bn_exp2.c

/*
 * Copyright 1995-2017 The OpenSSL Project Authors. All Rights Reserved.
 *
 * 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
 */

#include <stdio.h>
#include "internal/cryptlib.h"
#include "bn_lcl.h"

#define TABLE_SIZE      32

int BN_mod_exp2_mont(BIGNUM *rr, const BIGNUM *a1, const BIGNUM *p1,
                     const BIGNUM *a2, const BIGNUM *p2, const BIGNUM *m,
                     BN_CTX *ctx, BN_MONT_CTX *in_mont)
{
    int i, j, bits, b, bits1, bits2, ret =
        0, wpos1, wpos2, window1, window2, wvalue1, wvalue2;
    int r_is_one = 1;
    BIGNUM *d, *r;
    const BIGNUM *a_mod_m;
    /* Tables of variables obtained from 'ctx' */
    BIGNUM *val1[TABLE_SIZE], *val2[TABLE_SIZE];
    BN_MONT_CTX *mont = NULL;

    bn_check_top(a1);
    bn_check_top(p1);
    bn_check_top(a2);
    bn_check_top(p2);
    bn_check_top(m);

    if (!(m->d[0] & 1)) {
        BNerr(BN_F_BN_MOD_EXP2_MONT, BN_R_CALLED_WITH_EVEN_MODULUS);
        return 0;
    }
    bits1 = BN_num_bits(p1);
    bits2 = BN_num_bits(p2);
    if ((bits1 == 0) && (bits2 == 0)) {
        ret = BN_one(rr);
        return ret;
    }

    bits = (bits1 > bits2) ? bits1 : bits2;

    BN_CTX_start(ctx);
    d = BN_CTX_get(ctx);
    r = BN_CTX_get(ctx);
    val1[0] = BN_CTX_get(ctx);
    val2[0] = BN_CTX_get(ctx);
    if (val2[0] == NULL)
        goto err;

    if (in_mont != NULL)
        mont = in_mont;
    else {
        if ((mont = BN_MONT_CTX_new()) == NULL)
            goto err;
        if (!BN_MONT_CTX_set(mont, m, ctx))
            goto err;
    }

    window1 = BN_window_bits_for_exponent_size(bits1);
    window2 = BN_window_bits_for_exponent_size(bits2);

    /*
     * Build table for a1:   val1[i] := a1^(2*i + 1) mod m  for i = 0 .. 2^(window1-1)
     */
    if (a1->neg || BN_ucmp(a1, m) >= 0) {
        if (!BN_mod(val1[0], a1, m, ctx))
            goto err;
        a_mod_m = val1[0];
    } else
        a_mod_m = a1;
    if (BN_is_zero(a_mod_m)) {
        BN_zero(rr);
        ret = 1;
        goto err;
    }

    if (!BN_to_montgomery(val1[0], a_mod_m, mont, ctx))
        goto err;
    if (window1 > 1) {
        if (!BN_mod_mul_montgomery(d, val1[0], val1[0], mont, ctx))
            goto err;

        j = 1 << (window1 - 1);
        for (i = 1; i < j; i++) {
            if (((val1[i] = BN_CTX_get(ctx)) == NULL) ||
                !BN_mod_mul_montgomery(val1[i], val1[i - 1], d, mont, ctx))
                goto err;
        }
    }

    /*
     * Build table for a2:   val2[i] := a2^(2*i + 1) mod m  for i = 0 .. 2^(window2-1)
     */
    if (a2->neg || BN_ucmp(a2, m) >= 0) {
        if (!BN_mod(val2[0], a2, m, ctx))
            goto err;
        a_mod_m = val2[0];
    } else
        a_mod_m = a2;
    if (BN_is_zero(a_mod_m)) {
        BN_zero(rr);
        ret = 1;
        goto err;
    }
    if (!BN_to_montgomery(val2[0], a_mod_m, mont, ctx))
        goto err;
    if (window2 > 1) {
        if (!BN_mod_mul_montgomery(d, val2[0], val2[0], mont, ctx))
            goto err;

        j = 1 << (window2 - 1);
        for (i = 1; i < j; i++) {
            if (((val2[i] = BN_CTX_get(ctx)) == NULL) ||
                !BN_mod_mul_montgomery(val2[i], val2[i - 1], d, mont, ctx))
                goto err;
        }
    }

    /* Now compute the power product, using independent windows. */
    r_is_one = 1;
    wvalue1 = 0;                /* The 'value' of the first window */
    wvalue2 = 0;                /* The 'value' of the second window */
    wpos1 = 0;                  /* If wvalue1 > 0, the bottom bit of the
                                 * first window */
    wpos2 = 0;                  /* If wvalue2 > 0, the bottom bit of the
                                 * second window */

    if (!BN_to_montgomery(r, BN_value_one(), mont, ctx))
        goto err;
    for (b = bits - 1; b >= 0; b--) {
        if (!r_is_one) {
            if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
                goto err;
        }

        if (!wvalue1)
            if (BN_is_bit_set(p1, b)) {
                /*
                 * consider bits b-window1+1 .. b for this window
                 */
                i = b - window1 + 1;
                while (!BN_is_bit_set(p1, i)) /* works for i<0 */
                    i++;
                wpos1 = i;
                wvalue1 = 1;
                for (i = b - 1; i >= wpos1; i--) {
                    wvalue1 <<= 1;
                    if (BN_is_bit_set(p1, i))
                        wvalue1++;
                }
            }

        if (!wvalue2)
            if (BN_is_bit_set(p2, b)) {
                /*
                 * consider bits b-window2+1 .. b for this window
                 */
                i = b - window2 + 1;
                while (!BN_is_bit_set(p2, i))
                    i++;
                wpos2 = i;
                wvalue2 = 1;
                for (i = b - 1; i >= wpos2; i--) {
                    wvalue2 <<= 1;
                    if (BN_is_bit_set(p2, i))
                        wvalue2++;
                }
            }

        if (wvalue1 && b == wpos1) {
            /* wvalue1 is odd and < 2^window1 */
            if (!BN_mod_mul_montgomery(r, r, val1[wvalue1 >> 1], mont, ctx))
                goto err;
            wvalue1 = 0;
            r_is_one = 0;
        }

        if (wvalue2 && b == wpos2) {
            /* wvalue2 is odd and < 2^window2 */
            if (!BN_mod_mul_montgomery(r, r, val2[wvalue2 >> 1], mont, ctx))
                goto err;
            wvalue2 = 0;
            r_is_one = 0;
        }
    }
    if (!BN_from_montgomery(rr, r, mont, ctx))
        goto err;
    ret = 1;
 err:
    if (in_mont == NULL)
        BN_MONT_CTX_free(mont);
    BN_CTX_end(ctx);
    bn_check_top(rr);
    return ret;
}