Elliptic curve scalar multiplication with timing attack defenses

Co-authored-by: Nicola Tuveri <nic.tuv@gmail.com>
Co-authored-by: Cesar Pereida Garcia <cesar.pereidagarcia@tut.fi>
Co-authored-by: Sohaib ul Hassan <soh.19.hassan@gmail.com>

Reviewed-by: Andy Polyakov <appro@openssl.org>
Reviewed-by: Matt Caswell <matt@openssl.org>
(Merged from #6009)

(cherry picked from commit 40e48e5)

crypto/bn/bn_lib.c

@@ -824,6 +824,19 @@ void BN_consttime_swap(BN_ULONG condition, BIGNUM *a, BIGNUM *b, int nwords)
    a->top ^= t;
    b->top ^= t;

    t = (a->neg ^ b->neg) & condition;
    a->neg ^= t;
    b->neg ^= t;

    /*
     * cannot just arbitrarily swap flags.
     * The way a->d is allocated etc.
     * BN_FLG_MALLOCED, BN_FLG_STATIC_DATA, ...
     */
    t = (a->flags ^ b->flags) & condition & BN_FLG_CONSTTIME;
    a->flags ^= t;
    b->flags ^= t;

#define BN_CONSTTIME_SWAP(ind) \
        do { \
                t = (a->d[ind] ^ b->d[ind]) & condition; \

crypto/ec/ec_mult.c

@@ -105,6 +105,166 @@ void EC_ec_pre_comp_free(EC_PRE_COMP *pre)
    OPENSSL_free(pre);
}

#define EC_POINT_set_flags(P, flags) do { \
    BN_set_flags((P)->X, (flags)); \
    BN_set_flags((P)->Y, (flags)); \
    BN_set_flags((P)->Z, (flags)); \
} while(0)

/*
 * This functions computes (in constant time) a point multiplication over the
 * EC group.
 *
 * It performs either a fixed scalar point multiplication
 *          (scalar * generator)
 * when point is NULL, or a generic scalar point multiplication
 *          (scalar * point)
 * when point is not NULL.
 *
 * scalar should be in the range [0,n) otherwise all constant time bets are off.
 *
 * NB: This says nothing about EC_POINT_add and EC_POINT_dbl,
 * which of course are not constant time themselves.
 *
 * The product is stored in r.
 *
 * Returns 1 on success, 0 otherwise.
 */
static int ec_mul_consttime(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
                            const EC_POINT *point, BN_CTX *ctx)
{
    int i, order_bits, group_top, kbit, pbit, Z_is_one, ret;
    ret = 0;
    EC_POINT *s = NULL;
    BIGNUM *k = NULL;
    BIGNUM *lambda = NULL;
    BN_CTX *new_ctx = NULL;

    if (ctx == NULL)
        if ((ctx = new_ctx = BN_CTX_secure_new()) == NULL)
            return 0;

    if ((group->order == NULL) || (group->field == NULL))
        goto err;

    order_bits = BN_num_bits(group->order);

    s = EC_POINT_new(group);
    if (s == NULL)
        goto err;

    if (point == NULL) {
        if (group->generator == NULL)
            goto err;
        if (!EC_POINT_copy(s, group->generator))
            goto err;
    } else {
        if (!EC_POINT_copy(s, point))
            goto err;
    }

    EC_POINT_set_flags(s, BN_FLG_CONSTTIME);

    BN_CTX_start(ctx);
    lambda = BN_CTX_get(ctx);
    k = BN_CTX_get(ctx);
    if (k == NULL)
        goto err;

    /*
     * Group orders are often on a word boundary.
     * So when we pad the scalar, some timing diff might
     * pop if it needs to be expanded due to carries.
     * So expand ahead of time.
     */
    group_top = bn_get_top(group->order);
    if ((bn_wexpand(k, group_top + 1) == NULL)
        || (bn_wexpand(lambda, group_top + 1) == NULL))
        goto err;

    if (!BN_copy(k, scalar))
        goto err;

    BN_set_flags(k, BN_FLG_CONSTTIME);

    if ((BN_num_bits(k) > order_bits) || (BN_is_negative(k))) {
        /*
         * this is an unusual input, and we don't guarantee
         * constant-timeness
         */
        if(!BN_nnmod(k, k, group->order, ctx))
            goto err;
    }

    if (!BN_add(lambda, k, group->order))
        goto err;
    BN_set_flags(lambda, BN_FLG_CONSTTIME);
    if (!BN_add(k, lambda, group->order))
        goto err;
    /*
     * lambda := scalar + order
     * k := scalar + 2*order
     */
    kbit = BN_is_bit_set(lambda, order_bits);
    BN_consttime_swap(kbit, k, lambda, group_top + 1);

    group_top = bn_get_top(group->field);
    if ((bn_wexpand(s->X, group_top) == NULL)
        || (bn_wexpand(s->Y, group_top) == NULL)
        || (bn_wexpand(s->Z, group_top) == NULL)
        || (bn_wexpand(r->X, group_top) == NULL)
        || (bn_wexpand(r->Y, group_top) == NULL)
        || (bn_wexpand(r->Z, group_top) == NULL))
        goto err;

    /* top bit is a 1, in a fixed pos */
    if (!EC_POINT_copy(r, s))
        goto err;

    EC_POINT_set_flags(r, BN_FLG_CONSTTIME);

    if (!EC_POINT_dbl(group, s, s, ctx))
        goto err;

    pbit = 0;

#define EC_POINT_CSWAP(c, a, b, w, t) do {         \
        BN_consttime_swap(c, (a)->X, (b)->X, w);   \
        BN_consttime_swap(c, (a)->Y, (b)->Y, w);   \
        BN_consttime_swap(c, (a)->Z, (b)->Z, w);   \
        t = ((a)->Z_is_one ^ (b)->Z_is_one) & (c); \
        (a)->Z_is_one ^= (t);                      \
        (b)->Z_is_one ^= (t);                      \
} while(0)

    for (i = order_bits - 1; i >= 0; i--) {
        kbit = BN_is_bit_set(k, i) ^ pbit;
        EC_POINT_CSWAP(kbit, r, s, group_top, Z_is_one);
        if (!EC_POINT_add(group, s, r, s, ctx))
            goto err;
        if (!EC_POINT_dbl(group, r, r, ctx))
            goto err;
        /*
         * pbit logic merges this cswap with that of the
         * next iteration
         */
        pbit ^= kbit;
    }
    /* one final cswap to move the right value into r */
    EC_POINT_CSWAP(pbit, r, s, group_top, Z_is_one);
#undef EC_POINT_CSWAP

    ret = 1;

err:
    EC_POINT_free(s);
    BN_CTX_end(ctx);
    BN_CTX_free(new_ctx);

    return ret;
}
#undef EC_POINT_set_flags

/*
 * TODO: table should be optimised for the wNAF-based implementation,
 * sometimes smaller windows will give better performance (thus the
@@ -130,6 +290,28 @@ int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
                size_t num, const EC_POINT *points[], const BIGNUM *scalars[],
                BN_CTX *ctx)
{
    if ((scalar != NULL) && (num == 0)) {
        /* In this case we want to compute scalar * GeneratorPoint:
         * this codepath is reached most prominently by (ephemeral) key
         * generation of EC cryptosystems (i.e. ECDSA keygen and sign setup,
         * ECDH keygen/first half), where the scalar is always secret.
         * This is why we ignore if BN_FLG_CONSTTIME is actually set and we
         * always call the constant time version.
         */
        return ec_mul_consttime(group, r, scalar, NULL, ctx);
    }

    if ((scalar == NULL) && (num == 1)) {
        /* In this case we want to compute scalar * GenericPoint:
         * this codepath is reached most prominently by the second half of
         * ECDH, where the secret scalar is multiplied by the peer's public
         * point.
         * To protect the secret scalar, we ignore if BN_FLG_CONSTTIME is
         * actually set and we always call the constant time version.
         */
        return ec_mul_consttime(group, r, scalars[0], points[0], ctx);
    }

    BN_CTX *new_ctx = NULL;
    const EC_POINT *generator = NULL;
    EC_POINT *tmp = NULL;