Commit message: crypto/bn/x86_64-mont5.pl: constant-time gather procedure.

At the same time remove miniscule bias in final subtraction.
Performance penalty varies from platform to platform, and even with
key length. For rsa2048 sign it was observed to be 4% for Sandy
Bridge and 7% on Broadwell.

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_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
                              const BIGNUM *m, BN_CTX *ctx,
                              BN_MONT_CTX *in_mont)
{
    int i, bits, ret = 0, window, wvalue;
    int top;
    BN_MONT_CTX *mont = NULL;

    int numPowers;
    unsigned char *powerbufFree = NULL;
    int powerbufLen = 0;
    unsigned char *powerbuf = NULL;
    BIGNUM tmp, am;
#if defined(SPARC_T4_MONT)
    unsigned int t4 = 0;
#endif

    bn_check_top(a);
    bn_check_top(p);
    bn_check_top(m);

    if (!BN_is_odd(m)) {
        BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME, BN_R_CALLED_WITH_EVEN_MODULUS);
        return (0);
    }

    top = m->top;

    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);

    /*
     * Allocate a montgomery context if it was not supplied by the caller. 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;
    }

#ifdef RSAZ_ENABLED
    /*
     * If the size of the operands allow it, perform the optimized
     * RSAZ exponentiation. For further information see
     * crypto/bn/rsaz_exp.c and accompanying assembly modules.
     */
    if ((16 == a->top) && (16 == p->top) && (BN_num_bits(m) == 1024)
        && rsaz_avx2_eligible()) {
        if (NULL == bn_wexpand(rr, 16))
            goto err;
        RSAZ_1024_mod_exp_avx2(rr->d, a->d, p->d, m->d, mont->RR.d,
                               mont->n0[0]);
        rr->top = 16;
        rr->neg = 0;
        bn_correct_top(rr);
        ret = 1;
        goto err;
    } else if ((8 == a->top) && (8 == p->top) && (BN_num_bits(m) == 512)) {
        if (NULL == bn_wexpand(rr, 8))
            goto err;
        RSAZ_512_mod_exp(rr->d, a->d, p->d, m->d, mont->n0[0], mont->RR.d);
        rr->top = 8;
        rr->neg = 0;
        bn_correct_top(rr);
        ret = 1;
        goto err;
    }
#endif

    /* Get the window size to use with size of p. */
    window = BN_window_bits_for_ctime_exponent_size(bits);
#if defined(SPARC_T4_MONT)
    if (window >= 5 && (top & 15) == 0 && top <= 64 &&
        (OPENSSL_sparcv9cap_P[1] & (CFR_MONTMUL | CFR_MONTSQR)) ==
        (CFR_MONTMUL | CFR_MONTSQR) && (t4 = OPENSSL_sparcv9cap_P[0]))
        window = 5;
    else
#endif
#if defined(OPENSSL_BN_ASM_MONT5)
    if (window >= 5) {
        window = 5;             /* ~5% improvement for RSA2048 sign, and even
                                 * for RSA4096 */
        if ((top & 7) == 0)
            powerbufLen += 2 * top * sizeof(m->d[0]);
    }
#endif
    (void)0;

    /*
     * Allocate a buffer large enough to hold all of the pre-computed powers
     * of am, am itself and tmp.
     */
    numPowers = 1 << window;
    powerbufLen += sizeof(m->d[0]) * (top * numPowers +
                                      ((2 * top) >
                                       numPowers ? (2 * top) : numPowers));
#ifdef alloca
    if (powerbufLen < 3072)
        powerbufFree =
            alloca(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
    else
#endif
        if ((powerbufFree =
             OPENSSL_malloc(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH))
            == NULL)
        goto err;

    powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
    memset(powerbuf, 0, powerbufLen);

#ifdef alloca
    if (powerbufLen < 3072)
        powerbufFree = NULL;
#endif

    /* lay down tmp and am right after powers table */
    tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers);
    am.d = tmp.d + top;
    tmp.top = am.top = 0;
    tmp.dmax = am.dmax = top;
    tmp.neg = am.neg = 0;
    tmp.flags = am.flags = BN_FLG_STATIC_DATA;

    /* prepare a^0 in Montgomery domain */
#if 1                           /* by Shay Gueron's suggestion */
    if (m->d[top - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
        /* 2^(top*BN_BITS2) - m */
        tmp.d[0] = (0 - m->d[0]) & BN_MASK2;
        for (i = 1; i < top; i++)
            tmp.d[i] = (~m->d[i]) & BN_MASK2;
        tmp.top = top;
    } else
#endif
    if (!BN_to_montgomery(&tmp, BN_value_one(), mont, ctx))
        goto err;

    /* prepare a^1 in Montgomery domain */
    if (a->neg || BN_ucmp(a, m) >= 0) {
        if (!BN_mod(&am, a, m, ctx))
            goto err;
        if (!BN_to_montgomery(&am, &am, mont, ctx))
            goto err;
    } else if (!BN_to_montgomery(&am, a, mont, ctx))
        goto err;

#if defined(SPARC_T4_MONT)
    if (t4) {
        typedef int (*bn_pwr5_mont_f) (BN_ULONG *tp, const BN_ULONG *np,
                                       const BN_ULONG *n0, const void *table,
                                       int power, int bits);
        int bn_pwr5_mont_t4_8(BN_ULONG *tp, const BN_ULONG *np,
                              const BN_ULONG *n0, const void *table,
                              int power, int bits);
        int bn_pwr5_mont_t4_16(BN_ULONG *tp, const BN_ULONG *np,
                               const BN_ULONG *n0, const void *table,
                               int power, int bits);
        int bn_pwr5_mont_t4_24(BN_ULONG *tp, const BN_ULONG *np,
                               const BN_ULONG *n0, const void *table,
                               int power, int bits);
        int bn_pwr5_mont_t4_32(BN_ULONG *tp, const BN_ULONG *np,
                               const BN_ULONG *n0, const void *table,
                               int power, int bits);
        static const bn_pwr5_mont_f pwr5_funcs[4] = {
            bn_pwr5_mont_t4_8, bn_pwr5_mont_t4_16,
            bn_pwr5_mont_t4_24, bn_pwr5_mont_t4_32
        };
        bn_pwr5_mont_f pwr5_worker = pwr5_funcs[top / 16 - 1];

        typedef int (*bn_mul_mont_f) (BN_ULONG *rp, const BN_ULONG *ap,
                                      const void *bp, const BN_ULONG *np,
                                      const BN_ULONG *n0);
        int bn_mul_mont_t4_8(BN_ULONG *rp, const BN_ULONG *ap, const void *bp,
                             const BN_ULONG *np, const BN_ULONG *n0);
        int bn_mul_mont_t4_16(BN_ULONG *rp, const BN_ULONG *ap,
                              const void *bp, const BN_ULONG *np,
                              const BN_ULONG *n0);
        int bn_mul_mont_t4_24(BN_ULONG *rp, const BN_ULONG *ap,
                              const void *bp, const BN_ULONG *np,
                              const BN_ULONG *n0);
        int bn_mul_mont_t4_32(BN_ULONG *rp, const BN_ULONG *ap,
                              const void *bp, const BN_ULONG *np,
                              const BN_ULONG *n0);
        static const bn_mul_mont_f mul_funcs[4] = {
            bn_mul_mont_t4_8, bn_mul_mont_t4_16,
            bn_mul_mont_t4_24, bn_mul_mont_t4_32
        };
        bn_mul_mont_f mul_worker = mul_funcs[top / 16 - 1];

        void bn_mul_mont_vis3(BN_ULONG *rp, const BN_ULONG *ap,
                              const void *bp, const BN_ULONG *np,
                              const BN_ULONG *n0, int num);
        void bn_mul_mont_t4(BN_ULONG *rp, const BN_ULONG *ap,
                            const void *bp, const BN_ULONG *np,
                            const BN_ULONG *n0, int num);
        void bn_mul_mont_gather5_t4(BN_ULONG *rp, const BN_ULONG *ap,
                                    const void *table, const BN_ULONG *np,
                                    const BN_ULONG *n0, int num, int power);
        void bn_flip_n_scatter5_t4(const BN_ULONG *inp, size_t num,
                                   void *table, size_t power);
        void bn_gather5_t4(BN_ULONG *out, size_t num,
                           void *table, size_t power);
        void bn_flip_t4(BN_ULONG *dst, BN_ULONG *src, size_t num);

        BN_ULONG *np = mont->N.d, *n0 = mont->n0;
        int stride = 5 * (6 - (top / 16 - 1)); /* multiple of 5, but less
                                                * than 32 */

        /*
         * BN_to_montgomery can contaminate words above .top [in
         * BN_DEBUG[_DEBUG] build]...
         */
        for (i = am.top; i < top; i++)
            am.d[i] = 0;
        for (i = tmp.top; i < top; i++)
            tmp.d[i] = 0;

        bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 0);
        bn_flip_n_scatter5_t4(am.d, top, powerbuf, 1);
        if (!(*mul_worker) (tmp.d, am.d, am.d, np, n0) &&
            !(*mul_worker) (tmp.d, am.d, am.d, np, n0))
            bn_mul_mont_vis3(tmp.d, am.d, am.d, np, n0, top);
        bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 2);

        for (i = 3; i < 32; i++) {
            /* Calculate a^i = a^(i-1) * a */
            if (!(*mul_worker) (tmp.d, tmp.d, am.d, np, n0) &&
                !(*mul_worker) (tmp.d, tmp.d, am.d, np, n0))
                bn_mul_mont_vis3(tmp.d, tmp.d, am.d, np, n0, top);
            bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, i);
        }

        /* switch to 64-bit domain */
        np = alloca(top * sizeof(BN_ULONG));
        top /= 2;
        bn_flip_t4(np, mont->N.d, top);

        bits--;
        for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--)
            wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
        bn_gather5_t4(tmp.d, top, powerbuf, wvalue);

        /*
         * Scan the exponent one window at a time starting from the most
         * significant bits.
         */
        while (bits >= 0) {
            if (bits < stride)
                stride = bits + 1;
            bits -= stride;
            wvalue = bn_get_bits(p, bits + 1);

            if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride))
                continue;
            /* retry once and fall back */
            if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride))
                continue;

            bits += stride - 5;
            wvalue >>= stride - 5;
            wvalue &= 31;
            bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
            bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
            bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
            bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
            bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
            bn_mul_mont_gather5_t4(tmp.d, tmp.d, powerbuf, np, n0, top,
                                   wvalue);
        }

        bn_flip_t4(tmp.d, tmp.d, top);
        top *= 2;
        /* back to 32-bit domain */
        tmp.top = top;
        bn_correct_top(&tmp);
        OPENSSL_cleanse(np, top * sizeof(BN_ULONG));
    } else
#endif
#if defined(OPENSSL_BN_ASM_MONT5)
    if (window == 5 && top > 1) {
        /*
         * This optimization uses ideas from http://eprint.iacr.org/2011/239,
         * specifically optimization of cache-timing attack countermeasures
         * and pre-computation optimization.
         */

        /*
         * Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as
         * 512-bit RSA is hardly relevant, we omit it to spare size...
         */
        void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap,
                                 const void *table, const BN_ULONG *np,
                                 const BN_ULONG *n0, int num, int power);
        void bn_scatter5(const BN_ULONG *inp, size_t num,
                         void *table, size_t power);
        void bn_gather5(BN_ULONG *out, size_t num, void *table, size_t power);
        void bn_power5(BN_ULONG *rp, const BN_ULONG *ap,
                       const void *table, const BN_ULONG *np,
                       const BN_ULONG *n0, int num, int power);
        int bn_get_bits5(const BN_ULONG *ap, int off);
        int bn_from_montgomery(BN_ULONG *rp, const BN_ULONG *ap,
                               const BN_ULONG *not_used, const BN_ULONG *np,
                               const BN_ULONG *n0, int num);

        BN_ULONG *np = mont->N.d, *n0 = mont->n0, *np2;

        /*
         * BN_to_montgomery can contaminate words above .top [in
         * BN_DEBUG[_DEBUG] build]...
         */
        for (i = am.top; i < top; i++)
            am.d[i] = 0;
        for (i = tmp.top; i < top; i++)
            tmp.d[i] = 0;

        if (top & 7)
            np2 = np;
        else
            for (np2 = am.d + top, i = 0; i < top; i++)
                np2[2 * i] = np[i];

        bn_scatter5(tmp.d, top, powerbuf, 0);
        bn_scatter5(am.d, am.top, powerbuf, 1);
        bn_mul_mont(tmp.d, am.d, am.d, np, n0, top);
        bn_scatter5(tmp.d, top, powerbuf, 2);

# if 0
        for (i = 3; i < 32; i++) {
            /* Calculate a^i = a^(i-1) * a */
            bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np2, n0, top, i - 1);
            bn_scatter5(tmp.d, top, powerbuf, i);
        }
# else
        /* same as above, but uses squaring for 1/2 of operations */
        for (i = 4; i < 32; i *= 2) {
            bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
            bn_scatter5(tmp.d, top, powerbuf, i);
        }
        for (i = 3; i < 8; i += 2) {
            int j;
            bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np2, n0, top, i - 1);
            bn_scatter5(tmp.d, top, powerbuf, i);
            for (j = 2 * i; j < 32; j *= 2) {
                bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
                bn_scatter5(tmp.d, top, powerbuf, j);
            }
        }
        for (; i < 16; i += 2) {
            bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np2, n0, top, i - 1);
            bn_scatter5(tmp.d, top, powerbuf, i);
            bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
            bn_scatter5(tmp.d, top, powerbuf, 2 * i);
        }
        for (; i < 32; i += 2) {
            bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np2, n0, top, i - 1);
            bn_scatter5(tmp.d, top, powerbuf, i);
        }
# endif
        bits--;
        for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--)
            wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
        bn_gather5(tmp.d, top, powerbuf, wvalue);

        /*
         * Scan the exponent one window at a time starting from the most
         * significant bits.
         */
        if (top & 7)
            while (bits >= 0) {
                for (wvalue = 0, i = 0; i < 5; i++, bits--)
                    wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);

                bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
                bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
                bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
                bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
                bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
                bn_mul_mont_gather5(tmp.d, tmp.d, powerbuf, np, n0, top,
                                    wvalue);
        } else {
            while (bits >= 0) {
                wvalue = bn_get_bits5(p->d, bits - 4);
                bits -= 5;
                bn_power5(tmp.d, tmp.d, powerbuf, np2, n0, top, wvalue);
            }
        }

        ret = bn_from_montgomery(tmp.d, tmp.d, NULL, np2, n0, top);
        tmp.top = top;
        bn_correct_top(&tmp);
        if (ret) {
            if (!BN_copy(rr, &tmp))
                ret = 0;
            goto err;           /* non-zero ret means it's not error */
        }
    } else
#endif
    {
        if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, window))
            goto err;
        if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, window))
            goto err;

        /*
         * If the window size is greater than 1, then calculate
         * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even
         * powers could instead be computed as (a^(i/2))^2 to use the slight
         * performance advantage of sqr over mul).
         */
        if (window > 1) {
            if (!BN_mod_mul_montgomery(&tmp, &am, &am, mont, ctx))
                goto err;
            if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2,
                                              window))
                goto err;
            for (i = 3; i < numPowers; i++) {
                /* Calculate a^i = a^(i-1) * a */
                if (!BN_mod_mul_montgomery(&tmp, &am, &tmp, mont, ctx))
                    goto err;
                if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i,
                                                  window))
                    goto err;
            }
        }

        bits--;
        for (wvalue = 0, i = bits % window; i >= 0; i--, bits--)
            wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
        if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp, top, powerbuf, wvalue,
                                            window))
            goto err;

        /*
         * Scan the exponent one window at a time starting from the most
         * significant bits.
         */
        while (bits >= 0) {
            wvalue = 0;         /* The 'value' of the window */

            /* Scan the window, squaring the result as we go */
            for (i = 0; i < window; i++, bits--) {
                if (!BN_mod_mul_montgomery(&tmp, &tmp, &tmp, mont, ctx))
                    goto err;
                wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
            }

            /*
             * Fetch the appropriate pre-computed value from the pre-buf
             */
            if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue,
                                                window))
                goto err;

            /* Multiply the result into the intermediate result */
            if (!BN_mod_mul_montgomery(&tmp, &tmp, &am, mont, ctx))
                goto err;
        }
    }

    /* Convert the final result from montgomery to standard format */
#if defined(SPARC_T4_MONT)
    if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
        am.d[0] = 1;            /* borrow am */
        for (i = 1; i < top; i++)
            am.d[i] = 0;
        if (!BN_mod_mul_montgomery(rr, &tmp, &am, mont, ctx))
            goto err;
    } else
#endif
    if (!BN_from_montgomery(rr, &tmp, mont, ctx))
        goto err;
    ret = 1;
 err:
    if (in_mont == NULL)
        BN_MONT_CTX_free(mont);
    if (powerbuf != NULL) {
        OPENSSL_cleanse(powerbuf, powerbufLen);
        OPENSSL_free(powerbufFree);
    }
    BN_CTX_end(ctx);
    return (ret);
}