* https://www.openssl.org/source/license.html
*/
+#include <assert.h>
#include <openssl/bn.h>
#include "internal/cryptlib.h"
#include "bn_lcl.h"
# 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
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;
+}
- if (BN_is_zero(divisor)) {
- BNerr(BN_F_BN_DIV, BN_R_DIV_BY_ZERO);
- return 0;
- }
+/*
+ * 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 (!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;
- }
+ 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;
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)))
+ /*
+ * 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 (!(bn_lshift_fixed_top(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.
- */
- 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)
- 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;
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;
# endif
for (;;) {
- if ((t2h < rem) || ((t2h == rem) && (t2l <= wnump[-2])))
+ if ((t2h < rem) || ((t2h == rem) && (t2l <= n2)))
break;
q--;
rem += d0;
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
*/
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:
/*
- * 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
* https://www.openssl.org/source/license.html
*/
+#include <assert.h>
#include "internal/cryptlib.h"
#include "bn_lcl.h"
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;
- 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;
+
+ if (a->top != 0) {
+ lb = (unsigned int)n % BN_BITS2;
+ rb = BN_BITS2 - lb;
+ 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;
}
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;
+}
projects / openssl.git / commitdiff