Commit message: bn/bn_exp.c: constant-time MOD_EXP_CTIME_COPY_FROM_PREBUF.

Performance penalty varies from platform to platform, and even
key length. For rsa2048 sign it was observed to reach almost 10%.

CVE-2016-0702

Reviewed-by: Richard Levitte <levitte@openssl.org>
Reviewed-by: Rich Salz <rsalz@openssl.org>
CVE: CVE-2016-0702
CWE: CWE-200
Vulnerability description: The MOD_EXP_CTIME_COPY_FROM_PREBUF function in crypto/bn/bn_exp.c in OpenSSL 1.0.1 before 1.0.1s and 1.0.2 before 1.0.2g does not properly consider cache-bank access times during modular exponentiation, which makes it easier for local users to discover RSA keys by running a crafted application on the same Intel Sandy Bridge CPU core as a victim and leveraging cache-bank conflicts, aka a "CacheBleed" attack.

Project: openssl

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;
    /* Table of variables obtained from 'ctx' */
    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) {
        /* x**0 mod 1 is still zero. */
        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 this is not done, things will break in the montgomery part
     */

    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;               /* 1 */

    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;           /* 2 */
        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;                  /* This is used to avoid multiplication etc
                                 * when there is only the value '1' in the
                                 * buffer. */
    wvalue = 0;                 /* The 'value' of the window */
    wstart = bits - 1;          /* The top bit of the window */
    wend = 0;                   /* The bottom bit of the window */

#if 1                           /* by Shay Gueron's suggestion */
    j = m->top;                 /* borrow j */
    if (m->d[j - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
        if (bn_wexpand(r, j) == NULL)
            goto err;
        /* 2^(top*BN_BITS2) - m */
        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;
        /*
         * Upper words will be zero if the corresponding words of 'm' were
         * 0xfff[...], so decrement r->top accordingly.
         */
        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;
        }
        /*
         * We now have wstart on a 'set' bit, we now need to work out how bit
         * a window to do.  To do this we need to scan forward until the last
         * set bit before the end of the window
         */
        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;
            }
        }

        /* wend is the size of the current window */
        j = wend + 1;
        /* add the 'bytes above' */
        if (!start)
            for (i = 0; i < j; i++) {
                if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
                    goto err;
            }

        /* wvalue will be an odd number < 2^window */
        if (!BN_mod_mul_montgomery(r, r, val[wvalue >> 1], mont, ctx))
            goto err;

        /* move the 'window' down further */
        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;        /* borrow j */
        val[0]->d[0] = 1;       /* borrow val[0] */
        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);
}

Project: openssl

static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top,
                                          unsigned char *buf, int idx,
                                          int window)
{
    int i, j;
    int width = 1 << window;
    volatile BN_ULONG *table = (volatile BN_ULONG *)buf;

    if (bn_wexpand(b, top) == NULL)
        return 0;

    if (window <= 3) {
        for (i = 0; i < top; i++, table += width) {
            BN_ULONG acc = 0;

            for (j = 0; j < width; j++) {
                acc |= table[j] &
                       ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1));
            }

            b->d[i] = acc;
        }
    } else {
        int xstride = 1 << (window - 2);
        BN_ULONG y0, y1, y2, y3;

        i = idx >> (window - 2);        /* equivalent of idx / xstride */
        idx &= xstride - 1;             /* equivalent of idx % xstride */

        y0 = (BN_ULONG)0 - (constant_time_eq_int(i,0)&1);
        y1 = (BN_ULONG)0 - (constant_time_eq_int(i,1)&1);
        y2 = (BN_ULONG)0 - (constant_time_eq_int(i,2)&1);
        y3 = (BN_ULONG)0 - (constant_time_eq_int(i,3)&1);

        for (i = 0; i < top; i++, table += width) {
            BN_ULONG acc = 0;

            for (j = 0; j < xstride; j++) {
                acc |= ( (table[j + 0 * xstride] & y0) |
                         (table[j + 1 * xstride] & y1) |
                         (table[j + 2 * xstride] & y2) |
                         (table[j + 3 * xstride] & y3) )
                       & ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1));
            }

            b->d[i] = acc;
        }
    }

    b->top = top;
    bn_correct_top(b);
    return 1;
}

Project: openssl

static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top,
                                        unsigned char *buf, int idx,
                                        int window)
{
    int i, j;
    int width = 1 << window;
    BN_ULONG *table = (BN_ULONG *)buf;

    if (top > b->top)
        top = b->top;           /* this works because 'buf' is explicitly
                                 * zeroed */
    for (i = 0, j = idx; i < top; i++, j += width) {
        table[j] = b->d[i];
    }

    return 1;
}

Project: openssl

int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
{
    int i, bits, ret = 0;
    BIGNUM *v, *rr;

    if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
        /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
        BNerr(BN_F_BN_EXP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
        return -1;
    }

    BN_CTX_start(ctx);
    if ((r == a) || (r == p))
        rr = BN_CTX_get(ctx);
    else
        rr = r;
    v = BN_CTX_get(ctx);
    if (rr == NULL || v == NULL)
        goto err;

    if (BN_copy(v, a) == NULL)
        goto err;
    bits = BN_num_bits(p);

    if (BN_is_odd(p)) {
        if (BN_copy(rr, a) == NULL)
            goto err;
    } else {
        if (!BN_one(rr))
            goto err;
    }

    for (i = 1; i < bits; i++) {
        if (!BN_sqr(v, v, ctx))
            goto err;
        if (BN_is_bit_set(p, i)) {
            if (!BN_mul(rr, rr, v, ctx))
                goto err;
        }
    }
    if (r != rr)
        BN_copy(r, rr);
    ret = 1;
 err:
    BN_CTX_end(ctx);
    bn_check_top(r);
    return (ret);
}

Project: openssl

int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
                         const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
{
    BN_MONT_CTX *mont = NULL;
    int b, bits, ret = 0;
    int r_is_one;
    BN_ULONG w, next_w;
    BIGNUM *d, *r, *t;
    BIGNUM *swap_tmp;
#define BN_MOD_MUL_WORD(r, w, m) \
                (BN_mul_word(r, (w)) && \
                (/* BN_ucmp(r, (m)) < 0 ? 1 :*/  \
                        (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
    /*
     * BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is
     * probably more overhead than always using BN_mod (which uses BN_copy if
     * a similar test returns true).
     */
    /*
     * We can use BN_mod and do not need BN_nnmod because our accumulator is
     * never negative (the result of BN_mod does not depend on the sign of
     * the modulus).
     */
#define BN_TO_MONTGOMERY_WORD(r, w, mont) \
                (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))

    if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
        /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
        BNerr(BN_F_BN_MOD_EXP_MONT_WORD, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
        return -1;
    }

    bn_check_top(p);
    bn_check_top(m);

    if (!BN_is_odd(m)) {
        BNerr(BN_F_BN_MOD_EXP_MONT_WORD, BN_R_CALLED_WITH_EVEN_MODULUS);
        return (0);
    }
    if (m->top == 1)
        a %= m->d[0];           /* make sure that 'a' is reduced */

    bits = BN_num_bits(p);
    if (bits == 0) {
        /* x**0 mod 1 is still zero. */
        if (BN_is_one(m)) {
            ret = 1;
            BN_zero(rr);
        } else {
            ret = BN_one(rr);
        }
        return ret;
    }
    if (a == 0) {
        BN_zero(rr);
        ret = 1;
        return ret;
    }

    BN_CTX_start(ctx);
    d = BN_CTX_get(ctx);
    r = BN_CTX_get(ctx);
    t = BN_CTX_get(ctx);
    if (d == NULL || r == NULL || t == 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;
    }

    r_is_one = 1;               /* except for Montgomery factor */

    /* bits-1 >= 0 */

    /* The result is accumulated in the product r*w. */
    w = a;                      /* bit 'bits-1' of 'p' is always set */
    for (b = bits - 2; b >= 0; b--) {
        /* First, square r*w. */
        next_w = w * w;
        if ((next_w / w) != w) { /* overflow */
            if (r_is_one) {
                if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
                    goto err;
                r_is_one = 0;
            } else {
                if (!BN_MOD_MUL_WORD(r, w, m))
                    goto err;
            }
            next_w = 1;
        }
        w = next_w;
        if (!r_is_one) {
            if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
                goto err;
        }

        /* Second, multiply r*w by 'a' if exponent bit is set. */
        if (BN_is_bit_set(p, b)) {
            next_w = w * a;
            if ((next_w / a) != w) { /* overflow */
                if (r_is_one) {
                    if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
                        goto err;
                    r_is_one = 0;
                } else {
                    if (!BN_MOD_MUL_WORD(r, w, m))
                        goto err;
                }
                next_w = a;
            }
            w = next_w;
        }
    }

    /* Finally, set r:=r*w. */
    if (w != 1) {
        if (r_is_one) {
            if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
                goto err;
            r_is_one = 0;
        } else {
            if (!BN_MOD_MUL_WORD(r, w, m))
                goto err;
        }
    }

    if (r_is_one) {             /* can happen only if a == 1 */
        if (!BN_one(rr))
            goto err;
    } else {
        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);
}