scalar.c

/*
 * Copyright 2017-2019 The OpenSSL Project Authors. All Rights Reserved.
 * Copyright 2015-2016 Cryptography Research, Inc.
 *
 * 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
 *
 * Originally written by Mike Hamburg
 */
#include <openssl/crypto.h>

#include "word.h"
#include "point_448.h"

static const c448_word_t MONTGOMERY_FACTOR = (c448_word_t) 0x3bd440fae918bc5ULL;
static const curve448_scalar_t sc_p = {
    {
        {
            SC_LIMB(0x2378c292ab5844f3ULL), SC_LIMB(0x216cc2728dc58f55ULL),
            SC_LIMB(0xc44edb49aed63690ULL), SC_LIMB(0xffffffff7cca23e9ULL),
            SC_LIMB(0xffffffffffffffffULL), SC_LIMB(0xffffffffffffffffULL),
            SC_LIMB(0x3fffffffffffffffULL)
        }
    }
}, sc_r2 = {
    {
        {

            SC_LIMB(0xe3539257049b9b60ULL), SC_LIMB(0x7af32c4bc1b195d9ULL),
            SC_LIMB(0x0d66de2388ea1859ULL), SC_LIMB(0xae17cf725ee4d838ULL),
            SC_LIMB(0x1a9cc14ba3c47c44ULL), SC_LIMB(0x2052bcb7e4d070afULL),
            SC_LIMB(0x3402a939f823b729ULL)
        }
    }
};

#define WBITS C448_WORD_BITS   /* NB this may be different from ARCH_WORD_BITS */

const curve448_scalar_t curve448_scalar_one = {{{1}}};
const curve448_scalar_t curve448_scalar_zero = {{{0}}};

/*
 * {extra,accum} - sub +? p
 * Must have extra <= 1
 */
static void sc_subx(curve448_scalar_t out,
                    const c448_word_t accum[C448_SCALAR_LIMBS],
                    const curve448_scalar_t sub,
                    const curve448_scalar_t p, c448_word_t extra)
{
    c448_dsword_t chain = 0;
    unsigned int i;
    c448_word_t borrow;

    for (i = 0; i < C448_SCALAR_LIMBS; i++) {
        chain = (chain + accum[i]) - sub->limb[i];
        out->limb[i] = (c448_word_t)chain;
        chain >>= WBITS;
    }
    borrow = (c448_word_t)chain + extra;     /* = 0 or -1 */

    chain = 0;
    for (i = 0; i < C448_SCALAR_LIMBS; i++) {
        chain = (chain + out->limb[i]) + (p->limb[i] & borrow);
        out->limb[i] = (c448_word_t)chain;
        chain >>= WBITS;
    }
}

static void sc_montmul(curve448_scalar_t out, const curve448_scalar_t a,
                       const curve448_scalar_t b)
{
    unsigned int i, j;
    c448_word_t accum[C448_SCALAR_LIMBS + 1] = { 0 };
    c448_word_t hi_carry = 0;

    for (i = 0; i < C448_SCALAR_LIMBS; i++) {
        c448_word_t mand = a->limb[i];
        const c448_word_t *mier = b->limb;

        c448_dword_t chain = 0;
        for (j = 0; j < C448_SCALAR_LIMBS; j++) {
            chain += ((c448_dword_t) mand) * mier[j] + accum[j];
            accum[j] = (c448_word_t)chain;
            chain >>= WBITS;
        }
        accum[j] = (c448_word_t)chain;

        mand = accum[0] * MONTGOMERY_FACTOR;
        chain = 0;
        mier = sc_p->limb;
        for (j = 0; j < C448_SCALAR_LIMBS; j++) {
            chain += (c448_dword_t) mand *mier[j] + accum[j];
            if (j)
                accum[j - 1] = (c448_word_t)chain;
            chain >>= WBITS;
        }
        chain += accum[j];
        chain += hi_carry;
        accum[j - 1] = (c448_word_t)chain;
        hi_carry = chain >> WBITS;
    }

    sc_subx(out, accum, sc_p, sc_p, hi_carry);
}

void curve448_scalar_mul(curve448_scalar_t out, const curve448_scalar_t a,
                         const curve448_scalar_t b)
{
    sc_montmul(out, a, b);
    sc_montmul(out, out, sc_r2);
}

void curve448_scalar_sub(curve448_scalar_t out, const curve448_scalar_t a,
                         const curve448_scalar_t b)
{
    sc_subx(out, a->limb, b, sc_p, 0);
}

void curve448_scalar_add(curve448_scalar_t out, const curve448_scalar_t a,
                         const curve448_scalar_t b)
{
    c448_dword_t chain = 0;
    unsigned int i;

    for (i = 0; i < C448_SCALAR_LIMBS; i++) {
        chain = (chain + a->limb[i]) + b->limb[i];
        out->limb[i] = (c448_word_t)chain;
        chain >>= WBITS;
    }
    sc_subx(out, out->limb, sc_p, sc_p, (c448_word_t)chain);
}

static ossl_inline void scalar_decode_short(curve448_scalar_t s,
                                            const unsigned char *ser,
                                            size_t nbytes)
{
    size_t i, j, k = 0;

    for (i = 0; i < C448_SCALAR_LIMBS; i++) {
        c448_word_t out = 0;

        for (j = 0; j < sizeof(c448_word_t) && k < nbytes; j++, k++)
            out |= ((c448_word_t) ser[k]) << (8 * j);
        s->limb[i] = out;
    }
}

c448_error_t curve448_scalar_decode(
                                curve448_scalar_t s,
                                const unsigned char ser[C448_SCALAR_BYTES])
{
    unsigned int i;
    c448_dsword_t accum = 0;

    scalar_decode_short(s, ser, C448_SCALAR_BYTES);
    for (i = 0; i < C448_SCALAR_LIMBS; i++)
        accum = (accum + s->limb[i] - sc_p->limb[i]) >> WBITS;
    /* Here accum == 0 or -1 */

    curve448_scalar_mul(s, s, curve448_scalar_one); /* ham-handed reduce */

    return c448_succeed_if(~word_is_zero((uint32_t)accum));
}

void curve448_scalar_destroy(curve448_scalar_t scalar)
{
    OPENSSL_cleanse(scalar, sizeof(curve448_scalar_t));
}

void curve448_scalar_decode_long(curve448_scalar_t s,
                                 const unsigned char *ser, size_t ser_len)
{
    size_t i;
    curve448_scalar_t t1, t2;

    if (ser_len == 0) {
        curve448_scalar_copy(s, curve448_scalar_zero);
        return;
    }

    i = ser_len - (ser_len % C448_SCALAR_BYTES);
    if (i == ser_len)
        i -= C448_SCALAR_BYTES;

    scalar_decode_short(t1, &ser[i], ser_len - i);

    if (ser_len == sizeof(curve448_scalar_t)) {
        assert(i == 0);
        /* ham-handed reduce */
        curve448_scalar_mul(s, t1, curve448_scalar_one);
        curve448_scalar_destroy(t1);
        return;
    }

    while (i) {
        i -= C448_SCALAR_BYTES;
        sc_montmul(t1, t1, sc_r2);
        (void)curve448_scalar_decode(t2, ser + i);
        curve448_scalar_add(t1, t1, t2);
    }

    curve448_scalar_copy(s, t1);
    curve448_scalar_destroy(t1);
    curve448_scalar_destroy(t2);
}

void curve448_scalar_encode(unsigned char ser[C448_SCALAR_BYTES],
                            const curve448_scalar_t s)
{
    unsigned int i, j, k = 0;

    for (i = 0; i < C448_SCALAR_LIMBS; i++) {
        for (j = 0; j < sizeof(c448_word_t); j++, k++)
            ser[k] = s->limb[i] >> (8 * j);
    }
}

void curve448_scalar_halve(curve448_scalar_t out, const curve448_scalar_t a)
{
    c448_word_t mask = 0 - (a->limb[0] & 1);
    c448_dword_t chain = 0;
    unsigned int i;

    for (i = 0; i < C448_SCALAR_LIMBS; i++) {
        chain = (chain + a->limb[i]) + (sc_p->limb[i] & mask);
        out->limb[i] = (c448_word_t)chain;
        chain >>= C448_WORD_BITS;
    }
    for (i = 0; i < C448_SCALAR_LIMBS - 1; i++)
        out->limb[i] = out->limb[i] >> 1 | out->limb[i + 1] << (WBITS - 1);
    out->limb[i] = out->limb[i] >> 1 | (c448_word_t)(chain << (WBITS - 1));
}