Commit 8df98cd9 authored by Andy Polyakov's avatar Andy Polyakov Committed by Matt Caswell
Browse files

bn/bn_{div|shift}.c: introduce fixed-top interfaces. 



Fixed-top interfaces tolerate zero-padded inputs and facilitate
constant-time-ness. bn_div_fixed_top tolerates zero-padded dividend,
but not divisor. It's argued that divisor's length is public even
when value is secret.

[extended tests]

Reviewed-by: default avatarPaul Dale <paul.dale@oracle.com>
Reviewed-by: default avatarMatt Caswell <matt@openssl.org>
(Merged from https://github.com/openssl/openssl/pull/7589)

(cherry picked from commit 3a4a88f4)
parent a7e8ab41

crypto/bn/bn_div.c

+119 −132
Original line number Diff line number Diff line
@@ -7,6 +7,7 @@ 
 * https://www.openssl.org/source/license.html

 */



#include <assert.h>

#include <openssl/bn.h>

#include "internal/cryptlib.h"

#include "bn_lcl.h"
@@ -137,6 +138,26 @@ static BN_ULONG bn_div_3_words(const BN_ULONG *m, BN_ULONG d1, BN_ULONG d0) 
#  endif

# endif



static int bn_left_align(BIGNUM *num)

{

    BN_ULONG *d = num->d, n, m, rmask;

    int top = num->top;

    int rshift = BN_num_bits_word(d[top - 1]), lshift, i;



    lshift = BN_BITS2 - rshift;

    rshift %= BN_BITS2;            /* say no to undefined behaviour */

    rmask = (BN_ULONG)0 - rshift;  /* rmask = 0 - (rshift != 0) */

    rmask |= rmask >> 8;



    for (i = 0, m = 0; i < top; i++) {

        n = d[i];

        d[i] = ((n << lshift) | m) & BN_MASK2;

        m = (n >> rshift) & rmask;

    }



    return lshift;

}



# if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) \

    && !defined(PEDANTIC) && !defined(BN_DIV3W)

#  if defined(__GNUC__) && __GNUC__>=2
@@ -188,55 +209,73 @@ static BN_ULONG bn_div_3_words(const BN_ULONG *m, BN_ULONG d1, BN_ULONG d0) 
int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,

           BN_CTX *ctx)

{

    int norm_shift, i, j, loop;

    BIGNUM *tmp, wnum, *snum, *sdiv, *res;

    BN_ULONG *resp, *wnump;

    BN_ULONG d0, d1;

    int num_n, div_n;

    int no_branch = 0;

    int ret;



    if (BN_is_zero(divisor)) {

        BNerr(BN_F_BN_DIV, BN_R_DIV_BY_ZERO);

        return 0;

    }



    /*

     * Invalid zero-padding would have particularly bad consequences so don't

     * just rely on bn_check_top() here (bn_check_top() works only for

     * BN_DEBUG builds)

     */

    if ((num->top > 0 && num->d[num->top - 1] == 0) ||

        (divisor->top > 0 && divisor->d[divisor->top - 1] == 0)) {

    if (divisor->d[divisor->top - 1] == 0) {

        BNerr(BN_F_BN_DIV, BN_R_NOT_INITIALIZED);

        return 0;

    }



    bn_check_top(num);

    bn_check_top(divisor);

    ret = bn_div_fixed_top(dv, rm, num, divisor, ctx);



    if ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0)

        || (BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0)) {

        no_branch = 1;

    if (ret) {

        if (dv != NULL)

            bn_correct_top(dv);

        if (rm != NULL)

            bn_correct_top(rm);

    }



    bn_check_top(dv);

    bn_check_top(rm);

    /*- bn_check_top(num); *//*

     * 'num' has been checked already

     */

    /*- bn_check_top(divisor); *//*

     * 'divisor' has been checked already

    return ret;

}



/*

 * It's argued that *length* of *significant* part of divisor is public.

 * Even if it's private modulus that is. Again, *length* is assumed

 * public, but not *value*. Former is likely to be pre-defined by

 * algorithm with bit granularity, though below subroutine is invariant

 * of limb length. Thanks to this assumption we can require that |divisor|

 * may not be zero-padded, yet claim this subroutine "constant-time"(*).

 * This is because zero-padded dividend, |num|, is tolerated, so that

 * caller can pass dividend of public length(*), but with smaller amount

 * of significant limbs. This naturally means that quotient, |dv|, would

 * contain correspongly less significant limbs as well, and will be zero-

 * padded accordingly. Returned remainder, |rm|, will have same bit length

 * as divisor, also zero-padded if needed. These actually leave sign bits

 * in ambiguous state. In sense that we try to avoid negative zeros, while

 * zero-padded zeros would retain sign.

 *

 * (*) "Constant-time-ness" has two pre-conditions:

 *

 *     - availability of constant-time bn_div_3_words;

 *     - dividend is at least as "wide" as divisor, limb-wise, zero-padded

 *       if so requied, which shouldn't be a privacy problem, because

 *       divisor's length is considered public;

 */

int bn_div_fixed_top(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num,

                     const BIGNUM *divisor, BN_CTX *ctx)

{

    int norm_shift, i, j, loop;

    BIGNUM *tmp, *snum, *sdiv, *res;

    BN_ULONG *resp, *wnum, *wnumtop;

    BN_ULONG d0, d1;

    int num_n, div_n;



    if (BN_is_zero(divisor)) {

        BNerr(BN_F_BN_DIV, BN_R_DIV_BY_ZERO);

        return 0;

    }

    assert(divisor->top > 0 && divisor->d[divisor->top - 1] != 0);



    if (!no_branch && BN_ucmp(num, divisor) < 0) {

        if (rm != NULL) {

            if (BN_copy(rm, num) == NULL)

                return 0;

        }

        if (dv != NULL)

            BN_zero(dv);

        return 1;

    }

    bn_check_top(num);

    bn_check_top(divisor);

    bn_check_top(dv);

    bn_check_top(rm);



    BN_CTX_start(ctx);

    res = (dv == NULL) ? BN_CTX_get(ctx) : dv;
@@ -247,112 +286,72 @@ int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor, 
        goto err;



    /* First we normalise the numbers */

    norm_shift = BN_BITS2 - ((BN_num_bits(divisor)) % BN_BITS2);

    if (!(BN_lshift(sdiv, divisor, norm_shift)))

    if (!BN_copy(sdiv, divisor))

        goto err;

    norm_shift = bn_left_align(sdiv);

    sdiv->neg = 0;

    norm_shift += BN_BITS2;

    if (!(BN_lshift(snum, num, norm_shift)))

        goto err;

    snum->neg = 0;



    if (no_branch) {

    /*

         * Since we don't know whether snum is larger than sdiv, we pad snum

         * with enough zeroes without changing its value.

     * Note that bn_lshift_fixed_top's output is always one limb longer

     * than input, even when norm_shift is zero. This means that amount of

     * inner loop iterations is invariant of dividend value, and that one

     * doesn't need to compare dividend and divisor if they were originally

     * of the same bit length.

     */

        if (snum->top <= sdiv->top + 1) {

            if (bn_wexpand(snum, sdiv->top + 2) == NULL)

                goto err;

            for (i = snum->top; i < sdiv->top + 2; i++)

                snum->d[i] = 0;

            snum->top = sdiv->top + 2;

        } else {

            if (bn_wexpand(snum, snum->top + 1) == NULL)

    if (!(bn_lshift_fixed_top(snum, num, norm_shift)))

        goto err;

            snum->d[snum->top] = 0;

            snum->top++;

        }

    }



    div_n = sdiv->top;

    num_n = snum->top;



    if (num_n <= div_n) {

        /* caller didn't pad dividend -> no constant-time guarantee... */

        if (bn_wexpand(snum, div_n + 1) == NULL)

            goto err;

        memset(&(snum->d[num_n]), 0, (div_n - num_n + 1) * sizeof(BN_ULONG));

        snum->top = num_n = div_n + 1;

    }



    loop = num_n - div_n;

    /*

     * Lets setup a 'window' into snum This is the part that corresponds to

     * the current 'area' being divided

     */

    wnum.neg = 0;

    wnum.d = &(snum->d[loop]);

    wnum.top = div_n;

    wnum.flags = BN_FLG_STATIC_DATA;

    /*

     * only needed when BN_ucmp messes up the values between top and max

     */

    wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */

    wnum = &(snum->d[loop]);

    wnumtop = &(snum->d[num_n - 1]);



    /* Get the top 2 words of sdiv */

    /* div_n=sdiv->top; */

    d0 = sdiv->d[div_n - 1];

    d1 = (div_n == 1) ? 0 : sdiv->d[div_n - 2];



    /* pointer to the 'top' of snum */

    wnump = &(snum->d[num_n - 1]);



    /* Setup to 'res' */

    if (!bn_wexpand(res, (loop + 1)))

    /* Setup quotient */

    if (!bn_wexpand(res, loop))

        goto err;

    res->neg = (num->neg ^ divisor->neg);

    res->top = loop - no_branch;

    resp = &(res->d[loop - 1]);

    res->top = loop;

    res->flags |= BN_FLG_FIXED_TOP;

    resp = &(res->d[loop]);



    /* space for temp */

    if (!bn_wexpand(tmp, (div_n + 1)))

        goto err;



    if (!no_branch) {

        if (BN_ucmp(&wnum, sdiv) >= 0) {

            /*

             * If BN_DEBUG_RAND is defined BN_ucmp changes (via bn_pollute)

             * the const bignum arguments => clean the values between top and

             * max again

             */

            bn_clear_top2max(&wnum);

            bn_sub_words(wnum.d, wnum.d, sdiv->d, div_n);

            *resp = 1;

        } else

            res->top--;

    }



    /* Increase the resp pointer so that we never create an invalid pointer. */

    resp++;



    /*

     * if res->top == 0 then clear the neg value otherwise decrease the resp

     * pointer

     */

    if (res->top == 0)

        res->neg = 0;

    else

        resp--;



    for (i = 0; i < loop - 1; i++, wnump--) {

    for (i = 0; i < loop; i++, wnumtop--) {

        BN_ULONG q, l0;

        /*

         * the first part of the loop uses the top two words of snum and sdiv

         * to calculate a BN_ULONG q such that | wnum - sdiv * q | < sdiv

         */

# if defined(BN_DIV3W)

        q = bn_div_3_words(wnump, d1, d0);

        q = bn_div_3_words(wnumtop, d1, d0);

# else

        BN_ULONG n0, n1, rem = 0;



        n0 = wnump[0];

        n1 = wnump[-1];

        n0 = wnumtop[0];

        n1 = wnumtop[-1];

        if (n0 == d0)

            q = BN_MASK2;

        else {                  /* n0 < d0 */



            BN_ULONG n2 = (wnumtop == wnum) ? 0 : wnumtop[-2];

#  ifdef BN_LLONG

            BN_ULLONG t2;
@@ -372,7 +371,7 @@ int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor, 
            t2 = (BN_ULLONG) d1 *q;



            for (;;) {

                if (t2 <= ((((BN_ULLONG) rem) << BN_BITS2) | wnump[-2]))

                if (t2 <= ((((BN_ULLONG) rem) << BN_BITS2) | n2))

                    break;

                q--;

                rem += d0;
@@ -405,7 +404,7 @@ int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor, 
#   endif



            for (;;) {

                if ((t2h < rem) || ((t2h == rem) && (t2l <= wnump[-2])))

                if ((t2h < rem) || ((t2h == rem) && (t2l <= n2)))

                    break;

                q--;

                rem += d0;
@@ -421,12 +420,12 @@ int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor, 


        l0 = bn_mul_words(tmp->d, sdiv->d, div_n, q);

        tmp->d[div_n] = l0;

        wnum.d--;

        wnum--;

        /*

         * ingore top values of the bignums just sub the two BN_ULONG arrays

         * ignore top values of the bignums just sub the two BN_ULONG arrays

         * with bn_sub_words

         */

        l0 = bn_sub_words(wnum.d, wnum.d, tmp->d, div_n + 1);

        l0 = bn_sub_words(wnum, wnum, tmp->d, div_n + 1);

        q -= l0;

        /*

         * Note: As we have considered only the leading two BN_ULONGs in
@@ -435,31 +434,19 @@ int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor, 
         */

        for (l0 = 0 - l0, j = 0; j < div_n; j++)

            tmp->d[j] = sdiv->d[j] & l0;

        l0 = bn_add_words(wnum.d, wnum.d, tmp->d, div_n);

        /*

         * we can't have an overflow here (assuming that q != 0, but

         * if q == 0 then tmp is zero anyway)

         */

        (*wnump) += l0;

        l0 = bn_add_words(wnum, wnum, tmp->d, div_n);

        (*wnumtop) += l0;

        assert((*wnumtop) == 0);



        /* store part of the result */

        resp--;

        *resp = q;

    }

    bn_correct_top(snum);

    if (rm != NULL) {

        /*

         * Keep a copy of the neg flag in num because if rm==num BN_rshift()

         * will overwrite it.

         */

        int neg = num->neg;

        BN_rshift(rm, snum, norm_shift);

        if (!BN_is_zero(rm))

            rm->neg = neg;

        bn_check_top(rm);

        *--resp = q;

    }

    if (no_branch)

        bn_correct_top(res);

    /* snum holds remainder, it's as wide as divisor */

    snum->neg = num->neg;

    snum->top = div_n;

    snum->flags |= BN_FLG_FIXED_TOP;

    if (rm != NULL)

        bn_rshift_fixed_top(rm, snum, norm_shift);

    BN_CTX_end(ctx);

    return 1;

 err:

crypto/bn/bn_shift.c

+106 −24
Original line number Diff line number Diff line 
/*

 * Copyright 1995-2016 The OpenSSL Project Authors. All Rights Reserved.

 * Copyright 1995-2018 The OpenSSL Project Authors. 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
@@ -7,6 +7,7 @@ 
 * https://www.openssl.org/source/license.html

 */



#include <assert.h>

#include "internal/cryptlib.h"

#include "bn_lcl.h"
@@ -82,40 +83,70 @@ int BN_rshift1(BIGNUM *r, const BIGNUM *a) 


int BN_lshift(BIGNUM *r, const BIGNUM *a, int n)

{

    int i, nw, lb, rb;

    BN_ULONG *t, *f;

    BN_ULONG l;



    bn_check_top(r);

    bn_check_top(a);

    int ret;



    if (n < 0) {

        BNerr(BN_F_BN_LSHIFT, BN_R_INVALID_SHIFT);

        return 0;

    }



    ret = bn_lshift_fixed_top(r, a, n);



    bn_correct_top(r);

    bn_check_top(r);



    return ret;

}



/*

 * In respect to shift factor the execution time is invariant of

 * |n % BN_BITS2|, but not |n / BN_BITS2|. Or in other words pre-condition

 * for constant-time-ness is |n < BN_BITS2| or |n / BN_BITS2| being

 * non-secret.

 */

int bn_lshift_fixed_top(BIGNUM *r, const BIGNUM *a, int n)

{

    int i, nw;

    unsigned int lb, rb;

    BN_ULONG *t, *f;

    BN_ULONG l, m, rmask = 0;



    assert(n >= 0);



    bn_check_top(r);

    bn_check_top(a);



    nw = n / BN_BITS2;

    if (bn_wexpand(r, a->top + nw + 1) == NULL)

        return 0;

    r->neg = a->neg;

    lb = n % BN_BITS2;



    if (a->top != 0) {

        lb = (unsigned int)n % BN_BITS2;

        rb = BN_BITS2 - lb;

    f = a->d;

    t = r->d;

    t[a->top + nw] = 0;

    if (lb == 0)

        for (i = a->top - 1; i >= 0; i--)

            t[nw + i] = f[i];

    else

        for (i = a->top - 1; i >= 0; i--) {

            l = f[i];

            t[nw + i + 1] |= (l >> rb) & BN_MASK2;

            t[nw + i] = (l << lb) & BN_MASK2;

        }

    memset(t, 0, sizeof(*t) * nw);

        rb %= BN_BITS2;            /* say no to undefined behaviour */

        rmask = (BN_ULONG)0 - rb;  /* rmask = 0 - (rb != 0) */

        rmask |= rmask >> 8;

        f = &(a->d[0]);

        t = &(r->d[nw]);

        l = f[a->top - 1];

        t[a->top] = (l >> rb) & rmask;

        for (i = a->top - 1; i > 0; i--) {

            m = l << lb;

            l = f[i - 1];

            t[i] = (m | ((l >> rb) & rmask)) & BN_MASK2;

        }

        t[0] = (l << lb) & BN_MASK2;

    } else {

        /* shouldn't happen, but formally required */

        r->d[nw] = 0;

    }

    if (nw != 0)

        memset(r->d, 0, sizeof(*t) * nw);



    r->neg = a->neg;

    r->top = a->top + nw + 1;

    bn_correct_top(r);

    bn_check_top(r);

    r->flags |= BN_FLG_FIXED_TOP;



    return 1;

}
@@ -173,3 +204,54 @@ int BN_rshift(BIGNUM *r, const BIGNUM *a, int n) 
    bn_check_top(r);

    return 1;

}



/*

 * In respect to shift factor the execution time is invariant of

 * |n % BN_BITS2|, but not |n / BN_BITS2|. Or in other words pre-condition

 * for constant-time-ness for sufficiently[!] zero-padded inputs is

 * |n < BN_BITS2| or |n / BN_BITS2| being non-secret.

 */

int bn_rshift_fixed_top(BIGNUM *r, const BIGNUM *a, int n)

{

    int i, top, nw;

    unsigned int lb, rb;

    BN_ULONG *t, *f;

    BN_ULONG l, m, mask;



    bn_check_top(r);

    bn_check_top(a);



    assert(n >= 0);



    nw = n / BN_BITS2;

    if (nw >= a->top) {

        /* shouldn't happen, but formally required */

        BN_zero(r);

        return 1;

    }



    rb = (unsigned int)n % BN_BITS2;

    lb = BN_BITS2 - rb;

    lb %= BN_BITS2;            /* say no to undefined behaviour */

    mask = (BN_ULONG)0 - lb;   /* mask = 0 - (lb != 0) */

    mask |= mask >> 8;

    top = a->top - nw;

    if (r != a && bn_wexpand(r, top) == NULL)

        return 0;



    t = &(r->d[0]);

    f = &(a->d[nw]);

    l = f[0];

    for (i = 0; i < top - 1; i++) {

        m = f[i + 1];

        t[i] = (l >> rb) | ((m << lb) & mask);

        l = m;

    }

    t[i] = l >> rb;



    r->neg = a->neg;

    r->top = top;

    r->flags |= BN_FLG_FIXED_TOP;



    return 1;

}

crypto/include/internal/bn_int.h

+8 −1
Original line number Diff line number Diff line
@@ -65,7 +65,10 @@ int bn_set_words(BIGNUM *a, const BN_ULONG *words, int num_words); 
 * is customarily arranged by bn_correct_top. Output from below functions

 * is not processed with bn_correct_top, and for this reason it may not be

 * returned out of public API. It may only be passed internally into other

 * functions known to support non-minimal or zero-padded BIGNUMs.

 * functions known to support non-minimal or zero-padded BIGNUMs. Even

 * though the goal is to facilitate constant-time-ness, not each subroutine

 * is constant-time by itself. They all have pre-conditions, consult source

 * code...

 */

int bn_mul_mont_fixed_top(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,

                          BN_MONT_CTX *mont, BN_CTX *ctx);
@@ -79,5 +82,9 @@ int bn_mod_sub_fixed_top(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, 
                         const BIGNUM *m);

int bn_mul_fixed_top(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);

int bn_sqr_fixed_top(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx);

int bn_lshift_fixed_top(BIGNUM *r, const BIGNUM *a, int n);

int bn_rshift_fixed_top(BIGNUM *r, const BIGNUM *a, int n);

int bn_div_fixed_top(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m,

                     const BIGNUM *d, BN_CTX *ctx);



#endif