int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
                    const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
{
    int i, j, bits, ret = 0, wstart, wend, window, wvalue;
    int start = 1;
    BIGNUM *d, *r;
    const BIGNUM *aa;
    BIGNUM *val[TABLE_SIZE];
    BN_MONT_CTX *mont = NULL;
    if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
        return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
    }
    bn_check_top(a);
    bn_check_top(p);
    bn_check_top(m);
    if (!BN_is_odd(m)) {
        BNerr(BN_F_BN_MOD_EXP_MONT, BN_R_CALLED_WITH_EVEN_MODULUS);
        return (0);
    }
    bits = BN_num_bits(p);
    if (bits == 0) {
        if (BN_is_one(m)) {
            ret = 1;
            BN_zero(rr);
        } else {
            ret = BN_one(rr);
        }
        return ret;
    }
    BN_CTX_start(ctx);
    d = BN_CTX_get(ctx);
    r = BN_CTX_get(ctx);
    val[0] = BN_CTX_get(ctx);
    if (!d || !r || !val[0])
        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;
    }
    if (a->neg || BN_ucmp(a, m) >= 0) {
        if (!BN_nnmod(val[0], a, m, ctx))
            goto err;
        aa = val[0];
    } else
        aa = a;
    if (BN_is_zero(aa)) {
        BN_zero(rr);
        ret = 1;
        goto err;
    }
    if (!BN_to_montgomery(val[0], aa, mont, ctx))
        goto err;
    window = BN_window_bits_for_exponent_size(bits);
    if (window > 1) {
        if (!BN_mod_mul_montgomery(d, val[0], val[0], mont, ctx))
            goto err;
        j = 1 << (window - 1);
        for (i = 1; i < j; i++) {
            if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
                !BN_mod_mul_montgomery(val[i], val[i - 1], d, mont, ctx))
                goto err;
        }
    }
    start = 1;
    wvalue = 0;
    wstart = bits - 1;
    wend = 0;
#if 1
    j = m->top;
    if (m->d[j - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
        if (bn_wexpand(r, j) == NULL)
            goto err;
        r->d[0] = (0 - m->d[0]) & BN_MASK2;
        for (i = 1; i < j; i++)
            r->d[i] = (~m->d[i]) & BN_MASK2;
        r->top = j;
        bn_correct_top(r);
    } else
#endif
    if (!BN_to_montgomery(r, BN_value_one(), mont, ctx))
        goto err;
    for (;;) {
        if (BN_is_bit_set(p, wstart) == 0) {
            if (!start) {
                if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
                    goto err;
            }
            if (wstart == 0)
                break;
            wstart--;
            continue;
        }
        j = wstart;
        wvalue = 1;
        wend = 0;
        for (i = 1; i < window; i++) {
            if (wstart - i < 0)
                break;
            if (BN_is_bit_set(p, wstart - i)) {
                wvalue <<= (i - wend);
                wvalue |= 1;
                wend = i;
            }
        }
        j = wend + 1;
        if (!start)
            for (i = 0; i < j; i++) {
                if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
                    goto err;
            }
        if (!BN_mod_mul_montgomery(r, r, val[wvalue >> 1], mont, ctx))
            goto err;
        wstart -= wend + 1;
        wvalue = 0;
        start = 0;
        if (wstart < 0)
            break;
    }
#if defined(SPARC_T4_MONT)
    if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
        j = mont->N.top;
        val[0]->d[0] = 1;
        for (i = 1; i < j; i++)
            val[0]->d[i] = 0;
        val[0]->top = j;
        if (!BN_mod_mul_montgomery(rr, r, val[0], mont, ctx))
            goto err;
    } else
#endif
    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);
}
['static int srp_Verify_N_and_g(const BIGNUM *N, const BIGNUM *g)\n{\n    BN_CTX *bn_ctx = BN_CTX_new();\n    BIGNUM *p = BN_new();\n    BIGNUM *r = BN_new();\n    int ret =\n        g != NULL && N != NULL && bn_ctx != NULL && BN_is_odd(N) &&\n        BN_is_prime_ex(N, SRP_NUMBER_ITERATIONS_FOR_PRIME, bn_ctx, NULL) == 1 &&\n        p != NULL && BN_rshift1(p, N) &&\n        BN_is_prime_ex(p, SRP_NUMBER_ITERATIONS_FOR_PRIME, bn_ctx, NULL) == 1 &&\n        r != NULL &&\n        BN_mod_exp(r, g, p, N, bn_ctx) &&\n        BN_add_word(r, 1) && BN_cmp(r, N) == 0;\n    BN_free(r);\n    BN_free(p);\n    BN_CTX_free(bn_ctx);\n    return ret;\n}', 'int BN_is_prime_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed,\n                   BN_GENCB *cb)\n{\n    return BN_is_prime_fasttest_ex(a, checks, ctx_passed, 0, cb);\n}', 'int BN_is_prime_fasttest_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed,\n                            int do_trial_division, BN_GENCB *cb)\n{\n    int i, j, ret = -1;\n    int k;\n    BN_CTX *ctx = NULL;\n    BIGNUM *A1, *A1_odd, *check;\n    BN_MONT_CTX *mont = NULL;\n    if (BN_cmp(a, BN_value_one()) <= 0)\n        return 0;\n    if (checks == BN_prime_checks)\n        checks = BN_prime_checks_for_size(BN_num_bits(a));\n    if (!BN_is_odd(a))\n        return BN_is_word(a, 2);\n    if (do_trial_division) {\n        for (i = 1; i < NUMPRIMES; i++) {\n            BN_ULONG mod = BN_mod_word(a, primes[i]);\n            if (mod == (BN_ULONG)-1)\n                goto err;\n            if (mod == 0)\n                return BN_is_word(a, primes[i]);\n        }\n        if (!BN_GENCB_call(cb, 1, -1))\n            goto err;\n    }\n    if (ctx_passed != NULL)\n        ctx = ctx_passed;\n    else if ((ctx = BN_CTX_new()) == NULL)\n        goto err;\n    BN_CTX_start(ctx);\n    A1 = BN_CTX_get(ctx);\n    A1_odd = BN_CTX_get(ctx);\n    check = BN_CTX_get(ctx);\n    if (check == NULL)\n        goto err;\n    if (!BN_copy(A1, a))\n        goto err;\n    if (!BN_sub_word(A1, 1))\n        goto err;\n    if (BN_is_zero(A1)) {\n        ret = 0;\n        goto err;\n    }\n    k = 1;\n    while (!BN_is_bit_set(A1, k))\n        k++;\n    if (!BN_rshift(A1_odd, A1, k))\n        goto err;\n    mont = BN_MONT_CTX_new();\n    if (mont == NULL)\n        goto err;\n    if (!BN_MONT_CTX_set(mont, a, ctx))\n        goto err;\n    for (i = 0; i < checks; i++) {\n        if (!BN_pseudo_rand_range(check, A1))\n            goto err;\n        if (!BN_add_word(check, 1))\n            goto err;\n        j = witness(check, a, A1, A1_odd, k, ctx, mont);\n        if (j == -1)\n            goto err;\n        if (j) {\n            ret = 0;\n            goto err;\n        }\n        if (!BN_GENCB_call(cb, 1, i))\n            goto err;\n    }\n    ret = 1;\n err:\n    if (ctx != NULL) {\n        BN_CTX_end(ctx);\n        if (ctx_passed == NULL)\n            BN_CTX_free(ctx);\n    }\n    BN_MONT_CTX_free(mont);\n    return (ret);\n}', 'static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,\n                   const BIGNUM *a1_odd, int k, BN_CTX *ctx,\n                   BN_MONT_CTX *mont)\n{\n    if (!BN_mod_exp_mont(w, w, a1_odd, a, ctx, mont))\n        return -1;\n    if (BN_is_one(w))\n        return 0;\n    if (BN_cmp(w, a1) == 0)\n        return 0;\n    while (--k) {\n        if (!BN_mod_mul(w, w, w, a, ctx))\n            return -1;\n        if (BN_is_one(w))\n            return 1;\n        if (BN_cmp(w, a1) == 0)\n            return 0;\n    }\n    bn_check_top(w);\n    return 1;\n}', 'int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,\n                    const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)\n{\n    int i, j, bits, ret = 0, wstart, wend, window, wvalue;\n    int start = 1;\n    BIGNUM *d, *r;\n    const BIGNUM *aa;\n    BIGNUM *val[TABLE_SIZE];\n    BN_MONT_CTX *mont = NULL;\n    if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {\n        return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);\n    }\n    bn_check_top(a);\n    bn_check_top(p);\n    bn_check_top(m);\n    if (!BN_is_odd(m)) {\n        BNerr(BN_F_BN_MOD_EXP_MONT, BN_R_CALLED_WITH_EVEN_MODULUS);\n        return (0);\n    }\n    bits = BN_num_bits(p);\n    if (bits == 0) {\n        if (BN_is_one(m)) {\n            ret = 1;\n            BN_zero(rr);\n        } else {\n            ret = BN_one(rr);\n        }\n        return ret;\n    }\n    BN_CTX_start(ctx);\n    d = BN_CTX_get(ctx);\n    r = BN_CTX_get(ctx);\n    val[0] = BN_CTX_get(ctx);\n    if (!d || !r || !val[0])\n        goto err;\n    if (in_mont != NULL)\n        mont = in_mont;\n    else {\n        if ((mont = BN_MONT_CTX_new()) == NULL)\n            goto err;\n        if (!BN_MONT_CTX_set(mont, m, ctx))\n            goto err;\n    }\n    if (a->neg || BN_ucmp(a, m) >= 0) {\n        if (!BN_nnmod(val[0], a, m, ctx))\n            goto err;\n        aa = val[0];\n    } else\n        aa = a;\n    if (BN_is_zero(aa)) {\n        BN_zero(rr);\n        ret = 1;\n        goto err;\n    }\n    if (!BN_to_montgomery(val[0], aa, mont, ctx))\n        goto err;\n    window = BN_window_bits_for_exponent_size(bits);\n    if (window > 1) {\n        if (!BN_mod_mul_montgomery(d, val[0], val[0], mont, ctx))\n            goto err;\n        j = 1 << (window - 1);\n        for (i = 1; i < j; i++) {\n            if (((val[i] = BN_CTX_get(ctx)) == NULL) ||\n                !BN_mod_mul_montgomery(val[i], val[i - 1], d, mont, ctx))\n                goto err;\n        }\n    }\n    start = 1;\n    wvalue = 0;\n    wstart = bits - 1;\n    wend = 0;\n#if 1\n    j = m->top;\n    if (m->d[j - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {\n        if (bn_wexpand(r, j) == NULL)\n            goto err;\n        r->d[0] = (0 - m->d[0]) & BN_MASK2;\n        for (i = 1; i < j; i++)\n            r->d[i] = (~m->d[i]) & BN_MASK2;\n        r->top = j;\n        bn_correct_top(r);\n    } else\n#endif\n    if (!BN_to_montgomery(r, BN_value_one(), mont, ctx))\n        goto err;\n    for (;;) {\n        if (BN_is_bit_set(p, wstart) == 0) {\n            if (!start) {\n                if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))\n                    goto err;\n            }\n            if (wstart == 0)\n                break;\n            wstart--;\n            continue;\n        }\n        j = wstart;\n        wvalue = 1;\n        wend = 0;\n        for (i = 1; i < window; i++) {\n            if (wstart - i < 0)\n                break;\n            if (BN_is_bit_set(p, wstart - i)) {\n                wvalue <<= (i - wend);\n                wvalue |= 1;\n                wend = i;\n            }\n        }\n        j = wend + 1;\n        if (!start)\n            for (i = 0; i < j; i++) {\n                if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))\n                    goto err;\n            }\n        if (!BN_mod_mul_montgomery(r, r, val[wvalue >> 1], mont, ctx))\n            goto err;\n        wstart -= wend + 1;\n        wvalue = 0;\n        start = 0;\n        if (wstart < 0)\n            break;\n    }\n#if defined(SPARC_T4_MONT)\n    if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {\n        j = mont->N.top;\n        val[0]->d[0] = 1;\n        for (i = 1; i < j; i++)\n            val[0]->d[i] = 0;\n        val[0]->top = j;\n        if (!BN_mod_mul_montgomery(rr, r, val[0], mont, ctx))\n            goto err;\n    } else\n#endif\n    if (!BN_from_montgomery(rr, r, mont, ctx))\n        goto err;\n    ret = 1;\n err:\n    if (in_mont == NULL)\n        BN_MONT_CTX_free(mont);\n    BN_CTX_end(ctx);\n    bn_check_top(rr);\n    return (ret);\n}', 'int BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx)\n{\n    if (!(BN_mod(r, m, d, ctx)))\n        return 0;\n    if (!r->neg)\n        return 1;\n    return (d->neg ? BN_sub : BN_add) (r, r, d);\n}', 'int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,\n           BN_CTX *ctx)\n{\n    int norm_shift, i, loop;\n    BIGNUM *tmp, wnum, *snum, *sdiv, *res;\n    BN_ULONG *resp, *wnump;\n    BN_ULONG d0, d1;\n    int num_n, div_n;\n    int no_branch = 0;\n    if ((num->top > 0 && num->d[num->top - 1] == 0) ||\n        (divisor->top > 0 && divisor->d[divisor->top - 1] == 0)) {\n        BNerr(BN_F_BN_DIV, BN_R_NOT_INITIALIZED);\n        return 0;\n    }\n    bn_check_top(num);\n    bn_check_top(divisor);\n    if ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0)\n        || (BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0)) {\n        no_branch = 1;\n    }\n    bn_check_top(dv);\n    bn_check_top(rm);\n    if (BN_is_zero(divisor)) {\n        BNerr(BN_F_BN_DIV, BN_R_DIV_BY_ZERO);\n        return (0);\n    }\n    if (!no_branch && BN_ucmp(num, divisor) < 0) {\n        if (rm != NULL) {\n            if (BN_copy(rm, num) == NULL)\n                return (0);\n        }\n        if (dv != NULL)\n            BN_zero(dv);\n        return (1);\n    }\n    BN_CTX_start(ctx);\n    tmp = BN_CTX_get(ctx);\n    snum = BN_CTX_get(ctx);\n    sdiv = BN_CTX_get(ctx);\n    if (dv == NULL)\n        res = BN_CTX_get(ctx);\n    else\n        res = dv;\n    if (sdiv == NULL || res == NULL || tmp == NULL || snum == NULL)\n        goto err;\n    norm_shift = BN_BITS2 - ((BN_num_bits(divisor)) % BN_BITS2);\n    if (!(BN_lshift(sdiv, divisor, norm_shift)))\n        goto err;\n    sdiv->neg = 0;\n    norm_shift += BN_BITS2;\n    if (!(BN_lshift(snum, num, norm_shift)))\n        goto err;\n    snum->neg = 0;\n    if (no_branch) {\n        if (snum->top <= sdiv->top + 1) {\n            if (bn_wexpand(snum, sdiv->top + 2) == NULL)\n                goto err;\n            for (i = snum->top; i < sdiv->top + 2; i++)\n                snum->d[i] = 0;\n            snum->top = sdiv->top + 2;\n        } else {\n            if (bn_wexpand(snum, snum->top + 1) == NULL)\n                goto err;\n            snum->d[snum->top] = 0;\n            snum->top++;\n        }\n    }\n    div_n = sdiv->top;\n    num_n = snum->top;\n    loop = num_n - div_n;\n    wnum.neg = 0;\n    wnum.d = &(snum->d[loop]);\n    wnum.top = div_n;\n    wnum.dmax = snum->dmax - loop;\n    d0 = sdiv->d[div_n - 1];\n    d1 = (div_n == 1) ? 0 : sdiv->d[div_n - 2];\n    wnump = &(snum->d[num_n - 1]);\n    if (!bn_wexpand(res, (loop + 1)))\n        goto err;\n    res->neg = (num->neg ^ divisor->neg);\n    res->top = loop - no_branch;\n    resp = &(res->d[loop - 1]);\n    if (!bn_wexpand(tmp, (div_n + 1)))\n        goto err;\n    if (!no_branch) {\n        if (BN_ucmp(&wnum, sdiv) >= 0) {\n            bn_clear_top2max(&wnum);\n            bn_sub_words(wnum.d, wnum.d, sdiv->d, div_n);\n            *resp = 1;\n        } else\n            res->top--;\n    }\n    resp++;\n    if (res->top == 0)\n        res->neg = 0;\n    else\n        resp--;\n    for (i = 0; i < loop - 1; i++, wnump--) {\n        BN_ULONG q, l0;\n# if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)\n        BN_ULONG bn_div_3_words(BN_ULONG *, BN_ULONG, BN_ULONG);\n        q = bn_div_3_words(wnump, d1, d0);\n# else\n        BN_ULONG n0, n1, rem = 0;\n        n0 = wnump[0];\n        n1 = wnump[-1];\n        if (n0 == d0)\n            q = BN_MASK2;\n        else {\n#  ifdef BN_LLONG\n            BN_ULLONG t2;\n#   if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)\n            q = (BN_ULONG)(((((BN_ULLONG) n0) << BN_BITS2) | n1) / d0);\n#   else\n            q = bn_div_words(n0, n1, d0);\n#   endif\n#   ifndef REMAINDER_IS_ALREADY_CALCULATED\n            rem = (n1 - q * d0) & BN_MASK2;\n#   endif\n            t2 = (BN_ULLONG) d1 *q;\n            for (;;) {\n                if (t2 <= ((((BN_ULLONG) rem) << BN_BITS2) | wnump[-2]))\n                    break;\n                q--;\n                rem += d0;\n                if (rem < d0)\n                    break;\n                t2 -= d1;\n            }\n#  else\n            BN_ULONG t2l, t2h;\n            q = bn_div_words(n0, n1, d0);\n#   ifndef REMAINDER_IS_ALREADY_CALCULATED\n            rem = (n1 - q * d0) & BN_MASK2;\n#   endif\n#   if defined(BN_UMULT_LOHI)\n            BN_UMULT_LOHI(t2l, t2h, d1, q);\n#   elif defined(BN_UMULT_HIGH)\n            t2l = d1 * q;\n            t2h = BN_UMULT_HIGH(d1, q);\n#   else\n            {\n                BN_ULONG ql, qh;\n                t2l = LBITS(d1);\n                t2h = HBITS(d1);\n                ql = LBITS(q);\n                qh = HBITS(q);\n                mul64(t2l, t2h, ql, qh);\n            }\n#   endif\n            for (;;) {\n                if ((t2h < rem) || ((t2h == rem) && (t2l <= wnump[-2])))\n                    break;\n                q--;\n                rem += d0;\n                if (rem < d0)\n                    break;\n                if (t2l < d1)\n                    t2h--;\n                t2l -= d1;\n            }\n#  endif\n        }\n# endif\n        l0 = bn_mul_words(tmp->d, sdiv->d, div_n, q);\n        tmp->d[div_n] = l0;\n        wnum.d--;\n        if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n + 1)) {\n            q--;\n            if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))\n                (*wnump)++;\n        }\n        resp--;\n        *resp = q;\n    }\n    bn_correct_top(snum);\n    if (rm != NULL) {\n        int neg = num->neg;\n        BN_rshift(rm, snum, norm_shift);\n        if (!BN_is_zero(rm))\n            rm->neg = neg;\n        bn_check_top(rm);\n    }\n    if (no_branch)\n        bn_correct_top(res);\n    BN_CTX_end(ctx);\n    return (1);\n err:\n    bn_check_top(rm);\n    BN_CTX_end(ctx);\n    return (0);\n}', 'int BN_rshift1(BIGNUM *r, const BIGNUM *a)\n{\n    BN_ULONG *ap, *rp, t, c;\n    int i, j;\n    bn_check_top(r);\n    bn_check_top(a);\n    if (BN_is_zero(a)) {\n        BN_zero(r);\n        return (1);\n    }\n    i = a->top;\n    ap = a->d;\n    j = i - (ap[i - 1] == 1);\n    if (a != r) {\n        if (bn_wexpand(r, j) == NULL)\n            return (0);\n        r->neg = a->neg;\n    }\n    rp = r->d;\n    t = ap[--i];\n    c = (t & 1) ? BN_TBIT : 0;\n    if (t >>= 1)\n        rp[i] = t;\n    while (i > 0) {\n        t = ap[--i];\n        rp[i] = ((t >> 1) & BN_MASK2) | c;\n        c = (t & 1) ? BN_TBIT : 0;\n    }\n    r->top = j;\n    if (!r->top)\n        r->neg = 0;\n    bn_check_top(r);\n    return (1);\n}']