/*

 * Copyright 2017-2023 The OpenSSL Project Authors. All Rights Reserved.

 * Copyright 2015-2016 Cryptography Research, Inc.

 *

 * 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 Mike Hamburg

 */

#include <openssl/crypto.h>

#include "word.h"

#include "field.h"

#include "point_448.h"

#include "ed448.h"

#include "crypto/ecx.h"

#include "curve448_local.h"

#define COFACTOR 4

#define C448_WNAF_FIXED_TABLE_BITS 5

#define C448_WNAF_VAR_TABLE_BITS 3

#define EDWARDS_D       (-39081)

static const curve448_scalar_t precomputed_scalarmul_adjustment = {

    {

        {

            SC_LIMB(0xc873d6d54a7bb0cfULL), SC_LIMB(0xe933d8d723a70aadULL),

            SC_LIMB(0xbb124b65129c96fdULL), SC_LIMB(0x00000008335dc163ULL)

        }

    }

};

#define TWISTED_D (EDWARDS_D - 1)

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

/* Inverse. */

static void gf_invert(gf y, const gf x, int assert_nonzero)

{

    mask_t ret;

    gf t1, t2;

    ossl_gf_sqr(t1, x);              /* o^2 */

    ret = gf_isr(t2, t1);       /* +-1/sqrt(o^2) = +-1/o */

    (void)ret;

    if (assert_nonzero)

        assert(ret);

    ossl_gf_sqr(t1, t2);

    ossl_gf_mul(t2, t1, x);          /* not direct to y in case of alias. */

    gf_copy(y, t2);

}

/** identity = (0,1) */

const curve448_point_t ossl_curve448_point_identity =

    { {{{{0}}}, {{{1}}}, {{{1}}}, {{{0}}}} };

static void point_double_internal(curve448_point_t p, const curve448_point_t q,

                                  int before_double)

{

    gf a, b, c, d;

    ossl_gf_sqr(c, q->x);

    ossl_gf_sqr(a, q->y);

    gf_add_nr(d, c, a);         /* 2+e */

    gf_add_nr(p->t, q->y, q->x); /* 2+e */

    ossl_gf_sqr(b, p->t);

    gf_subx_nr(b, b, d, 3);     /* 4+e */

    gf_sub_nr(p->t, a, c);      /* 3+e */

    ossl_gf_sqr(p->x, q->z);

    gf_add_nr(p->z, p->x, p->x); /* 2+e */

    gf_subx_nr(a, p->z, p->t, 4); /* 6+e */

    if (GF_HEADROOM == 5)

        gf_weak_reduce(a);      /* or 1+e */

    ossl_gf_mul(p->x, a, b);

    ossl_gf_mul(p->z, p->t, a);

    ossl_gf_mul(p->y, p->t, d);

    if (!before_double)

        ossl_gf_mul(p->t, b, d);

}

void ossl_curve448_point_double(curve448_point_t p, const curve448_point_t q)

{

    point_double_internal(p, q, 0);

}

/* Operations on [p]niels */

static ossl_inline void cond_neg_niels(niels_t n, mask_t neg)

{

    gf_cond_swap(n->a, n->b, neg);

    gf_cond_neg(n->c, neg);

}

static void pt_to_pniels(pniels_t b, const curve448_point_t a)

{

    gf_sub(b->n->a, a->y, a->x);

    gf_add(b->n->b, a->x, a->y);

    gf_mulw(b->n->c, a->t, 2 * TWISTED_D);

    gf_add(b->z, a->z, a->z);

}

static void pniels_to_pt(curve448_point_t e, const pniels_t d)

{

    gf eu;

    gf_add(eu, d->n->b, d->n->a);

    gf_sub(e->y, d->n->b, d->n->a);

    ossl_gf_mul(e->t, e->y, eu);

    ossl_gf_mul(e->x, d->z, e->y);

    ossl_gf_mul(e->y, d->z, eu);

    ossl_gf_sqr(e->z, d->z);

}

static void niels_to_pt(curve448_point_t e, const niels_t n)

{

    gf_add(e->y, n->b, n->a);

    gf_sub(e->x, n->b, n->a);

    ossl_gf_mul(e->t, e->y, e->x);

    gf_copy(e->z, ONE);

}

static void add_niels_to_pt(curve448_point_t d, const niels_t e,

                            int before_double)

{

    gf a, b, c;

    gf_sub_nr(b, d->y, d->x);   /* 3+e */

    ossl_gf_mul(a, e->a, b);

    gf_add_nr(b, d->x, d->y);   /* 2+e */

    ossl_gf_mul(d->y, e->b, b);

    ossl_gf_mul(d->x, e->c, d->t);

    gf_add_nr(c, a, d->y);      /* 2+e */

    gf_sub_nr(b, d->y, a);      /* 3+e */

    gf_sub_nr(d->y, d->z, d->x); /* 3+e */

    gf_add_nr(a, d->x, d->z);   /* 2+e */

    ossl_gf_mul(d->z, a, d->y);

    ossl_gf_mul(d->x, d->y, b);

    ossl_gf_mul(d->y, a, c);

    if (!before_double)

        ossl_gf_mul(d->t, b, c);

}

static void sub_niels_from_pt(curve448_point_t d, const niels_t e,

                              int before_double)

{

    gf a, b, c;

    gf_sub_nr(b, d->y, d->x);   /* 3+e */

    ossl_gf_mul(a, e->b, b);

    gf_add_nr(b, d->x, d->y);   /* 2+e */

    ossl_gf_mul(d->y, e->a, b);

    ossl_gf_mul(d->x, e->c, d->t);

    gf_add_nr(c, a, d->y);      /* 2+e */

    gf_sub_nr(b, d->y, a);      /* 3+e */

    gf_add_nr(d->y, d->z, d->x); /* 2+e */

    gf_sub_nr(a, d->z, d->x);   /* 3+e */

    ossl_gf_mul(d->z, a, d->y);

    ossl_gf_mul(d->x, d->y, b);

    ossl_gf_mul(d->y, a, c);

    if (!before_double)

        ossl_gf_mul(d->t, b, c);

}

static void add_pniels_to_pt(curve448_point_t p, const pniels_t pn,

                             int before_double)

{

    gf L0;

    ossl_gf_mul(L0, p->z, pn->z);

    gf_copy(p->z, L0);

    add_niels_to_pt(p, pn->n, before_double);

}

static void sub_pniels_from_pt(curve448_point_t p, const pniels_t pn,

                               int before_double)

{

    gf L0;

    ossl_gf_mul(L0, p->z, pn->z);

    gf_copy(p->z, L0);

    sub_niels_from_pt(p, pn->n, before_double);

}

c448_bool_t

ossl_curve448_point_eq(const curve448_point_t p,

                       const curve448_point_t q)

{

    mask_t succ;

    gf a, b;

    /* equality mod 2-torsion compares x/y */

    ossl_gf_mul(a, p->y, q->x);

    ossl_gf_mul(b, q->y, p->x);

    succ = gf_eq(a, b);

    return mask_to_bool(succ);

}

c448_bool_t

ossl_curve448_point_valid(const curve448_point_t p)

{

    mask_t out;

    gf a, b, c;

    ossl_gf_mul(a, p->x, p->y);

    ossl_gf_mul(b, p->z, p->t);

    out = gf_eq(a, b);

    ossl_gf_sqr(a, p->x);

    ossl_gf_sqr(b, p->y);

    gf_sub(a, b, a);

    ossl_gf_sqr(b, p->t);

    gf_mulw(c, b, TWISTED_D);

    ossl_gf_sqr(b, p->z);

    gf_add(b, b, c);

    out &= gf_eq(a, b);

    out &= ~gf_eq(p->z, ZERO);

    return mask_to_bool(out);

}

static ossl_inline void constant_time_lookup_niels(niels_s * RESTRICT ni,

                                                   const niels_t *table,

                                                   int nelts, int idx)

{

    constant_time_lookup(ni, table, sizeof(niels_s), nelts, idx);

}

void

ossl_curve448_precomputed_scalarmul(curve448_point_t out,

                                    const curve448_precomputed_s *table,

                                    const curve448_scalar_t scalar)

{

    unsigned int i, j, k;

    const unsigned int n = COMBS_N, t = COMBS_T, s = COMBS_S;

    niels_t ni;

    curve448_scalar_t scalar1x;

    ossl_curve448_scalar_add(scalar1x, scalar, precomputed_scalarmul_adjustment);

    ossl_curve448_scalar_halve(scalar1x, scalar1x);

    for (i = s; i > 0; i--) {

        if (i != s)

            point_double_internal(out, out, 0);

        for (j = 0; j < n; j++) {

            int tab = 0;

            mask_t invert;

            for (k = 0; k < t; k++) {

                unsigned int bit = (i - 1) + s * (k + j * t);

                if (bit < C448_SCALAR_BITS)

                    tab |=

                        (scalar1x->limb[bit / WBITS] >> (bit % WBITS) & 1) << k;

            }

            invert = (tab >> (t - 1)) - 1;

            tab ^= invert;

            tab &= (1 << (t - 1)) - 1;

            constant_time_lookup_niels(ni, &table->table[j << (t - 1)],

                                       1 << (t - 1), tab);

            cond_neg_niels(ni, invert);

            if ((i != s) || j != 0)

                add_niels_to_pt(out, ni, j == n - 1 && i != 1);

            else

                niels_to_pt(out, ni);

        }

    }

    OPENSSL_cleanse(ni, sizeof(ni));

    OPENSSL_cleanse(scalar1x, sizeof(scalar1x));

}

void

ossl_curve448_point_mul_by_ratio_and_encode_like_eddsa(

                                    uint8_t enc[EDDSA_448_PUBLIC_BYTES],

                                    const curve448_point_t p)

{

    gf x, y, z, t;

    curve448_point_t q;

    /* The point is now on the twisted curve.  Move it to untwisted. */

    curve448_point_copy(q, p);

    {

        /* 4-isogeny: 2xy/(y^+x^2), (y^2-x^2)/(2z^2-y^2+x^2) */

        gf u;

        ossl_gf_sqr(x, q->x);

        ossl_gf_sqr(t, q->y);

        gf_add(u, x, t);

        gf_add(z, q->y, q->x);

        ossl_gf_sqr(y, z);

        gf_sub(y, y, u);

        gf_sub(z, t, x);

        ossl_gf_sqr(x, q->z);

        gf_add(t, x, x);

        gf_sub(t, t, z);

        ossl_gf_mul(x, t, y);

        ossl_gf_mul(y, z, u);

        ossl_gf_mul(z, u, t);

        OPENSSL_cleanse(u, sizeof(u));

    }

    /* Affinize */

    gf_invert(z, z, 1);

    ossl_gf_mul(t, x, z);

    ossl_gf_mul(x, y, z);

    /* Encode */

    enc[EDDSA_448_PRIVATE_BYTES - 1] = 0;

    gf_serialize(enc, x, 1);

    enc[EDDSA_448_PRIVATE_BYTES - 1] |= 0x80 & gf_lobit(t);

    OPENSSL_cleanse(x, sizeof(x));

    OPENSSL_cleanse(y, sizeof(y));

    OPENSSL_cleanse(z, sizeof(z));

    OPENSSL_cleanse(t, sizeof(t));

    ossl_curve448_point_destroy(q);

}

c448_error_t

ossl_curve448_point_decode_like_eddsa_and_mul_by_ratio(

                                curve448_point_t p,

                                const uint8_t enc[EDDSA_448_PUBLIC_BYTES])

{

    uint8_t enc2[EDDSA_448_PUBLIC_BYTES];

    mask_t low;

    mask_t succ;

    memcpy(enc2, enc, sizeof(enc2));

    low = ~word_is_zero(enc2[EDDSA_448_PRIVATE_BYTES - 1] & 0x80);

    enc2[EDDSA_448_PRIVATE_BYTES - 1] &= ~0x80;

    succ = gf_deserialize(p->y, enc2, 1, 0);

    succ &= word_is_zero(enc2[EDDSA_448_PRIVATE_BYTES - 1]);

    ossl_gf_sqr(p->x, p->y);

    gf_sub(p->z, ONE, p->x);    /* num = 1-y^2 */

    gf_mulw(p->t, p->x, EDWARDS_D); /* dy^2 */

    gf_sub(p->t, ONE, p->t);    /* denom = 1-dy^2 or 1-d + dy^2 */

    ossl_gf_mul(p->x, p->z, p->t);

    succ &= gf_isr(p->t, p->x); /* 1/sqrt(num * denom) */

    ossl_gf_mul(p->x, p->t, p->z);   /* sqrt(num / denom) */

    gf_cond_neg(p->x, gf_lobit(p->x) ^ low);

    gf_copy(p->z, ONE);

    {

        gf a, b, c, d;

        /* 4-isogeny 2xy/(y^2-ax^2), (y^2+ax^2)/(2-y^2-ax^2) */

        ossl_gf_sqr(c, p->x);

        ossl_gf_sqr(a, p->y);

        gf_add(d, c, a);

        gf_add(p->t, p->y, p->x);

        ossl_gf_sqr(b, p->t);

        gf_sub(b, b, d);

        gf_sub(p->t, a, c);

        ossl_gf_sqr(p->x, p->z);

        gf_add(p->z, p->x, p->x);

        gf_sub(a, p->z, d);

        ossl_gf_mul(p->x, a, b);

        ossl_gf_mul(p->z, p->t, a);

        ossl_gf_mul(p->y, p->t, d);

        ossl_gf_mul(p->t, b, d);

        OPENSSL_cleanse(a, sizeof(a));

        OPENSSL_cleanse(b, sizeof(b));

        OPENSSL_cleanse(c, sizeof(c));

        OPENSSL_cleanse(d, sizeof(d));

    }

    OPENSSL_cleanse(enc2, sizeof(enc2));

    assert(ossl_curve448_point_valid(p) || ~succ);

    return c448_succeed_if(mask_to_bool(succ));

}

c448_error_t

ossl_x448_int(uint8_t out[X_PUBLIC_BYTES],

              const uint8_t base[X_PUBLIC_BYTES],

              const uint8_t scalar[X_PRIVATE_BYTES])

{

    gf x1, x2, z2, x3, z3, t1, t2;

    int t;

    mask_t swap = 0;

    mask_t nz;

    (void)gf_deserialize(x1, base, 1, 0);

    gf_copy(x2, ONE);

    gf_copy(z2, ZERO);

    gf_copy(x3, x1);

    gf_copy(z3, ONE);

    for (t = X_PRIVATE_BITS - 1; t >= 0; t--) {

        uint8_t sb = scalar[t / 8];

        mask_t k_t;

        /* Scalar conditioning */

        if (t / 8 == 0)

            sb &= -(uint8_t)COFACTOR;

        else if (t == X_PRIVATE_BITS - 1)

            sb = -1;

        k_t = (sb >> (t % 8)) & 1;

        k_t = 0 - k_t;             /* set to all 0s or all 1s */

        swap ^= k_t;

        gf_cond_swap(x2, x3, swap);

        gf_cond_swap(z2, z3, swap);

        swap = k_t;

        /*

         * The "_nr" below skips coefficient reduction. In the following

         * comments, "2+e" is saying that the coefficients are at most 2+epsilon

         * times the reduction limit.

         */

        gf_add_nr(t1, x2, z2);  /* A = x2 + z2 */ /* 2+e */

        gf_sub_nr(t2, x2, z2);  /* B = x2 - z2 */ /* 3+e */

        gf_sub_nr(z2, x3, z3);  /* D = x3 - z3 */ /* 3+e */

        ossl_gf_mul(x2, t1, z2);     /* DA */

        gf_add_nr(z2, z3, x3);  /* C = x3 + z3 */ /* 2+e */

        ossl_gf_mul(x3, t2, z2);     /* CB */

        gf_sub_nr(z3, x2, x3);  /* DA-CB */ /* 3+e */

        ossl_gf_sqr(z2, z3);         /* (DA-CB)^2 */

        ossl_gf_mul(z3, x1, z2);     /* z3 = x1(DA-CB)^2 */

        gf_add_nr(z2, x2, x3);  /* (DA+CB) */ /* 2+e */

        ossl_gf_sqr(x3, z2);         /* x3 = (DA+CB)^2 */

        ossl_gf_sqr(z2, t1);         /* AA = A^2 */

        ossl_gf_sqr(t1, t2);         /* BB = B^2 */

        ossl_gf_mul(x2, z2, t1);     /* x2 = AA*BB */

        gf_sub_nr(t2, z2, t1);  /* E = AA-BB */ /* 3+e */

        gf_mulw(t1, t2, -EDWARDS_D); /* E*-d = a24*E */

        gf_add_nr(t1, t1, z2);  /* AA + a24*E */ /* 2+e */

        ossl_gf_mul(z2, t2, t1);     /* z2 = E(AA+a24*E) */

    }

    /* Finish */

    gf_cond_swap(x2, x3, swap);

    gf_cond_swap(z2, z3, swap);

    gf_invert(z2, z2, 0);

    ossl_gf_mul(x1, x2, z2);

    gf_serialize(out, x1, 1);

    nz = ~gf_eq(x1, ZERO);

    OPENSSL_cleanse(x1, sizeof(x1));

    OPENSSL_cleanse(x2, sizeof(x2));

    OPENSSL_cleanse(z2, sizeof(z2));

    OPENSSL_cleanse(x3, sizeof(x3));

    OPENSSL_cleanse(z3, sizeof(z3));

    OPENSSL_cleanse(t1, sizeof(t1));

    OPENSSL_cleanse(t2, sizeof(t2));

    return c448_succeed_if(mask_to_bool(nz));

}

void

ossl_curve448_point_mul_by_ratio_and_encode_like_x448(uint8_t

                                                      out[X_PUBLIC_BYTES],

                                                      const curve448_point_t p)

{

    curve448_point_t q;

    curve448_point_copy(q, p);

    gf_invert(q->t, q->x, 0);   /* 1/x */

    ossl_gf_mul(q->z, q->t, q->y);   /* y/x */

    ossl_gf_sqr(q->y, q->z);         /* (y/x)^2 */

    gf_serialize(out, q->y, 1);

    ossl_curve448_point_destroy(q);

}

void ossl_x448_derive_public_key(uint8_t out[X_PUBLIC_BYTES],

                                 const uint8_t scalar[X_PRIVATE_BYTES])

{

    /* Scalar conditioning */

    uint8_t scalar2[X_PRIVATE_BYTES];

    curve448_scalar_t the_scalar;

    curve448_point_t p;

    unsigned int i;

    memcpy(scalar2, scalar, sizeof(scalar2));

    scalar2[0] &= -(uint8_t)COFACTOR;

    scalar2[X_PRIVATE_BYTES - 1] &= ~((0u - 1u) << ((X_PRIVATE_BITS + 7) % 8));

    scalar2[X_PRIVATE_BYTES - 1] |= 1 << ((X_PRIVATE_BITS + 7) % 8);

    ossl_curve448_scalar_decode_long(the_scalar, scalar2, sizeof(scalar2));

    /* Compensate for the encoding ratio */

    for (i = 1; i < X448_ENCODE_RATIO; i <<= 1)

        ossl_curve448_scalar_halve(the_scalar, the_scalar);

    ossl_curve448_precomputed_scalarmul(p, ossl_curve448_precomputed_base,

                                        the_scalar);

    ossl_curve448_point_mul_by_ratio_and_encode_like_x448(out, p);

    ossl_curve448_point_destroy(p);

}

/* Control for variable-time scalar multiply algorithms. */

struct smvt_control {

    int power, addend;

};

#if defined(__GNUC__) && (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ > 3))

# define NUMTRAILINGZEROS       __builtin_ctz

#else

# define NUMTRAILINGZEROS       numtrailingzeros

static uint32_t numtrailingzeros(uint32_t i)

{

    uint32_t tmp;

    uint32_t num = 31;

    if (i == 0)

        return 32;

    tmp = i << 16;

    if (tmp != 0) {

        i = tmp;

        num -= 16;

    }

    tmp = i << 8;

    if (tmp != 0) {

        i = tmp;

        num -= 8;

    }

    tmp = i << 4;

    if (tmp != 0) {

        i = tmp;

        num -= 4;

    }

    tmp = i << 2;

    if (tmp != 0) {

        i = tmp;

        num -= 2;

    }

    tmp = i << 1;

    if (tmp != 0)

        num--;

    return num;

}

#endif

static int recode_wnaf(struct smvt_control *control,

                       /* [nbits/(table_bits + 1) + 3] */

                       const curve448_scalar_t scalar,

                       unsigned int table_bits)

{

    unsigned int table_size = C448_SCALAR_BITS / (table_bits + 1) + 3;

    int position = table_size - 1; /* at the end */

    uint64_t current = scalar->limb[0] & 0xFFFF;

    uint32_t mask = (1 << (table_bits + 1)) - 1;

    unsigned int w;

    const unsigned int B_OVER_16 = sizeof(scalar->limb[0]) / 2;

    unsigned int n, i;

    /* place the end marker */

    control[position].power = -1;

    control[position].addend = 0;

    position--;

    /*

     * PERF: Could negate scalar if it's large.  But then would need more cases

     * in the actual code that uses it, all for an expected reduction of like

     * 1/5 op. Probably not worth it.

     */

    for (w = 1; w < (C448_SCALAR_BITS - 1) / 16 + 3; w++) {

        if (w < (C448_SCALAR_BITS - 1) / 16 + 1) {

            /* Refill the 16 high bits of current */

            current += (uint32_t)((scalar->limb[w / B_OVER_16]

                       >> (16 * (w % B_OVER_16))) << 16);

        }

        while (current & 0xFFFF) {

            uint32_t pos = NUMTRAILINGZEROS((uint32_t)current);

            uint32_t odd = (uint32_t)current >> pos;

            int32_t delta = odd & mask;

            assert(position >= 0);

            if (odd & (1 << (table_bits + 1)))

                delta -= (1 << (table_bits + 1));

            /*

             * Coverity gets confused by the value of pos, thinking it might be

             * 32.  This would require current & 0xFFFF to be zero which isn't

             * possible.  Suppress this false positive, since adding a check

             * isn't desirable.

             */

            /* coverity[overflow_before_widen] */

            current -= delta * (1 << pos);

            control[position].power = pos + 16 * (w - 1);

            control[position].addend = delta;

            position--;

        }

        current >>= 16;

    }

    assert(current == 0);

    position++;

    n = table_size - position;

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

        control[i] = control[i + position];

    return n - 1;

}

static void prepare_wnaf_table(pniels_t *output,

                               const curve448_point_t working,

                               unsigned int tbits)

{

    curve448_point_t tmp;

    int i;

    pniels_t twop;

    pt_to_pniels(output[0], working);

    if (tbits == 0)

        return;

    ossl_curve448_point_double(tmp, working);

    pt_to_pniels(twop, tmp);

    add_pniels_to_pt(tmp, output[0], 0);

    pt_to_pniels(output[1], tmp);

    for (i = 2; i < 1 << tbits; i++) {

        add_pniels_to_pt(tmp, twop, 0);

        pt_to_pniels(output[i], tmp);

    }

    ossl_curve448_point_destroy(tmp);

    OPENSSL_cleanse(twop, sizeof(twop));

}

void

ossl_curve448_base_double_scalarmul_non_secret(curve448_point_t combo,

                                               const curve448_scalar_t scalar1,

                                               const curve448_point_t base2,

                                               const curve448_scalar_t scalar2)

{

    const int table_bits_var = C448_WNAF_VAR_TABLE_BITS;

    const int table_bits_pre = C448_WNAF_FIXED_TABLE_BITS;

    struct smvt_control control_var[C448_SCALAR_BITS /

                                    (C448_WNAF_VAR_TABLE_BITS + 1) + 3];

    struct smvt_control control_pre[C448_SCALAR_BITS /

                                    (C448_WNAF_FIXED_TABLE_BITS + 1) + 3];

    int ncb_pre = recode_wnaf(control_pre, scalar1, table_bits_pre);

    int ncb_var = recode_wnaf(control_var, scalar2, table_bits_var);

    pniels_t precmp_var[1 << C448_WNAF_VAR_TABLE_BITS];

    int contp = 0, contv = 0, i;

    prepare_wnaf_table(precmp_var, base2, table_bits_var);

    i = control_var[0].power;

    if (i < 0) {

        curve448_point_copy(combo, ossl_curve448_point_identity);

        return;

    }

    if (i > control_pre[0].power) {

        pniels_to_pt(combo, precmp_var[control_var[0].addend >> 1]);

        contv++;

    } else if (i == control_pre[0].power && i >= 0) {

        pniels_to_pt(combo, precmp_var[control_var[0].addend >> 1]);

        add_niels_to_pt(combo,

                        ossl_curve448_wnaf_base[control_pre[0].addend >> 1],

                        i);

        contv++;

        contp++;

    } else {

        i = control_pre[0].power;

        niels_to_pt(combo, ossl_curve448_wnaf_base[control_pre[0].addend >> 1]);

        contp++;

    }

    for (i--; i >= 0; i--) {

        int cv = (i == control_var[contv].power);

        int cp = (i == control_pre[contp].power);

        point_double_internal(combo, combo, i && !(cv || cp));

        if (cv) {

            assert(control_var[contv].addend);

            if (control_var[contv].addend > 0)

                add_pniels_to_pt(combo,

                                 precmp_var[control_var[contv].addend >> 1],

                                 i && !cp);

            else

                sub_pniels_from_pt(combo,

                                   precmp_var[(-control_var[contv].addend)

                                              >> 1], i && !cp);

            contv++;

        }

        if (cp) {

            assert(control_pre[contp].addend);

            if (control_pre[contp].addend > 0)

                add_niels_to_pt(combo,

                                ossl_curve448_wnaf_base[control_pre[contp].addend

                                                   >> 1], i);

            else

                sub_niels_from_pt(combo,

                                  ossl_curve448_wnaf_base[(-control_pre

                                                      [contp].addend) >> 1], i);

            contp++;

        }

    }

    /* This function is non-secret, but whatever this is cheap. */

    OPENSSL_cleanse(control_var, sizeof(control_var));

    OPENSSL_cleanse(control_pre, sizeof(control_pre));

    OPENSSL_cleanse(precmp_var, sizeof(precmp_var));

    assert(contv == ncb_var);

    (void)ncb_var;

    assert(contp == ncb_pre);

    (void)ncb_pre;

}

void ossl_curve448_point_destroy(curve448_point_t point)

{

    OPENSSL_cleanse(point, sizeof(curve448_point_t));

}

int ossl_x448(uint8_t out_shared_key[56], const uint8_t private_key[56],

              const uint8_t peer_public_value[56])

{

    return ossl_x448_int(out_shared_key, peer_public_value, private_key)

           == C448_SUCCESS;

}

void ossl_x448_public_from_private(uint8_t out_public_value[56],

                                   const uint8_t private_key[56])

{

    ossl_x448_derive_public_key(out_public_value, private_key);

}