/*

 * Copyright 2014-2024 The OpenSSL Project Authors. All Rights Reserved.

 * Copyright (c) 2014, Intel Corporation. All Rights Reserved.

 * Copyright (c) 2015, CloudFlare, 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 Shay Gueron (1, 2), and Vlad Krasnov (1, 3)

 * (1) Intel Corporation, Israel Development Center, Haifa, Israel

 * (2) University of Haifa, Israel

 * (3) CloudFlare, Inc.

 *

 * Reference:

 * S.Gueron and V.Krasnov, "Fast Prime Field Elliptic Curve Cryptography with

 *                          256 Bit Primes"

 */

/*

 * ECDSA low level APIs are deprecated for public use, but still ok for

 * internal use.

 */

#include "internal/deprecated.h"

#include <string.h>

#include "internal/cryptlib.h"

#include "crypto/bn.h"

#include "ec_local.h"

#include "internal/refcount.h"

#if BN_BITS2 != 64

# define TOBN(hi,lo)    lo,hi

#else

# define TOBN(hi,lo)    ((BN_ULONG)hi<<32|lo)

#endif

#define ALIGNPTR(p,N)   ((unsigned char *)p+N-(size_t)p%N)

#define P256_LIMBS      (256/BN_BITS2)

typedef unsigned short u16;

typedef struct {

    BN_ULONG X[P256_LIMBS];

    BN_ULONG Y[P256_LIMBS];

    BN_ULONG Z[P256_LIMBS];

} P256_POINT;

typedef struct {

    BN_ULONG X[P256_LIMBS];

    BN_ULONG Y[P256_LIMBS];

} P256_POINT_AFFINE;

typedef P256_POINT_AFFINE PRECOMP256_ROW[64];

/* structure for precomputed multiples of the generator */

struct nistz256_pre_comp_st {

    const EC_GROUP *group;      /* Parent EC_GROUP object */

    size_t w;                   /* Window size */

    /*

     * Constant time access to the X and Y coordinates of the pre-computed,

     * generator multiplies, in the Montgomery domain. Pre-calculated

     * multiplies are stored in affine form.

     */

    PRECOMP256_ROW *precomp;

    void *precomp_storage;

    CRYPTO_REF_COUNT references;

};

/* Functions implemented in assembly */

/*

 * Most of below mentioned functions *preserve* the property of inputs

 * being fully reduced, i.e. being in [0, modulus) range. Simply put if

 * inputs are fully reduced, then output is too. Note that reverse is

 * not true, in sense that given partially reduced inputs output can be

 * either, not unlikely reduced. And "most" in first sentence refers to

 * the fact that given the calculations flow one can tolerate that

 * addition, 1st function below, produces partially reduced result *if*

 * multiplications by 2 and 3, which customarily use addition, fully

 * reduce it. This effectively gives two options: a) addition produces

 * fully reduced result [as long as inputs are, just like remaining

 * functions]; b) addition is allowed to produce partially reduced

 * result, but multiplications by 2 and 3 perform additional reduction

 * step. Choice between the two can be platform-specific, but it was a)

 * in all cases so far...

 */

/* Modular add: res = a+b mod P   */

void ecp_nistz256_add(BN_ULONG res[P256_LIMBS],

                      const BN_ULONG a[P256_LIMBS],

                      const BN_ULONG b[P256_LIMBS]);

/* Modular mul by 2: res = 2*a mod P */

void ecp_nistz256_mul_by_2(BN_ULONG res[P256_LIMBS],

                           const BN_ULONG a[P256_LIMBS]);

/* Modular mul by 3: res = 3*a mod P */

void ecp_nistz256_mul_by_3(BN_ULONG res[P256_LIMBS],

                           const BN_ULONG a[P256_LIMBS]);

/* Modular div by 2: res = a/2 mod P */

void ecp_nistz256_div_by_2(BN_ULONG res[P256_LIMBS],

                           const BN_ULONG a[P256_LIMBS]);

/* Modular sub: res = a-b mod P   */

void ecp_nistz256_sub(BN_ULONG res[P256_LIMBS],

                      const BN_ULONG a[P256_LIMBS],

                      const BN_ULONG b[P256_LIMBS]);

/* Modular neg: res = -a mod P    */

void ecp_nistz256_neg(BN_ULONG res[P256_LIMBS], const BN_ULONG a[P256_LIMBS]);

/* Montgomery mul: res = a*b*2^-256 mod P */

void ecp_nistz256_mul_mont(BN_ULONG res[P256_LIMBS],

                           const BN_ULONG a[P256_LIMBS],

                           const BN_ULONG b[P256_LIMBS]);

/* Montgomery sqr: res = a*a*2^-256 mod P */

void ecp_nistz256_sqr_mont(BN_ULONG res[P256_LIMBS],

                           const BN_ULONG a[P256_LIMBS]);

/* Convert a number from Montgomery domain, by multiplying with 1 */

void ecp_nistz256_from_mont(BN_ULONG res[P256_LIMBS],

                            const BN_ULONG in[P256_LIMBS]);

/* Convert a number to Montgomery domain, by multiplying with 2^512 mod P*/

void ecp_nistz256_to_mont(BN_ULONG res[P256_LIMBS],

                          const BN_ULONG in[P256_LIMBS]);

/* Functions that perform constant time access to the precomputed tables */

void ecp_nistz256_scatter_w5(P256_POINT *val,

                             const P256_POINT *in_t, int idx);

void ecp_nistz256_gather_w5(P256_POINT *val,

                            const P256_POINT *in_t, int idx);

void ecp_nistz256_scatter_w7(P256_POINT_AFFINE *val,

                             const P256_POINT_AFFINE *in_t, int idx);

void ecp_nistz256_gather_w7(P256_POINT_AFFINE *val,

                            const P256_POINT_AFFINE *in_t, int idx);

/* One converted into the Montgomery domain */

static const BN_ULONG ONE[P256_LIMBS] = {

    TOBN(0x00000000, 0x00000001), TOBN(0xffffffff, 0x00000000),

    TOBN(0xffffffff, 0xffffffff), TOBN(0x00000000, 0xfffffffe)

};

static NISTZ256_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group);

/* Precomputed tables for the default generator */

extern const PRECOMP256_ROW ecp_nistz256_precomputed[37];

/* Recode window to a signed digit, see ecp_nistputil.c for details */

static unsigned int _booth_recode_w5(unsigned int in)

{

    unsigned int s, d;

    s = ~((in >> 5) - 1);

    d = (1 << 6) - in - 1;

    d = (d & s) | (in & ~s);

    d = (d >> 1) + (d & 1);

    return (d << 1) + (s & 1);

}

static unsigned int _booth_recode_w7(unsigned int in)

{

    unsigned int s, d;

    s = ~((in >> 7) - 1);

    d = (1 << 8) - in - 1;

    d = (d & s) | (in & ~s);

    d = (d >> 1) + (d & 1);

    return (d << 1) + (s & 1);

}

static void copy_conditional(BN_ULONG dst[P256_LIMBS],

                             const BN_ULONG src[P256_LIMBS], BN_ULONG move)

{

    BN_ULONG mask1 = 0-move;

    BN_ULONG mask2 = ~mask1;

    dst[0] = (src[0] & mask1) ^ (dst[0] & mask2);

    dst[1] = (src[1] & mask1) ^ (dst[1] & mask2);

    dst[2] = (src[2] & mask1) ^ (dst[2] & mask2);

    dst[3] = (src[3] & mask1) ^ (dst[3] & mask2);

    if (P256_LIMBS == 8) {

        dst[4] = (src[4] & mask1) ^ (dst[4] & mask2);

        dst[5] = (src[5] & mask1) ^ (dst[5] & mask2);

        dst[6] = (src[6] & mask1) ^ (dst[6] & mask2);

        dst[7] = (src[7] & mask1) ^ (dst[7] & mask2);

    }

}

static BN_ULONG is_zero(BN_ULONG in)

{

    in |= (0 - in);

    in = ~in;

    in >>= BN_BITS2 - 1;

    return in;

}

static BN_ULONG is_equal(const BN_ULONG a[P256_LIMBS],

                         const BN_ULONG b[P256_LIMBS])

{

    BN_ULONG res;

    res = a[0] ^ b[0];

    res |= a[1] ^ b[1];

    res |= a[2] ^ b[2];

    res |= a[3] ^ b[3];

    if (P256_LIMBS == 8) {

        res |= a[4] ^ b[4];

        res |= a[5] ^ b[5];

        res |= a[6] ^ b[6];

        res |= a[7] ^ b[7];

    }

    return is_zero(res);

}

static BN_ULONG is_one(const BIGNUM *z)

{

    BN_ULONG res = 0;

    BN_ULONG *a = bn_get_words(z);

    if (bn_get_top(z) == (P256_LIMBS - P256_LIMBS / 8)) {

        res = a[0] ^ ONE[0];

        res |= a[1] ^ ONE[1];

        res |= a[2] ^ ONE[2];

        res |= a[3] ^ ONE[3];

        if (P256_LIMBS == 8) {

            res |= a[4] ^ ONE[4];

            res |= a[5] ^ ONE[5];

            res |= a[6] ^ ONE[6];

            /*

             * no check for a[7] (being zero) on 32-bit platforms,

             * because value of "one" takes only 7 limbs.

             */

        }

        res = is_zero(res);

    }

    return res;

}

/*

 * For reference, this macro is used only when new ecp_nistz256 assembly

 * module is being developed.  For example, configure with

 * -DECP_NISTZ256_REFERENCE_IMPLEMENTATION and implement only functions

 * performing simplest arithmetic operations on 256-bit vectors. Then

 * work on implementation of higher-level functions performing point

 * operations. Then remove ECP_NISTZ256_REFERENCE_IMPLEMENTATION

 * and never define it again. (The correct macro denoting presence of

 * ecp_nistz256 module is ECP_NISTZ256_ASM.)

 */

#ifndef ECP_NISTZ256_REFERENCE_IMPLEMENTATION

void ecp_nistz256_point_double(P256_POINT *r, const P256_POINT *a);

void ecp_nistz256_point_add(P256_POINT *r,

                            const P256_POINT *a, const P256_POINT *b);

void ecp_nistz256_point_add_affine(P256_POINT *r,

                                   const P256_POINT *a,

                                   const P256_POINT_AFFINE *b);

#else

/* Point double: r = 2*a */

static void ecp_nistz256_point_double(P256_POINT *r, const P256_POINT *a)

{

    BN_ULONG S[P256_LIMBS];

    BN_ULONG M[P256_LIMBS];

    BN_ULONG Zsqr[P256_LIMBS];

    BN_ULONG tmp0[P256_LIMBS];

    const BN_ULONG *in_x = a->X;

    const BN_ULONG *in_y = a->Y;

    const BN_ULONG *in_z = a->Z;

    BN_ULONG *res_x = r->X;

    BN_ULONG *res_y = r->Y;

    BN_ULONG *res_z = r->Z;

    ecp_nistz256_mul_by_2(S, in_y);

    ecp_nistz256_sqr_mont(Zsqr, in_z);

    ecp_nistz256_sqr_mont(S, S);

    ecp_nistz256_mul_mont(res_z, in_z, in_y);

    ecp_nistz256_mul_by_2(res_z, res_z);

    ecp_nistz256_add(M, in_x, Zsqr);

    ecp_nistz256_sub(Zsqr, in_x, Zsqr);

    ecp_nistz256_sqr_mont(res_y, S);

    ecp_nistz256_div_by_2(res_y, res_y);

    ecp_nistz256_mul_mont(M, M, Zsqr);

    ecp_nistz256_mul_by_3(M, M);

    ecp_nistz256_mul_mont(S, S, in_x);

    ecp_nistz256_mul_by_2(tmp0, S);

    ecp_nistz256_sqr_mont(res_x, M);

    ecp_nistz256_sub(res_x, res_x, tmp0);

    ecp_nistz256_sub(S, S, res_x);

    ecp_nistz256_mul_mont(S, S, M);

    ecp_nistz256_sub(res_y, S, res_y);

}

/* Point addition: r = a+b */

static void ecp_nistz256_point_add(P256_POINT *r,

                                   const P256_POINT *a, const P256_POINT *b)

{

    BN_ULONG U2[P256_LIMBS], S2[P256_LIMBS];

    BN_ULONG U1[P256_LIMBS], S1[P256_LIMBS];

    BN_ULONG Z1sqr[P256_LIMBS];

    BN_ULONG Z2sqr[P256_LIMBS];

    BN_ULONG H[P256_LIMBS], R[P256_LIMBS];

    BN_ULONG Hsqr[P256_LIMBS];

    BN_ULONG Rsqr[P256_LIMBS];

    BN_ULONG Hcub[P256_LIMBS];

    BN_ULONG res_x[P256_LIMBS];

    BN_ULONG res_y[P256_LIMBS];

    BN_ULONG res_z[P256_LIMBS];

    BN_ULONG in1infty, in2infty;

    const BN_ULONG *in1_x = a->X;

    const BN_ULONG *in1_y = a->Y;

    const BN_ULONG *in1_z = a->Z;

    const BN_ULONG *in2_x = b->X;

    const BN_ULONG *in2_y = b->Y;

    const BN_ULONG *in2_z = b->Z;

    /*

     * Infinity in encoded as (,,0)

     */

    in1infty = (in1_z[0] | in1_z[1] | in1_z[2] | in1_z[3]);

    if (P256_LIMBS == 8)

        in1infty |= (in1_z[4] | in1_z[5] | in1_z[6] | in1_z[7]);

    in2infty = (in2_z[0] | in2_z[1] | in2_z[2] | in2_z[3]);

    if (P256_LIMBS == 8)

        in2infty |= (in2_z[4] | in2_z[5] | in2_z[6] | in2_z[7]);

    in1infty = is_zero(in1infty);

    in2infty = is_zero(in2infty);

    ecp_nistz256_sqr_mont(Z2sqr, in2_z);        /* Z2^2 */

    ecp_nistz256_sqr_mont(Z1sqr, in1_z);        /* Z1^2 */

    ecp_nistz256_mul_mont(S1, Z2sqr, in2_z);    /* S1 = Z2^3 */

    ecp_nistz256_mul_mont(S2, Z1sqr, in1_z);    /* S2 = Z1^3 */

    ecp_nistz256_mul_mont(S1, S1, in1_y);       /* S1 = Y1*Z2^3 */

    ecp_nistz256_mul_mont(S2, S2, in2_y);       /* S2 = Y2*Z1^3 */

    ecp_nistz256_sub(R, S2, S1);                /* R = S2 - S1 */

    ecp_nistz256_mul_mont(U1, in1_x, Z2sqr);    /* U1 = X1*Z2^2 */

    ecp_nistz256_mul_mont(U2, in2_x, Z1sqr);    /* U2 = X2*Z1^2 */

    ecp_nistz256_sub(H, U2, U1);                /* H = U2 - U1 */

    /*

     * The formulae are incorrect if the points are equal so we check for

     * this and do doubling if this happens.

     *

     * Points here are in Jacobian projective coordinates (Xi, Yi, Zi)

     * that are bound to the affine coordinates (xi, yi) by the following

     * equations:

     *     - xi = Xi / (Zi)^2

     *     - y1 = Yi / (Zi)^3

     *

     * For the sake of optimization, the algorithm operates over

     * intermediate variables U1, U2 and S1, S2 that are derived from

     * the projective coordinates:

     *     - U1 = X1 * (Z2)^2 ; U2 = X2 * (Z1)^2

     *     - S1 = Y1 * (Z2)^3 ; S2 = Y2 * (Z1)^3

     *

     * It is easy to prove that is_equal(U1, U2) implies that the affine

     * x-coordinates are equal, or either point is at infinity.

     * Likewise is_equal(S1, S2) implies that the affine y-coordinates are

     * equal, or either point is at infinity.

     *

     * The special case of either point being the point at infinity (Z1 or Z2

     * is zero), is handled separately later on in this function, so we avoid

     * jumping to point_double here in those special cases.

     *

     * When both points are inverse of each other, we know that the affine

     * x-coordinates are equal, and the y-coordinates have different sign.

     * Therefore since U1 = U2, we know H = 0, and therefore Z3 = H*Z1*Z2

     * will equal 0, thus the result is infinity, if we simply let this

     * function continue normally.

     *

     * We use bitwise operations to avoid potential side-channels introduced by

     * the short-circuiting behaviour of boolean operators.

     */

    if (is_equal(U1, U2) & ~in1infty & ~in2infty & is_equal(S1, S2)) {

        /*

         * This is obviously not constant-time but it should never happen during

         * single point multiplication, so there is no timing leak for ECDH or

         * ECDSA signing.

         */

        ecp_nistz256_point_double(r, a);

        return;

    }

    ecp_nistz256_sqr_mont(Rsqr, R);             /* R^2 */

    ecp_nistz256_mul_mont(res_z, H, in1_z);     /* Z3 = H*Z1*Z2 */

    ecp_nistz256_sqr_mont(Hsqr, H);             /* H^2 */

    ecp_nistz256_mul_mont(res_z, res_z, in2_z); /* Z3 = H*Z1*Z2 */

    ecp_nistz256_mul_mont(Hcub, Hsqr, H);       /* H^3 */

    ecp_nistz256_mul_mont(U2, U1, Hsqr);        /* U1*H^2 */

    ecp_nistz256_mul_by_2(Hsqr, U2);            /* 2*U1*H^2 */

    ecp_nistz256_sub(res_x, Rsqr, Hsqr);

    ecp_nistz256_sub(res_x, res_x, Hcub);

    ecp_nistz256_sub(res_y, U2, res_x);

    ecp_nistz256_mul_mont(S2, S1, Hcub);

    ecp_nistz256_mul_mont(res_y, R, res_y);

    ecp_nistz256_sub(res_y, res_y, S2);

    copy_conditional(res_x, in2_x, in1infty);

    copy_conditional(res_y, in2_y, in1infty);

    copy_conditional(res_z, in2_z, in1infty);

    copy_conditional(res_x, in1_x, in2infty);

    copy_conditional(res_y, in1_y, in2infty);

    copy_conditional(res_z, in1_z, in2infty);

    memcpy(r->X, res_x, sizeof(res_x));

    memcpy(r->Y, res_y, sizeof(res_y));

    memcpy(r->Z, res_z, sizeof(res_z));

}

/* Point addition when b is known to be affine: r = a+b */

static void ecp_nistz256_point_add_affine(P256_POINT *r,

                                          const P256_POINT *a,

                                          const P256_POINT_AFFINE *b)

{

    BN_ULONG U2[P256_LIMBS], S2[P256_LIMBS];

    BN_ULONG Z1sqr[P256_LIMBS];

    BN_ULONG H[P256_LIMBS], R[P256_LIMBS];

    BN_ULONG Hsqr[P256_LIMBS];

    BN_ULONG Rsqr[P256_LIMBS];

    BN_ULONG Hcub[P256_LIMBS];

    BN_ULONG res_x[P256_LIMBS];

    BN_ULONG res_y[P256_LIMBS];

    BN_ULONG res_z[P256_LIMBS];

    BN_ULONG in1infty, in2infty;

    const BN_ULONG *in1_x = a->X;

    const BN_ULONG *in1_y = a->Y;

    const BN_ULONG *in1_z = a->Z;

    const BN_ULONG *in2_x = b->X;

    const BN_ULONG *in2_y = b->Y;

    /*

     * Infinity in encoded as (,,0)

     */

    in1infty = (in1_z[0] | in1_z[1] | in1_z[2] | in1_z[3]);

    if (P256_LIMBS == 8)

        in1infty |= (in1_z[4] | in1_z[5] | in1_z[6] | in1_z[7]);

    /*

     * In affine representation we encode infinity as (0,0), which is

     * not on the curve, so it is OK

     */

    in2infty = (in2_x[0] | in2_x[1] | in2_x[2] | in2_x[3] |

                in2_y[0] | in2_y[1] | in2_y[2] | in2_y[3]);

    if (P256_LIMBS == 8)

        in2infty |= (in2_x[4] | in2_x[5] | in2_x[6] | in2_x[7] |

                     in2_y[4] | in2_y[5] | in2_y[6] | in2_y[7]);

    in1infty = is_zero(in1infty);

    in2infty = is_zero(in2infty);

    ecp_nistz256_sqr_mont(Z1sqr, in1_z);        /* Z1^2 */

    ecp_nistz256_mul_mont(U2, in2_x, Z1sqr);    /* U2 = X2*Z1^2 */

    ecp_nistz256_sub(H, U2, in1_x);             /* H = U2 - U1 */

    ecp_nistz256_mul_mont(S2, Z1sqr, in1_z);    /* S2 = Z1^3 */

    ecp_nistz256_mul_mont(res_z, H, in1_z);     /* Z3 = H*Z1*Z2 */

    ecp_nistz256_mul_mont(S2, S2, in2_y);       /* S2 = Y2*Z1^3 */

    ecp_nistz256_sub(R, S2, in1_y);             /* R = S2 - S1 */

    ecp_nistz256_sqr_mont(Hsqr, H);             /* H^2 */

    ecp_nistz256_sqr_mont(Rsqr, R);             /* R^2 */

    ecp_nistz256_mul_mont(Hcub, Hsqr, H);       /* H^3 */

    ecp_nistz256_mul_mont(U2, in1_x, Hsqr);     /* U1*H^2 */

    ecp_nistz256_mul_by_2(Hsqr, U2);            /* 2*U1*H^2 */

    ecp_nistz256_sub(res_x, Rsqr, Hsqr);

    ecp_nistz256_sub(res_x, res_x, Hcub);

    ecp_nistz256_sub(H, U2, res_x);

    ecp_nistz256_mul_mont(S2, in1_y, Hcub);

    ecp_nistz256_mul_mont(H, H, R);

    ecp_nistz256_sub(res_y, H, S2);

    copy_conditional(res_x, in2_x, in1infty);

    copy_conditional(res_x, in1_x, in2infty);

    copy_conditional(res_y, in2_y, in1infty);

    copy_conditional(res_y, in1_y, in2infty);

    copy_conditional(res_z, ONE, in1infty);

    copy_conditional(res_z, in1_z, in2infty);

    memcpy(r->X, res_x, sizeof(res_x));

    memcpy(r->Y, res_y, sizeof(res_y));

    memcpy(r->Z, res_z, sizeof(res_z));

}

#endif

/* r = in^-1 mod p */

static void ecp_nistz256_mod_inverse(BN_ULONG r[P256_LIMBS],

                                     const BN_ULONG in[P256_LIMBS])

{

    /*

     * The poly is ffffffff 00000001 00000000 00000000 00000000 ffffffff

     * ffffffff ffffffff We use FLT and used poly-2 as exponent

     */

    BN_ULONG p2[P256_LIMBS];

    BN_ULONG p4[P256_LIMBS];

    BN_ULONG p8[P256_LIMBS];

    BN_ULONG p16[P256_LIMBS];

    BN_ULONG p32[P256_LIMBS];

    BN_ULONG res[P256_LIMBS];

    int i;

    ecp_nistz256_sqr_mont(res, in);

    ecp_nistz256_mul_mont(p2, res, in);         /* 3*p */

    ecp_nistz256_sqr_mont(res, p2);

    ecp_nistz256_sqr_mont(res, res);

    ecp_nistz256_mul_mont(p4, res, p2);         /* f*p */

    ecp_nistz256_sqr_mont(res, p4);

    ecp_nistz256_sqr_mont(res, res);

    ecp_nistz256_sqr_mont(res, res);

    ecp_nistz256_sqr_mont(res, res);

    ecp_nistz256_mul_mont(p8, res, p4);         /* ff*p */

    ecp_nistz256_sqr_mont(res, p8);

    for (i = 0; i < 7; i++)

        ecp_nistz256_sqr_mont(res, res);

    ecp_nistz256_mul_mont(p16, res, p8);        /* ffff*p */

    ecp_nistz256_sqr_mont(res, p16);

    for (i = 0; i < 15; i++)

        ecp_nistz256_sqr_mont(res, res);

    ecp_nistz256_mul_mont(p32, res, p16);       /* ffffffff*p */

    ecp_nistz256_sqr_mont(res, p32);

    for (i = 0; i < 31; i++)

        ecp_nistz256_sqr_mont(res, res);

    ecp_nistz256_mul_mont(res, res, in);

    for (i = 0; i < 32 * 4; i++)

        ecp_nistz256_sqr_mont(res, res);

    ecp_nistz256_mul_mont(res, res, p32);

    for (i = 0; i < 32; i++)

        ecp_nistz256_sqr_mont(res, res);

    ecp_nistz256_mul_mont(res, res, p32);

    for (i = 0; i < 16; i++)

        ecp_nistz256_sqr_mont(res, res);

    ecp_nistz256_mul_mont(res, res, p16);

    for (i = 0; i < 8; i++)

        ecp_nistz256_sqr_mont(res, res);

    ecp_nistz256_mul_mont(res, res, p8);

    ecp_nistz256_sqr_mont(res, res);

    ecp_nistz256_sqr_mont(res, res);

    ecp_nistz256_sqr_mont(res, res);

    ecp_nistz256_sqr_mont(res, res);

    ecp_nistz256_mul_mont(res, res, p4);

    ecp_nistz256_sqr_mont(res, res);

    ecp_nistz256_sqr_mont(res, res);

    ecp_nistz256_mul_mont(res, res, p2);

    ecp_nistz256_sqr_mont(res, res);

    ecp_nistz256_sqr_mont(res, res);

    ecp_nistz256_mul_mont(res, res, in);

    memcpy(r, res, sizeof(res));

}

/*

 * ecp_nistz256_bignum_to_field_elem copies the contents of |in| to |out| and

 * returns one if it fits. Otherwise it returns zero.

 */

__owur static int ecp_nistz256_bignum_to_field_elem(BN_ULONG out[P256_LIMBS],

                                                    const BIGNUM *in)

{

    return bn_copy_words(out, in, P256_LIMBS);

}

/* r = sum(scalar[i]*point[i]) */

__owur static int ecp_nistz256_windowed_mul(const EC_GROUP *group,

                                            P256_POINT *r,

                                            const BIGNUM **scalar,

                                            const EC_POINT **point,

                                            size_t num, BN_CTX *ctx)

{

    size_t i;

    int j, ret = 0;

    unsigned int idx;

    unsigned char (*p_str)[33] = NULL;

    const unsigned int window_size = 5;

    const unsigned int mask = (1 << (window_size + 1)) - 1;

    unsigned int wvalue;

    P256_POINT *temp;           /* place for 5 temporary points */

    const BIGNUM **scalars = NULL;

    P256_POINT (*table)[16] = NULL;

    void *table_storage = NULL;

    if ((num * 16 + 6) > OPENSSL_MALLOC_MAX_NELEMS(P256_POINT)

        || (table_storage =

            OPENSSL_malloc((num * 16 + 5) * sizeof(P256_POINT) + 64)) == NULL

        || (p_str =

            OPENSSL_malloc(num * 33 * sizeof(unsigned char))) == NULL

        || (scalars = OPENSSL_malloc(num * sizeof(BIGNUM *))) == NULL)

        goto err;

    table = (void *)ALIGNPTR(table_storage, 64);

    temp = (P256_POINT *)(table + num);

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

        P256_POINT *row = table[i];

        /* This is an unusual input, we don't guarantee constant-timeness. */

        if ((BN_num_bits(scalar[i]) > 256) || BN_is_negative(scalar[i])) {

            BIGNUM *mod;

            if ((mod = BN_CTX_get(ctx)) == NULL)

                goto err;

            if (!BN_nnmod(mod, scalar[i], group->order, ctx)) {

                ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);

                goto err;

            }

            scalars[i] = mod;

        } else

            scalars[i] = scalar[i];

        for (j = 0; j < bn_get_top(scalars[i]) * BN_BYTES; j += BN_BYTES) {

            BN_ULONG d = bn_get_words(scalars[i])[j / BN_BYTES];

            p_str[i][j + 0] = (unsigned char)d;

            p_str[i][j + 1] = (unsigned char)(d >> 8);

            p_str[i][j + 2] = (unsigned char)(d >> 16);

            p_str[i][j + 3] = (unsigned char)(d >>= 24);

            if (BN_BYTES == 8) {

                d >>= 8;

                p_str[i][j + 4] = (unsigned char)d;

                p_str[i][j + 5] = (unsigned char)(d >> 8);

                p_str[i][j + 6] = (unsigned char)(d >> 16);

                p_str[i][j + 7] = (unsigned char)(d >> 24);

            }

        }

        for (; j < 33; j++)

            p_str[i][j] = 0;

        if (!ecp_nistz256_bignum_to_field_elem(temp[0].X, point[i]->X)

            || !ecp_nistz256_bignum_to_field_elem(temp[0].Y, point[i]->Y)

            || !ecp_nistz256_bignum_to_field_elem(temp[0].Z, point[i]->Z)) {

            ERR_raise(ERR_LIB_EC, EC_R_COORDINATES_OUT_OF_RANGE);

            goto err;

        }

        /*

         * row[0] is implicitly (0,0,0) (the point at infinity), therefore it

         * is not stored. All other values are actually stored with an offset

         * of -1 in table.

         */

        ecp_nistz256_scatter_w5  (row, &temp[0], 1);

        ecp_nistz256_point_double(&temp[1], &temp[0]);              /*1+1=2  */

        ecp_nistz256_scatter_w5  (row, &temp[1], 2);

        ecp_nistz256_point_add   (&temp[2], &temp[1], &temp[0]);    /*2+1=3  */

        ecp_nistz256_scatter_w5  (row, &temp[2], 3);

        ecp_nistz256_point_double(&temp[1], &temp[1]);              /*2*2=4  */

        ecp_nistz256_scatter_w5  (row, &temp[1], 4);

        ecp_nistz256_point_double(&temp[2], &temp[2]);              /*2*3=6  */

        ecp_nistz256_scatter_w5  (row, &temp[2], 6);

        ecp_nistz256_point_add   (&temp[3], &temp[1], &temp[0]);    /*4+1=5  */

        ecp_nistz256_scatter_w5  (row, &temp[3], 5);

        ecp_nistz256_point_add   (&temp[4], &temp[2], &temp[0]);    /*6+1=7  */

        ecp_nistz256_scatter_w5  (row, &temp[4], 7);

        ecp_nistz256_point_double(&temp[1], &temp[1]);              /*2*4=8  */

        ecp_nistz256_scatter_w5  (row, &temp[1], 8);

        ecp_nistz256_point_double(&temp[2], &temp[2]);              /*2*6=12 */

        ecp_nistz256_scatter_w5  (row, &temp[2], 12);

        ecp_nistz256_point_double(&temp[3], &temp[3]);              /*2*5=10 */

        ecp_nistz256_scatter_w5  (row, &temp[3], 10);

        ecp_nistz256_point_double(&temp[4], &temp[4]);              /*2*7=14 */

        ecp_nistz256_scatter_w5  (row, &temp[4], 14);

        ecp_nistz256_point_add   (&temp[2], &temp[2], &temp[0]);    /*12+1=13*/

        ecp_nistz256_scatter_w5  (row, &temp[2], 13);

        ecp_nistz256_point_add   (&temp[3], &temp[3], &temp[0]);    /*10+1=11*/

        ecp_nistz256_scatter_w5  (row, &temp[3], 11);

        ecp_nistz256_point_add   (&temp[4], &temp[4], &temp[0]);    /*14+1=15*/

        ecp_nistz256_scatter_w5  (row, &temp[4], 15);

        ecp_nistz256_point_add   (&temp[2], &temp[1], &temp[0]);    /*8+1=9  */

        ecp_nistz256_scatter_w5  (row, &temp[2], 9);

        ecp_nistz256_point_double(&temp[1], &temp[1]);              /*2*8=16 */

        ecp_nistz256_scatter_w5  (row, &temp[1], 16);

    }

    idx = 255;

    wvalue = p_str[0][(idx - 1) / 8];

    wvalue = (wvalue >> ((idx - 1) % 8)) & mask;

    /*

     * We gather to temp[0], because we know it's position relative

     * to table

     */

    ecp_nistz256_gather_w5(&temp[0], table[0], _booth_recode_w5(wvalue) >> 1);

    memcpy(r, &temp[0], sizeof(temp[0]));

    while (idx >= 5) {

        for (i = (idx == 255 ? 1 : 0); i < num; i++) {

            unsigned int off = (idx - 1) / 8;

            wvalue = p_str[i][off] | p_str[i][off + 1] << 8;

            wvalue = (wvalue >> ((idx - 1) % 8)) & mask;

            wvalue = _booth_recode_w5(wvalue);

            ecp_nistz256_gather_w5(&temp[0], table[i], wvalue >> 1);

            ecp_nistz256_neg(temp[1].Y, temp[0].Y);

            copy_conditional(temp[0].Y, temp[1].Y, (wvalue & 1));

            ecp_nistz256_point_add(r, r, &temp[0]);

        }

        idx -= window_size;

        ecp_nistz256_point_double(r, r);

        ecp_nistz256_point_double(r, r);

        ecp_nistz256_point_double(r, r);

        ecp_nistz256_point_double(r, r);

        ecp_nistz256_point_double(r, r);

    }

    /* Final window */

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

        wvalue = p_str[i][0];

        wvalue = (wvalue << 1) & mask;

        wvalue = _booth_recode_w5(wvalue);

        ecp_nistz256_gather_w5(&temp[0], table[i], wvalue >> 1);

        ecp_nistz256_neg(temp[1].Y, temp[0].Y);

        copy_conditional(temp[0].Y, temp[1].Y, wvalue & 1);

        ecp_nistz256_point_add(r, r, &temp[0]);

    }

    ret = 1;

 err:

    OPENSSL_free(table_storage);

    OPENSSL_free(p_str);

    OPENSSL_free(scalars);

    return ret;

}

/* Coordinates of G, for which we have precomputed tables */

static const BN_ULONG def_xG[P256_LIMBS] = {

    TOBN(0x79e730d4, 0x18a9143c), TOBN(0x75ba95fc, 0x5fedb601),

    TOBN(0x79fb732b, 0x77622510), TOBN(0x18905f76, 0xa53755c6)

};

static const BN_ULONG def_yG[P256_LIMBS] = {

    TOBN(0xddf25357, 0xce95560a), TOBN(0x8b4ab8e4, 0xba19e45c),

    TOBN(0xd2e88688, 0xdd21f325), TOBN(0x8571ff18, 0x25885d85)

};

/*

 * ecp_nistz256_is_affine_G returns one if |generator| is the standard, P-256

 * generator.

 */

static int ecp_nistz256_is_affine_G(const EC_POINT *generator)

{

    return (bn_get_top(generator->X) == P256_LIMBS) &&

        (bn_get_top(generator->Y) == P256_LIMBS) &&

        is_equal(bn_get_words(generator->X), def_xG) &&

        is_equal(bn_get_words(generator->Y), def_yG) &&

        is_one(generator->Z);

}

__owur static int ecp_nistz256_mult_precompute(EC_GROUP *group, BN_CTX *ctx)

{

    /*

     * We precompute a table for a Booth encoded exponent (wNAF) based

     * computation. Each table holds 64 values for safe access, with an

     * implicit value of infinity at index zero. We use window of size 7, and

     * therefore require ceil(256/7) = 37 tables.

     */

    const BIGNUM *order;

    EC_POINT *P = NULL, *T = NULL;

    const EC_POINT *generator;

    NISTZ256_PRE_COMP *pre_comp;

    BN_CTX *new_ctx = NULL;

    int i, j, k, ret = 0;

    size_t w;

    PRECOMP256_ROW *preComputedTable = NULL;

    unsigned char *precomp_storage = NULL;

    /* if there is an old NISTZ256_PRE_COMP object, throw it away */

    EC_pre_comp_free(group);

    generator = EC_GROUP_get0_generator(group);

    if (generator == NULL) {

        ERR_raise(ERR_LIB_EC, EC_R_UNDEFINED_GENERATOR);

        return 0;

    }

    if (ecp_nistz256_is_affine_G(generator)) {

        /*

         * No need to calculate tables for the standard generator because we

         * have them statically.

         */

        return 1;

    }

    if ((pre_comp = ecp_nistz256_pre_comp_new(group)) == NULL)

        return 0;

    if (ctx == NULL) {

        ctx = new_ctx = BN_CTX_new_ex(group->libctx);

        if (ctx == NULL)

            goto err;

    }

    BN_CTX_start(ctx);

    order = EC_GROUP_get0_order(group);

    if (order == NULL)

        goto err;

    if (BN_is_zero(order)) {

        ERR_raise(ERR_LIB_EC, EC_R_UNKNOWN_ORDER);

        goto err;

    }

    w = 7;

    if ((precomp_storage =

         OPENSSL_malloc(37 * 64 * sizeof(P256_POINT_AFFINE) + 64)) == NULL)

        goto err;

    preComputedTable = (void *)ALIGNPTR(precomp_storage, 64);

    P = EC_POINT_new(group);

    T = EC_POINT_new(group);

    if (P == NULL || T == NULL)

        goto err;

    /*

     * The zero entry is implicitly infinity, and we skip it, storing other

     * values with -1 offset.

     */

    if (!EC_POINT_copy(T, generator))

        goto err;

    for (k = 0; k < 64; k++) {

        if (!EC_POINT_copy(P, T))

            goto err;

        for (j = 0; j < 37; j++) {

            P256_POINT_AFFINE temp;

            /*

             * It would be faster to use EC_POINTs_make_affine and

             * make multiple points affine at the same time.

             */

            if (group->meth->make_affine == NULL

                || !group->meth->make_affine(group, P, ctx))

                goto err;

            if (!ecp_nistz256_bignum_to_field_elem(temp.X, P->X) ||

                !ecp_nistz256_bignum_to_field_elem(temp.Y, P->Y)) {

                ERR_raise(ERR_LIB_EC, EC_R_COORDINATES_OUT_OF_RANGE);

                goto err;

            }

            ecp_nistz256_scatter_w7(preComputedTable[j], &temp, k);

            for (i = 0; i < 7; i++) {

                if (!EC_POINT_dbl(group, P, P, ctx))

                    goto err;

            }

        }

        if (!EC_POINT_add(group, T, T, generator, ctx))

            goto err;

    }

    pre_comp->group = group;

    pre_comp->w = w;

    pre_comp->precomp = preComputedTable;

    pre_comp->precomp_storage = precomp_storage;

    precomp_storage = NULL;

    SETPRECOMP(group, nistz256, pre_comp);

    pre_comp = NULL;

    ret = 1;

 err:

    BN_CTX_end(ctx);

    BN_CTX_free(new_ctx);

    EC_nistz256_pre_comp_free(pre_comp);

    OPENSSL_free(precomp_storage);

    EC_POINT_free(P);

    EC_POINT_free(T);

    return ret;

}

__owur static int ecp_nistz256_set_from_affine(EC_POINT *out, const EC_GROUP *group,

                                               const P256_POINT_AFFINE *in,

                                               BN_CTX *ctx)

{

    int ret = 0;

    if ((ret = bn_set_words(out->X, in->X, P256_LIMBS))

        && (ret = bn_set_words(out->Y, in->Y, P256_LIMBS))

        && (ret = bn_set_words(out->Z, ONE, P256_LIMBS)))

        out->Z_is_one = 1;

    return ret;

}

/* r = scalar*G + sum(scalars[i]*points[i]) */

__owur static int ecp_nistz256_points_mul(const EC_GROUP *group,

                                          EC_POINT *r,

                                          const BIGNUM *scalar,

                                          size_t num,

                                          const EC_POINT *points[],

                                          const BIGNUM *scalars[], BN_CTX *ctx)

{

    int i = 0, ret = 0, no_precomp_for_generator = 0, p_is_infinity = 0;

    unsigned char p_str[33] = { 0 };

    const PRECOMP256_ROW *preComputedTable = NULL;

    const NISTZ256_PRE_COMP *pre_comp = NULL;

    const EC_POINT *generator = NULL;

    const BIGNUM **new_scalars = NULL;

    const EC_POINT **new_points = NULL;

    unsigned int idx = 0;

    const unsigned int window_size = 7;

    const unsigned int mask = (1 << (window_size + 1)) - 1;

    unsigned int wvalue;

    ALIGN32 union {

        P256_POINT p;

        P256_POINT_AFFINE a;

    } t, p;

    BIGNUM *tmp_scalar;

    if ((num + 1) == 0 || (num + 1) > OPENSSL_MALLOC_MAX_NELEMS(void *)) {

        ERR_raise(ERR_LIB_EC, ERR_R_PASSED_INVALID_ARGUMENT);

        return 0;

    }

    memset(&p, 0, sizeof(p));

    BN_CTX_start(ctx);

    if (scalar) {

        generator = EC_GROUP_get0_generator(group);

        if (generator == NULL) {

            ERR_raise(ERR_LIB_EC, EC_R_UNDEFINED_GENERATOR);

            goto err;

        }