686184, 6581310,

    5341501, 3523897, 3866901, 269760, 2213111, 7404533, 1717735, 472078,

    7953734, 1723600, 6577327, 1910376, 6712985, 7276084, 8119771, 4546524,

    5441381, 6144432, 7959518, 6094090, 183443, 7403526, 1612842, 4834730,

    7826001, 3919660, 8332111, 7018208, 3937738, 1400424, 7534263, 1976782

};

/*

 * @brief When multiplying 2 numbers mod q that are in montgomery form, the

 * product mod q needs to be multiplied by 2^-32 to be in montgomery form.

 * See FIPS 204, Algorithm 49, MontgomeryReduce()

 * Note it is slightly different due to the input range being positive

 *

 * @param a is the result of a multiply of 2 numbers in montgomery form,

 *          in the range 0...(2^32)*q

 * @returns The Montgomery form of 'a' with multiplier 2^32 in the range 0..q-1

 *          The result is congruent to x * 2^-32 mod q

 */

static uint32_t reduce_montgomery(uint64_t a)

{

    uint64_t t = (uint32_t)a * (uint32_t)ML_DSA_Q_NEG_INV; /* a * -qinv */

    uint64_t b = a + t * ML_DSA_Q; /* a - t * q */

    uint32_t c = b >> 32; /* /2^32  = 0..2q */

    return reduce_once(c); /* 0..q */

}

/*

 * Scalar (fallback) implementations of NTT operations.

 * These are used when AVX2 is not available.

 */

static void poly_ntt_mult_scalar(const POLY *lhs, const POLY *rhs, POLY *out)

{

    int i;

    for (i = 0; i < ML_DSA_NUM_POLY_COEFFICIENTS; i++)

        out->coeff[i] = reduce_montgomery((uint64_t)lhs->coeff[i]

            * (uint64_t)rhs->coeff[i]);

}

static void poly_ntt_scalar(POLY *p)

{

    int i, j, k;

    int step;

    int offset = ML_DSA_NUM_POLY_COEFFICIENTS;

    /* Step: 1, 2, 4, 8, ..., 128 */

    for (step = 1; step < ML_DSA_NUM_POLY_COEFFICIENTS; step <<= 1) {

        k = 0;

        offset >>= 1; /* Offset: 128, 64, 32, 16, ..., 1 */

        for (i = 0; i < step; i++) {

            const uint32_t z_step_root = zetas_montgomery[step + i];

            for (j = k; j < k + offset; j++) {

                uint32_t w_even = p->coeff[j];

                uint32_t t_odd = reduce_montgomery((uint64_t)z_step_root

                    * (uint64_t)p->coeff[j + offset]);

                p->coeff[j] = reduce_once(w_even + t_odd);

                p->coeff[j + offset] = mod_sub(w_even, t_odd);

            }

            k += 2 * offset;

        }

    }

}

static void poly_ntt_inverse_scalar(POLY *p)

{

    /*

     * Step: 128, 64, 32, 16, ..., 1

     * Offset: 1, 2, 4, 8, ..., 128

     */

    int i, j, k, offset, step = ML_DSA_NUM_POLY_COEFFICIENTS;

    /*

     * The multiplicative inverse of 256 mod q, in Montgomery form is

     * ((256^-1 mod q) * ((2^32 * 2^32) mod q)) mod q = (8347681 * 2365951) mod 8380417

     */

    static const uint32_t inverse_degree_montgomery = 41978;

    for (offset = 1; offset < ML_DSA_NUM_POLY_COEFFICIENTS; offset <<= 1) {

        step >>= 1;

        k = 0;

        for (i = 0; i < step; i++) {

            const uint32_t step_root = ML_DSA_Q - zetas_montgomery[step + (step - 1 - i)];

            for (j = k; j < k + offset; j++) {

                uint32_t even = p->coeff[j];

                uint32_t odd = p->coeff[j + offset];

                p->coeff[j] = reduce_once(odd + even);

                p->coeff[j + offset] = reduce_montgomery((uint64_t)step_root

                    * (uint64_t)(ML_DSA_Q + even - odd));

            }

            k += 2 * offset;

        }

    }

    for (i = 0; i < ML_DSA_NUM_POLY_COEFFICIENTS; i++)

        p->coeff[i] = reduce_montgomery((uint64_t)p->coeff[i]

            * (uint64_t)inverse_degree_montgomery);

}

/*

 * AVX2 wrapper functions

 */

#ifdef ML_DSA_NTT_ASM

static void poly_ntt_mult_avx2_wrapper(const POLY *lhs, const POLY *rhs,

    POLY *out)

{

    ml_dsa_poly_ntt_mult_avx2(&lhs->coeff[0], &rhs->coeff[0], &out->coeff[0]);

}

static void poly_ntt_avx2_wrapper(POLY *p)

{

    ml_dsa_poly_ntt_avx2(&p->coeff[0], zetas_montgomery);

}

static void poly_ntt_inverse_avx2_wrapper(POLY *p)

{

    ml_dsa_poly_ntt_inverse_avx2(&p->coeff[0]);

}

#endif

/*

 * Initialize NTT function pointers to AVX2 implementations if available.

 * Scalar implementations are used by default.

 */

static void ml_dsa_ntt_init(void)

{

#ifdef ML_DSA_NTT_ASM

    if (ml_dsa_ntt_avx2_capable()) {

        poly_ntt_impl = poly_ntt_avx2_wrapper;

        poly_ntt_inverse_impl = poly_ntt_inverse_avx2_wrapper;

        poly_ntt_mult_impl = poly_ntt_mult_avx2_wrapper;

    }

#endif

}

/*

 * @brief Multiply two polynomials in the number theoretically transformed state.

 * See FIPS 204, Algorithm 45, MultiplyNTT()

 * This function has been modified to use montgomery multiplication

 *

 * @param lhs A polynomial multiplicand

 * @param rhs A polynomial multiplier

 * @param out The returned result of the polynomial multiply

 */

void ossl_ml_dsa_poly_ntt_mult(const POLY *lhs, const POLY *rhs, POLY *out)

{

    (void)CRYPTO_THREAD_run_once(&ml_dsa_ntt_once, ml_dsa_ntt_init);

    poly_ntt_mult_impl(lhs, rhs, out);

}

/*

 * In place number theoretic transform of a given polynomial.

 *

 * See FIPS 204, Algorithm 41, NTT()

 * This function uses montgomery multiplication.

 *

 * @param p a polynomial that is used as the input, that is replaced with

 *        the NTT of the polynomial

 */

void ossl_ml_dsa_poly_ntt(POLY *p)

{

    (void)CRYPTO_THREAD_run_once(&ml_dsa_ntt_once, ml_dsa_ntt_init);

    poly_ntt_impl(p);

}

/*

 * @brief In place inverse number theoretic transform of a given polynomial.

 * See FIPS 204, Algorithm 42,  NTT^-1()

 *

 * @param p a polynomial that is used as the input, that is overwritten with

 *          the inverse of the NTT.

 */

void ossl_ml_dsa_poly_ntt_inverse(POLY *p)

{

    (void)CRYPTO_THREAD_run_once(&ml_dsa_ntt_once, ml_dsa_ntt_init);

    poly_ntt_inverse_impl(p);

}