/*
- * Copyright 1995-2016 The OpenSSL Project Authors. All Rights Reserved.
+ * Copyright 1995-2022 The OpenSSL Project Authors. All Rights Reserved.
*
- * Licensed under the OpenSSL license (the "License"). You may not use
+ * Licensed under the Apache License 2.0 (the "License"). You may not use
* this file except in compliance with the License. You can obtain a copy
* in the file LICENSE in the source distribution or at
* https://www.openssl.org/source/license.html
*/
+#include <assert.h>
#include <openssl/bn.h>
#include "internal/cryptlib.h"
-#include "bn_lcl.h"
+#include "bn_local.h"
/* The old slow way */
#if 0
bn_check_top(m);
bn_check_top(d);
if (BN_is_zero(d)) {
- BNerr(BN_F_BN_DIV, BN_R_DIV_BY_ZERO);
- return (0);
+ ERR_raise(ERR_LIB_BN, BN_R_DIV_BY_ZERO);
+ return 0;
}
if (BN_ucmp(m, d) < 0) {
if (rem != NULL) {
if (BN_copy(rem, m) == NULL)
- return (0);
+ return 0;
}
if (dv != NULL)
BN_zero(dv);
- return (1);
+ return 1;
}
BN_CTX_start(ctx);
ret = 1;
end:
BN_CTX_end(ctx);
- return (ret);
+ return ret;
}
#else
+# if defined(BN_DIV3W)
+BN_ULONG bn_div_3_words(const BN_ULONG *m, BN_ULONG d1, BN_ULONG d0);
+# elif 0
+/*
+ * This is #if-ed away, because it's a reference for assembly implementations,
+ * where it can and should be made constant-time. But if you want to test it,
+ * just replace 0 with 1.
+ */
+# if BN_BITS2 == 64 && defined(__SIZEOF_INT128__) && __SIZEOF_INT128__==16
+# undef BN_ULLONG
+# define BN_ULLONG uint128_t
+# define BN_LLONG
+# endif
+
+# ifdef BN_LLONG
+# define BN_DIV3W
+/*
+ * Interface is somewhat quirky, |m| is pointer to most significant limb,
+ * and less significant limb is referred at |m[-1]|. This means that caller
+ * is responsible for ensuring that |m[-1]| is valid. Second condition that
+ * has to be met is that |d0|'s most significant bit has to be set. Or in
+ * other words divisor has to be "bit-aligned to the left." bn_div_fixed_top
+ * does all this. The subroutine considers four limbs, two of which are
+ * "overlapping," hence the name...
+ */
+static BN_ULONG bn_div_3_words(const BN_ULONG *m, BN_ULONG d1, BN_ULONG d0)
+{
+ BN_ULLONG R = ((BN_ULLONG)m[0] << BN_BITS2) | m[-1];
+ BN_ULLONG D = ((BN_ULLONG)d0 << BN_BITS2) | d1;
+ BN_ULONG Q = 0, mask;
+ int i;
+
+ for (i = 0; i < BN_BITS2; i++) {
+ Q <<= 1;
+ if (R >= D) {
+ Q |= 1;
+ R -= D;
+ }
+ D >>= 1;
+ }
+
+ mask = 0 - (Q >> (BN_BITS2 - 1)); /* does it overflow? */
+
+ Q <<= 1;
+ Q |= (R >= D);
+
+ return (Q | mask) & BN_MASK2;
+}
+# 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
* understand why...);
* - divl doesn't only calculate quotient, but also leaves
* remainder in %edx which we can definitely use here:-)
- *
- * <appro@fy.chalmers.se>
*/
# undef bn_div_words
# define bn_div_words(n0,n1,d0) \
({ asm volatile ( \
"divl %4" \
: "=a"(q), "=d"(rem) \
- : "a"(n1), "d"(n0), "g"(d0) \
+ : "a"(n1), "d"(n0), "r"(d0) \
: "cc"); \
q; \
})
# elif defined(__x86_64) && defined(SIXTY_FOUR_BIT_LONG)
/*
* Same story here, but it's 128-bit by 64-bit division. Wow!
- * <appro@fy.chalmers.se>
*/
# undef bn_div_words
# define bn_div_words(n0,n1,d0) \
({ asm volatile ( \
"divq %4" \
: "=a"(q), "=d"(rem) \
- : "a"(n1), "d"(n0), "g"(d0) \
+ : "a"(n1), "d"(n0), "r"(d0) \
: "cc"); \
q; \
})
int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
BN_CTX *ctx)
{
- int norm_shift, i, 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)) {
+ ERR_raise(ERR_LIB_BN, 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)) {
- BNerr(BN_F_BN_DIV, BN_R_NOT_INITIALIZED);
+ if (divisor->d[divisor->top - 1] == 0) {
+ ERR_raise(ERR_LIB_BN, 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 required, 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, num_neg;
- 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;
tmp = BN_CTX_get(ctx);
snum = BN_CTX_get(ctx);
sdiv = BN_CTX_get(ctx);
- if (dv == NULL)
- res = BN_CTX_get(ctx);
- else
- res = dv;
- if (sdiv == NULL || res == NULL || tmp == NULL || snum == NULL)
+ if (sdiv == NULL)
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;
- /*
- * 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' */
- res->neg = (num->neg ^ divisor->neg);
- if (!bn_wexpand(res, (loop + 1)))
+ /* Setup quotient */
+ if (!bn_wexpand(res, loop))
goto err;
- res->top = loop - no_branch;
- resp = &(res->d[loop - 1]);
+ num_neg = num->neg;
+ res->neg = (num_neg ^ divisor->neg);
+ 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) && !defined(OPENSSL_NO_ASM)
- BN_ULONG bn_div_3_words(BN_ULONG *, BN_ULONG, BN_ULONG);
- q = bn_div_3_words(wnump, d1, d0);
+# if defined(BN_DIV3W)
+ 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
*/
- if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n + 1)) {
- /*
- * Note: As we have considered only the leading two BN_ULONGs in
- * the calculation of q, sdiv * q might be greater than wnum (but
- * then (q-1) * sdiv is less or equal than wnum)
- */
- q--;
- if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))
- /*
- * we can't have an overflow here (assuming that q != 0, but
- * if q == 0 then tmp is zero anyway)
- */
- (*wnump)++;
- }
- /* store part of the result */
- resp--;
- *resp = q;
- }
- bn_correct_top(snum);
- if (rm != NULL) {
+ l0 = bn_sub_words(wnum, wnum, tmp->d, div_n + 1);
+ q -= l0;
/*
- * Keep a copy of the neg flag in num because if rm==num BN_rshift()
- * will overwrite it.
+ * Note: As we have considered only the leading two BN_ULONGs in
+ * the calculation of q, sdiv * q might be greater than wnum (but
+ * then (q-1) * sdiv is less or equal than wnum)
*/
- int neg = num->neg;
- BN_rshift(rm, snum, norm_shift);
- if (!BN_is_zero(rm))
- rm->neg = neg;
- bn_check_top(rm);
+ for (l0 = 0 - l0, j = 0; j < div_n; j++)
+ tmp->d[j] = sdiv->d[j] & l0;
+ l0 = bn_add_words(wnum, wnum, tmp->d, div_n);
+ (*wnumtop) += l0;
+ assert((*wnumtop) == 0);
+
+ /* store part of the result */
+ *--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) == 0)
+ goto err;
+
BN_CTX_end(ctx);
- return (1);
+ return 1;
err:
bn_check_top(rm);
BN_CTX_end(ctx);
- return (0);
+ return 0;
}
#endif
projects / openssl.git / blobdiff