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

Browse source 
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: Paul Dale <paul.dale@oracle.com>
Reviewed-by: Matt Caswell <matt@openssl.org>
(Merged from https://github.com/openssl/openssl/pull/7589)

(cherry picked from commit 3a4a88f436)
This commit is contained in:
Andy Polyakov 2018-11-23 17:23:31 +01:00 committed by Matt Caswell
parent a7e8ab41fd
commit 8df98cd988
3 changed files with 241 additions and 165 deletions
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257
crypto/bn/bn_div.c
View file

@ -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
@ -188,56 +209,74 @@ 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;
/*
* 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)) {
BNerr(BN_F_BN_DIV, BN_R_NOT_INITIALIZED);
return 0;
}
bn_check_top(num);
bn_check_top(divisor);
if ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0)
|| (BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0)) {
no_branch = 1;
}
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
*/
int ret;
if (BN_is_zero(divisor)) {
BNerr(BN_F_BN_DIV, BN_R_DIV_BY_ZERO);
return 0;
}
if (!no_branch && BN_ucmp(num, divisor) < 0) {
if (rm != NULL) {
if (BN_copy(rm, num) == NULL)
/*
* 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 (divisor->d[divisor->top - 1] == 0) {
BNerr(BN_F_BN_DIV, BN_R_NOT_INITIALIZED);
return 0;
}
ret = bn_div_fixed_top(dv, rm, num, divisor, ctx);
if (ret) {
if (dv != NULL)
BN_zero(dv);
return 1;
bn_correct_top(dv);
if (rm != NULL)
bn_correct_top(rm);
}
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;
assert(divisor->top > 0 && divisor->d[divisor->top - 1] != 0);
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;
tmp = BN_CTX_get(ctx);
@ -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)
if (!(bn_lshift_fixed_top(snum, num, norm_shift)))
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)
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;
*--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);
}
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:

128
crypto/bn/bn_shift.c
View file

@ -1,5 +1,5 @@
/*
* 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;
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;
}
memset(t, 0, sizeof(*t) * nw);
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;
}

9
crypto/include/internal/bn_int.h
View file

@ -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