/*

 * Copyright 2001-2020 The OpenSSL Project Authors. All Rights Reserved.

 * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved

 *

 * 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

 */

#include <string.h>

#include <openssl/err.h>

#include "internal/cryptlib.h"

#include "crypto/bn.h"

#include "ec_local.h"

#include "internal/refcount.h"

/*

 * This file implements the wNAF-based interleaving multi-exponentiation method

 * Formerly at:

 *   http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp

 * You might now find it here:

 *   http://link.springer.com/chapter/10.1007%2F3-540-45537-X_13

 *   http://www.bmoeller.de/pdf/TI-01-08.multiexp.pdf

 * For multiplication with precomputation, we use wNAF splitting, formerly at:

 *   http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#fastexp

 */

/* structure for precomputed multiples of the generator */

struct ec_pre_comp_st {

    const EC_GROUP *group;      /* parent EC_GROUP object */

    size_t blocksize;           /* block size for wNAF splitting */

    size_t numblocks;           /* max. number of blocks for which we have

                                 * precomputation */

    size_t w;                   /* window size */

    EC_POINT **points;          /* array with pre-calculated multiples of

                                 * generator: 'num' pointers to EC_POINT

                                 * objects followed by a NULL */

    size_t num;                 /* numblocks * 2^(w-1) */

    CRYPTO_REF_COUNT references;

    CRYPTO_RWLOCK *lock;

};

static EC_PRE_COMP *ec_pre_comp_new(const EC_GROUP *group)

{

    EC_PRE_COMP *ret = NULL;

    if (!group)

        return NULL;

    ret = OPENSSL_zalloc(sizeof(*ret));

    if (ret == NULL) {

        ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);

        return ret;

    }

    ret->group = group;

    ret->blocksize = 8;         /* default */

    ret->w = 4;                 /* default */

    ret->references = 1;

    ret->lock = CRYPTO_THREAD_lock_new();

    if (ret->lock == NULL) {

        ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);

        OPENSSL_free(ret);

        return NULL;

    }

    return ret;

}

EC_PRE_COMP *EC_ec_pre_comp_dup(EC_PRE_COMP *pre)

{

    int i;

    if (pre != NULL)

        CRYPTO_UP_REF(&pre->references, &i, pre->lock);

    return pre;

}

void EC_ec_pre_comp_free(EC_PRE_COMP *pre)

{

    int i;

    if (pre == NULL)

        return;

    CRYPTO_DOWN_REF(&pre->references, &i, pre->lock);

    REF_PRINT_COUNT("EC_ec", pre);

    if (i > 0)

        return;

    REF_ASSERT_ISNT(i < 0);

    if (pre->points != NULL) {

        EC_POINT **pts;

        for (pts = pre->points; *pts != NULL; pts++)

            EC_POINT_free(*pts);

        OPENSSL_free(pre->points);

    }

    CRYPTO_THREAD_lock_free(pre->lock);

    OPENSSL_free(pre);

}

#define EC_POINT_BN_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 a single point multiplication over the EC group,

 * using, at a high level, a Montgomery ladder with conditional swaps, with

 * various timing attack defenses.

 *

 * It performs either a fixed point multiplication

 *          (scalar * generator)

 * when point is NULL, or a variable point multiplication

 *          (scalar * point)

 * when point is not NULL.

 *

 * `scalar` cannot be NULL and should be in the range [0,n) otherwise all

 * constant time bets are off (where n is the cardinality of the EC group).

 *

 * This function expects `group->order` and `group->cardinality` to be well

 * defined and non-zero: it fails with an error code otherwise.

 *

 * NB: This says nothing about the constant-timeness of the ladder step

 * implementation (i.e., the default implementation is based on EC_POINT_add and

 * EC_POINT_dbl, which of course are not constant time themselves) or the

 * underlying multiprecision arithmetic.

 *

 * The product is stored in `r`.

 *

 * This is an internal function: callers are in charge of ensuring that the

 * input parameters `group`, `r`, `scalar` and `ctx` are not NULL.

 *

 * Returns 1 on success, 0 otherwise.

 */

int ec_scalar_mul_ladder(const EC_GROUP *group, EC_POINT *r,

                         const BIGNUM *scalar, const EC_POINT *point,

                         BN_CTX *ctx)

{

    int i, cardinality_bits, group_top, kbit, pbit, Z_is_one;

    EC_POINT *p = NULL;

    EC_POINT *s = NULL;

    BIGNUM *k = NULL;

    BIGNUM *lambda = NULL;

    BIGNUM *cardinality = NULL;

    int ret = 0;

    /* early exit if the input point is the point at infinity */

    if (point != NULL && EC_POINT_is_at_infinity(group, point))

        return EC_POINT_set_to_infinity(group, r);

    if (BN_is_zero(group->order)) {

        ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_UNKNOWN_ORDER);

        return 0;

    }

    if (BN_is_zero(group->cofactor)) {

        ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_UNKNOWN_COFACTOR);

        return 0;

    }

    BN_CTX_start(ctx);

    if (((p = EC_POINT_new(group)) == NULL)

        || ((s = EC_POINT_new(group)) == NULL)) {

        ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_MALLOC_FAILURE);

        goto err;

    }

    if (point == NULL) {

        if (!EC_POINT_copy(p, group->generator)) {

            ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_EC_LIB);

            goto err;

        }

    } else {

        if (!EC_POINT_copy(p, point)) {

            ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_EC_LIB);

            goto err;

        }

    }

    EC_POINT_BN_set_flags(p, BN_FLG_CONSTTIME);

    EC_POINT_BN_set_flags(r, BN_FLG_CONSTTIME);

    EC_POINT_BN_set_flags(s, BN_FLG_CONSTTIME);

    cardinality = BN_CTX_get(ctx);

    lambda = BN_CTX_get(ctx);

    k = BN_CTX_get(ctx);

    if (k == NULL) {

        ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_MALLOC_FAILURE);

        goto err;

    }

    if (!BN_mul(cardinality, group->order, group->cofactor, ctx)) {

        ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB);

        goto err;

    }

    /*

     * Group cardinalities 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.

     */

    cardinality_bits = BN_num_bits(cardinality);

    group_top = bn_get_top(cardinality);

    if ((bn_wexpand(k, group_top + 2) == NULL)

        || (bn_wexpand(lambda, group_top + 2) == NULL)) {

        ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB);

        goto err;

    }

    if (!BN_copy(k, scalar)) {

        ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB);

        goto err;

    }

    BN_set_flags(k, BN_FLG_CONSTTIME);

    if ((BN_num_bits(k) > cardinality_bits) || (BN_is_negative(k))) {

        /*-

         * this is an unusual input, and we don't guarantee

         * constant-timeness

         */

        if (!BN_nnmod(k, k, cardinality, ctx)) {

            ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB);

            goto err;

        }

    }

    if (!BN_add(lambda, k, cardinality)) {

        ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB);

        goto err;

    }

    BN_set_flags(lambda, BN_FLG_CONSTTIME);

    if (!BN_add(k, lambda, cardinality)) {

        ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB);

        goto err;

    }

    /*

     * lambda := scalar + cardinality

     * k := scalar + 2*cardinality

     */

    kbit = BN_is_bit_set(lambda, cardinality_bits);

    BN_consttime_swap(kbit, k, lambda, group_top + 2);

    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)

        || (bn_wexpand(p->X, group_top) == NULL)

        || (bn_wexpand(p->Y, group_top) == NULL)

        || (bn_wexpand(p->Z, group_top) == NULL)) {

        ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB);

        goto err;

    }

    /* ensure input point is in affine coords for ladder step efficiency */

    if (!p->Z_is_one && !EC_POINT_make_affine(group, p, ctx)) {

            ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_EC_LIB);

            goto err;

    }

    /* Initialize the Montgomery ladder */

    if (!ec_point_ladder_pre(group, r, s, p, ctx)) {

        ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_LADDER_PRE_FAILURE);

        goto err;

    }

    /* top bit is a 1, in a fixed pos */

    pbit = 1;

#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)

    /*-

     * The ladder step, with branches, is

     *

     * k[i] == 0: S = add(R, S), R = dbl(R)

     * k[i] == 1: R = add(S, R), S = dbl(S)

     *

     * Swapping R, S conditionally on k[i] leaves you with state

     *

     * k[i] == 0: T, U = R, S

     * k[i] == 1: T, U = S, R

     *

     * Then perform the ECC ops.

     *

     * U = add(T, U)

     * T = dbl(T)

     *

     * Which leaves you with state

     *

     * k[i] == 0: U = add(R, S), T = dbl(R)

     * k[i] == 1: U = add(S, R), T = dbl(S)

     *

     * Swapping T, U conditionally on k[i] leaves you with state

     *

     * k[i] == 0: R, S = T, U

     * k[i] == 1: R, S = U, T

     *

     * Which leaves you with state

     *

     * k[i] == 0: S = add(R, S), R = dbl(R)

     * k[i] == 1: R = add(S, R), S = dbl(S)

     *

     * So we get the same logic, but instead of a branch it's a

     * conditional swap, followed by ECC ops, then another conditional swap.

     *

     * Optimization: The end of iteration i and start of i-1 looks like

     *

     * ...

     * CSWAP(k[i], R, S)

     * ECC

     * CSWAP(k[i], R, S)

     * (next iteration)

     * CSWAP(k[i-1], R, S)

     * ECC

     * CSWAP(k[i-1], R, S)

     * ...

     *

     * So instead of two contiguous swaps, you can merge the condition

     * bits and do a single swap.

     *

     * k[i]   k[i-1]    Outcome

     * 0      0         No Swap

     * 0      1         Swap

     * 1      0         Swap

     * 1      1         No Swap

     *

     * This is XOR. pbit tracks the previous bit of k.

     */

    for (i = cardinality_bits - 1; i >= 0; i--) {

        kbit = BN_is_bit_set(k, i) ^ pbit;

        EC_POINT_CSWAP(kbit, r, s, group_top, Z_is_one);

        /* Perform a single step of the Montgomery ladder */

        if (!ec_point_ladder_step(group, r, s, p, ctx)) {

            ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_LADDER_STEP_FAILURE);

            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

    /* Finalize ladder (and recover full point coordinates) */

    if (!ec_point_ladder_post(group, r, s, p, ctx)) {

        ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_LADDER_POST_FAILURE);

        goto err;

    }

    ret = 1;

 err:

    EC_POINT_free(p);

    EC_POINT_clear_free(s);

    BN_CTX_end(ctx);

    return ret;

}

#undef EC_POINT_BN_set_flags

/*

 * TODO: table should be optimised for the wNAF-based implementation,

 * sometimes smaller windows will give better performance (thus the

 * boundaries should be increased)

 */

#define EC_window_bits_for_scalar_size(b) \

                ((size_t) \

                 ((b) >= 2000 ? 6 : \

                  (b) >=  800 ? 5 : \

                  (b) >=  300 ? 4 : \

                  (b) >=   70 ? 3 : \

                  (b) >=   20 ? 2 : \

                  1))

/*-

 * Compute

 *      \sum scalars[i]*points[i],

 * also including

 *      scalar*generator

 * in the addition if scalar != NULL

 */

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)

{

    const EC_POINT *generator = NULL;

    EC_POINT *tmp = NULL;

    size_t totalnum;

    size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */

    size_t pre_points_per_block = 0;

    size_t i, j;

    int k;

    int r_is_inverted = 0;

    int r_is_at_infinity = 1;

    size_t *wsize = NULL;       /* individual window sizes */

    signed char **wNAF = NULL;  /* individual wNAFs */

    size_t *wNAF_len = NULL;

    size_t max_len = 0;

    size_t num_val;

    EC_POINT **val = NULL;      /* precomputation */

    EC_POINT **v;

    EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or

                                 * 'pre_comp->points' */

    const EC_PRE_COMP *pre_comp = NULL;

    int num_scalar = 0;         /* flag: will be set to 1 if 'scalar' must be

                                 * treated like other scalars, i.e.

                                 * precomputation is not available */

    int ret = 0;

    if (!BN_is_zero(group->order) && !BN_is_zero(group->cofactor)) {

        /*-

         * Handle the common cases where the scalar is secret, enforcing a

         * scalar multiplication implementation based on a Montgomery ladder,

         * with various timing attack defenses.

         */

        if ((scalar != group->order) && (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 ladder version.

             */

            return ec_scalar_mul_ladder(group, r, scalar, NULL, ctx);

        }

        if ((scalar == NULL) && (num == 1) && (scalars[0] != group->order)) {

            /*-

             * In this case we want to compute scalar * VariablePoint: 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 ladder version.

             */

            return ec_scalar_mul_ladder(group, r, scalars[0], points[0], ctx);

        }

    }

    if (scalar != NULL) {

        generator = EC_GROUP_get0_generator(group);

        if (generator == NULL) {

            ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR);

            goto err;

        }

        /* look if we can use precomputed multiples of generator */

        pre_comp = group->pre_comp.ec;

        if (pre_comp && pre_comp->numblocks

            && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) ==

                0)) {

            blocksize = pre_comp->blocksize;

            /*

             * determine maximum number of blocks that wNAF splitting may

             * yield (NB: maximum wNAF length is bit length plus one)

             */

            numblocks = (BN_num_bits(scalar) / blocksize) + 1;

            /*

             * we cannot use more blocks than we have precomputation for

             */

            if (numblocks > pre_comp->numblocks)

                numblocks = pre_comp->numblocks;

            pre_points_per_block = (size_t)1 << (pre_comp->w - 1);

            /* check that pre_comp looks sane */

            if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block)) {

                ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);

                goto err;

            }

        } else {

            /* can't use precomputation */

            pre_comp = NULL;

            numblocks = 1;

            num_scalar = 1;     /* treat 'scalar' like 'num'-th element of

                                 * 'scalars' */

        }

    }

    totalnum = num + numblocks;

    wsize = OPENSSL_malloc(totalnum * sizeof(wsize[0]));

    wNAF_len = OPENSSL_malloc(totalnum * sizeof(wNAF_len[0]));

    /* include space for pivot */

    wNAF = OPENSSL_malloc((totalnum + 1) * sizeof(wNAF[0]));

    val_sub = OPENSSL_malloc(totalnum * sizeof(val_sub[0]));

    /* Ensure wNAF is initialised in case we end up going to err */

    if (wNAF != NULL)

        wNAF[0] = NULL;         /* preliminary pivot */

    if (wsize == NULL || wNAF_len == NULL || wNAF == NULL || val_sub == NULL) {

        ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);

        goto err;

    }

    /*

     * num_val will be the total number of temporarily precomputed points

     */

    num_val = 0;

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

        size_t bits;

        bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar);

        wsize[i] = EC_window_bits_for_scalar_size(bits);

        num_val += (size_t)1 << (wsize[i] - 1);

        wNAF[i + 1] = NULL;     /* make sure we always have a pivot */

        wNAF[i] =

            bn_compute_wNAF((i < num ? scalars[i] : scalar), wsize[i],

                            &wNAF_len[i]);

        if (wNAF[i] == NULL)

            goto err;

        if (wNAF_len[i] > max_len)

            max_len = wNAF_len[i];

    }

    if (numblocks) {

        /* we go here iff scalar != NULL */

        if (pre_comp == NULL) {

            if (num_scalar != 1) {

                ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);

                goto err;

            }

            /* we have already generated a wNAF for 'scalar' */

        } else {

            signed char *tmp_wNAF = NULL;

            size_t tmp_len = 0;

            if (num_scalar != 0) {

                ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);

                goto err;

            }

            /*

             * use the window size for which we have precomputation

             */

            wsize[num] = pre_comp->w;

            tmp_wNAF = bn_compute_wNAF(scalar, wsize[num], &tmp_len);

            if (!tmp_wNAF)

                goto err;

            if (tmp_len <= max_len) {

                /*

                 * One of the other wNAFs is at least as long as the wNAF

                 * belonging to the generator, so wNAF splitting will not buy

                 * us anything.

                 */

                numblocks = 1;

                totalnum = num + 1; /* don't use wNAF splitting */

                wNAF[num] = tmp_wNAF;

                wNAF[num + 1] = NULL;

                wNAF_len[num] = tmp_len;

                /*

                 * pre_comp->points starts with the points that we need here:

                 */

                val_sub[num] = pre_comp->points;

            } else {

                /*

                 * don't include tmp_wNAF directly into wNAF array - use wNAF

                 * splitting and include the blocks

                 */

                signed char *pp;

                EC_POINT **tmp_points;

                if (tmp_len < numblocks * blocksize) {

                    /*

                     * possibly we can do with fewer blocks than estimated

                     */

                    numblocks = (tmp_len + blocksize - 1) / blocksize;

                    if (numblocks > pre_comp->numblocks) {

                        ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);

                        OPENSSL_free(tmp_wNAF);

                        goto err;

                    }

                    totalnum = num + numblocks;

                }

                /* split wNAF in 'numblocks' parts */

                pp = tmp_wNAF;

                tmp_points = pre_comp->points;

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

                    if (i < totalnum - 1) {

                        wNAF_len[i] = blocksize;

                        if (tmp_len < blocksize) {

                            ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);

                            OPENSSL_free(tmp_wNAF);

                            goto err;

                        }

                        tmp_len -= blocksize;

                    } else

                        /*

                         * last block gets whatever is left (this could be

                         * more or less than 'blocksize'!)

                         */

                        wNAF_len[i] = tmp_len;

                    wNAF[i + 1] = NULL;

                    wNAF[i] = OPENSSL_malloc(wNAF_len[i]);

                    if (wNAF[i] == NULL) {

                        ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);

                        OPENSSL_free(tmp_wNAF);

                        goto err;

                    }

                    memcpy(wNAF[i], pp, wNAF_len[i]);

                    if (wNAF_len[i] > max_len)

                        max_len = wNAF_len[i];

                    if (*tmp_points == NULL) {

                        ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);

                        OPENSSL_free(tmp_wNAF);

                        goto err;

                    }

                    val_sub[i] = tmp_points;

                    tmp_points += pre_points_per_block;

                    pp += blocksize;

                }

                OPENSSL_free(tmp_wNAF);

            }

        }

    }

    /*

     * All points we precompute now go into a single array 'val'.

     * 'val_sub[i]' is a pointer to the subarray for the i-th point, or to a

     * subarray of 'pre_comp->points' if we already have precomputation.

     */

    val = OPENSSL_malloc((num_val + 1) * sizeof(val[0]));

    if (val == NULL) {

        ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);

        goto err;

    }

    val[num_val] = NULL;        /* pivot element */

    /* allocate points for precomputation */

    v = val;

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

        val_sub[i] = v;

        for (j = 0; j < ((size_t)1 << (wsize[i] - 1)); j++) {

            *v = EC_POINT_new(group);

            if (*v == NULL)

                goto err;

            v++;

        }

    }

    if (!(v == val + num_val)) {

        ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);

        goto err;

    }

    if ((tmp = EC_POINT_new(group)) == NULL)

        goto err;

    /*-

     * prepare precomputed values:

     *    val_sub[i][0] :=     points[i]

     *    val_sub[i][1] := 3 * points[i]

     *    val_sub[i][2] := 5 * points[i]

     *    ...

     */

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

        if (i < num) {

            if (!EC_POINT_copy(val_sub[i][0], points[i]))

                goto err;

        } else {

            if (!EC_POINT_copy(val_sub[i][0], generator))

                goto err;

        }

        if (wsize[i] > 1) {

            if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx))

                goto err;

            for (j = 1; j < ((size_t)1 << (wsize[i] - 1)); j++) {

                if (!EC_POINT_add

                    (group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx))

                    goto err;

            }

        }

    }

    if (!EC_POINTs_make_affine(group, num_val, val, ctx))

        goto err;

    r_is_at_infinity = 1;

    for (k = max_len - 1; k >= 0; k--) {

        if (!r_is_at_infinity) {

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

                goto err;

        }

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

            if (wNAF_len[i] > (size_t)k) {

                int digit = wNAF[i][k];

                int is_neg;

                if (digit) {

                    is_neg = digit < 0;

                    if (is_neg)

                        digit = -digit;

                    if (is_neg != r_is_inverted) {

                        if (!r_is_at_infinity) {

                            if (!EC_POINT_invert(group, r, ctx))

                                goto err;

                        }

                        r_is_inverted = !r_is_inverted;

                    }

                    /* digit > 0 */

                    if (r_is_at_infinity) {

                        if (!EC_POINT_copy(r, val_sub[i][digit >> 1]))

                            goto err;

                        /*-

                         * Apply coordinate blinding for EC_POINT.

                         *

                         * The underlying EC_METHOD can optionally implement this function:

                         * ec_point_blind_coordinates() returns 0 in case of errors or 1 on

                         * success or if coordinate blinding is not implemented for this

                         * group.

                         */

                        if (!ec_point_blind_coordinates(group, r, ctx)) {

                            ECerr(EC_F_EC_WNAF_MUL, EC_R_POINT_COORDINATES_BLIND_FAILURE);

                            goto err;

                        }

                        r_is_at_infinity = 0;

                    } else {

                        if (!EC_POINT_add

                            (group, r, r, val_sub[i][digit >> 1], ctx))

                            goto err;

                    }

                }

            }

        }

    }

    if (r_is_at_infinity) {

        if (!EC_POINT_set_to_infinity(group, r))

            goto err;

    } else {

        if (r_is_inverted)

            if (!EC_POINT_invert(group, r, ctx))

                goto err;

    }

    ret = 1;

 err:

    EC_POINT_free(tmp);

    OPENSSL_free(wsize);

    OPENSSL_free(wNAF_len);

    if (wNAF != NULL) {

        signed char **w;

        for (w = wNAF; *w != NULL; w++)

            OPENSSL_free(*w);

        OPENSSL_free(wNAF);

    }

    if (val != NULL) {

        for (v = val; *v != NULL; v++)

            EC_POINT_clear_free(*v);

        OPENSSL_free(val);

    }

    OPENSSL_free(val_sub);

    return ret;

}

/*-

 * ec_wNAF_precompute_mult()

 * creates an EC_PRE_COMP object with preprecomputed multiples of the generator

 * for use with wNAF splitting as implemented in ec_wNAF_mul().

 *

 * 'pre_comp->points' is an array of multiples of the generator

 * of the following form:

 * points[0] =     generator;

 * points[1] = 3 * generator;

 * ...

 * points[2^(w-1)-1] =     (2^(w-1)-1) * generator;

 * points[2^(w-1)]   =     2^blocksize * generator;

 * points[2^(w-1)+1] = 3 * 2^blocksize * generator;

 * ...

 * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) *  2^(blocksize*(numblocks-2)) * generator

 * points[2^(w-1)*(numblocks-1)]   =              2^(blocksize*(numblocks-1)) * generator

 * ...

 * points[2^(w-1)*numblocks-1]     = (2^(w-1)) *  2^(blocksize*(numblocks-1)) * generator

 * points[2^(w-1)*numblocks]       = NULL

 */

int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx)

{

    const EC_POINT *generator;

    EC_POINT *tmp_point = NULL, *base = NULL, **var;

    BN_CTX *new_ctx = NULL;

    const BIGNUM *order;

    size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num;

    EC_POINT **points = NULL;

    EC_PRE_COMP *pre_comp;

    int ret = 0;

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

    EC_pre_comp_free(group);

    if ((pre_comp = ec_pre_comp_new(group)) == NULL)

        return 0;

    generator = EC_GROUP_get0_generator(group);

    if (generator == NULL) {

        ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR);

        goto err;

    }

    if (ctx == NULL) {

        ctx = new_ctx = BN_CTX_new();

        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)) {

        ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER);

        goto err;

    }

    bits = BN_num_bits(order);

    /*

     * The following parameters mean we precompute (approximately) one point

     * per bit. TBD: The combination 8, 4 is perfect for 160 bits; for other

     * bit lengths, other parameter combinations might provide better

     * efficiency.

     */

    blocksize = 8;

    w = 4;

    if (EC_window_bits_for_scalar_size(bits) > w) {

        /* let's not make the window too small ... */

        w = EC_window_bits_for_scalar_size(bits);

    }

    numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks

                                                     * to use for wNAF

                                                     * splitting */

    pre_points_per_block = (size_t)1 << (w - 1);

    num = pre_points_per_block * numblocks; /* number of points to compute

                                             * and store */