--- /dev/null
+/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
+ * All rights reserved.
+ *
+ * This package is an SSL implementation written
+ * by Eric Young (eay@cryptsoft.com).
+ * The implementation was written so as to conform with Netscapes SSL.
+ *
+ * This library is free for commercial and non-commercial use as long as
+ * the following conditions are aheared to. The following conditions
+ * apply to all code found in this distribution, be it the RC4, RSA,
+ * lhash, DES, etc., code; not just the SSL code. The SSL documentation
+ * included with this distribution is covered by the same copyright terms
+ * except that the holder is Tim Hudson (tjh@cryptsoft.com).
+ *
+ * Copyright remains Eric Young's, and as such any Copyright notices in
+ * the code are not to be removed.
+ * If this package is used in a product, Eric Young should be given attribution
+ * as the author of the parts of the library used.
+ * This can be in the form of a textual message at program startup or
+ * in documentation (online or textual) provided with the package.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the copyright
+ * notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ * notice, this list of conditions and the following disclaimer in the
+ * documentation and/or other materials provided with the distribution.
+ * 3. All advertising materials mentioning features or use of this software
+ * must display the following acknowledgement:
+ * "This product includes cryptographic software written by
+ * Eric Young (eay@cryptsoft.com)"
+ * The word 'cryptographic' can be left out if the rouines from the library
+ * being used are not cryptographic related :-).
+ * 4. If you include any Windows specific code (or a derivative thereof) from
+ * the apps directory (application code) you must include an acknowledgement:
+ * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
+ *
+ * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ *
+ * The licence and distribution terms for any publically available version or
+ * derivative of this code cannot be changed. i.e. this code cannot simply be
+ * copied and put under another distribution licence
+ * [including the GNU Public Licence.] */
+
+#include <openssl/bn.h>
+
+#include <assert.h>
+#include <string.h>
+
+#include <openssl/err.h>
+#include <openssl/mem.h>
+#include <openssl/type_check.h>
+
+#include "internal.h"
+#include "../../internal.h"
+
+
+#define BN_MUL_RECURSIVE_SIZE_NORMAL 16
+#define BN_SQR_RECURSIVE_SIZE_NORMAL BN_MUL_RECURSIVE_SIZE_NORMAL
+
+
+static void bn_abs_sub_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
+ size_t num, BN_ULONG *tmp) {
+ BN_ULONG borrow = bn_sub_words(tmp, a, b, num);
+ bn_sub_words(r, b, a, num);
+ bn_select_words(r, 0 - borrow, r /* tmp < 0 */, tmp /* tmp >= 0 */, num);
+}
+
+static void bn_mul_normal(BN_ULONG *r, const BN_ULONG *a, size_t na,
+ const BN_ULONG *b, size_t nb) {
+ if (na < nb) {
+ size_t itmp = na;
+ na = nb;
+ nb = itmp;
+ const BN_ULONG *ltmp = a;
+ a = b;
+ b = ltmp;
+ }
+ BN_ULONG *rr = &(r[na]);
+ if (nb == 0) {
+ OPENSSL_memset(r, 0, na * sizeof(BN_ULONG));
+ return;
+ }
+ rr[0] = bn_mul_words(r, a, na, b[0]);
+
+ for (;;) {
+ if (--nb == 0) {
+ return;
+ }
+ rr[1] = bn_mul_add_words(&(r[1]), a, na, b[1]);
+ if (--nb == 0) {
+ return;
+ }
+ rr[2] = bn_mul_add_words(&(r[2]), a, na, b[2]);
+ if (--nb == 0) {
+ return;
+ }
+ rr[3] = bn_mul_add_words(&(r[3]), a, na, b[3]);
+ if (--nb == 0) {
+ return;
+ }
+ rr[4] = bn_mul_add_words(&(r[4]), a, na, b[4]);
+ rr += 4;
+ r += 4;
+ b += 4;
+ }
+}
+
+#if !defined(OPENSSL_X86) || defined(OPENSSL_NO_ASM)
+// Here follows specialised variants of bn_add_words() and bn_sub_words(). They
+// have the property performing operations on arrays of different sizes. The
+// sizes of those arrays is expressed through cl, which is the common length (
+// basicall, min(len(a),len(b)) ), and dl, which is the delta between the two
+// lengths, calculated as len(a)-len(b). All lengths are the number of
+// BN_ULONGs... For the operations that require a result array as parameter,
+// it must have the length cl+abs(dl). These functions should probably end up
+// in bn_asm.c as soon as there are assembler counterparts for the systems that
+// use assembler files.
+
+static BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a,
+ const BN_ULONG *b, int cl, int dl) {
+ BN_ULONG c, t;
+
+ assert(cl >= 0);
+ c = bn_sub_words(r, a, b, cl);
+
+ if (dl == 0) {
+ return c;
+ }
+
+ r += cl;
+ a += cl;
+ b += cl;
+
+ if (dl < 0) {
+ for (;;) {
+ t = b[0];
+ r[0] = 0 - t - c;
+ if (t != 0) {
+ c = 1;
+ }
+ if (++dl >= 0) {
+ break;
+ }
+
+ t = b[1];
+ r[1] = 0 - t - c;
+ if (t != 0) {
+ c = 1;
+ }
+ if (++dl >= 0) {
+ break;
+ }
+
+ t = b[2];
+ r[2] = 0 - t - c;
+ if (t != 0) {
+ c = 1;
+ }
+ if (++dl >= 0) {
+ break;
+ }
+
+ t = b[3];
+ r[3] = 0 - t - c;
+ if (t != 0) {
+ c = 1;
+ }
+ if (++dl >= 0) {
+ break;
+ }
+
+ b += 4;
+ r += 4;
+ }
+ } else {
+ int save_dl = dl;
+ while (c) {
+ t = a[0];
+ r[0] = t - c;
+ if (t != 0) {
+ c = 0;
+ }
+ if (--dl <= 0) {
+ break;
+ }
+
+ t = a[1];
+ r[1] = t - c;
+ if (t != 0) {
+ c = 0;
+ }
+ if (--dl <= 0) {
+ break;
+ }
+
+ t = a[2];
+ r[2] = t - c;
+ if (t != 0) {
+ c = 0;
+ }
+ if (--dl <= 0) {
+ break;
+ }
+
+ t = a[3];
+ r[3] = t - c;
+ if (t != 0) {
+ c = 0;
+ }
+ if (--dl <= 0) {
+ break;
+ }
+
+ save_dl = dl;
+ a += 4;
+ r += 4;
+ }
+ if (dl > 0) {
+ if (save_dl > dl) {
+ switch (save_dl - dl) {
+ case 1:
+ r[1] = a[1];
+ if (--dl <= 0) {
+ break;
+ }
+ OPENSSL_FALLTHROUGH;
+ case 2:
+ r[2] = a[2];
+ if (--dl <= 0) {
+ break;
+ }
+ OPENSSL_FALLTHROUGH;
+ case 3:
+ r[3] = a[3];
+ if (--dl <= 0) {
+ break;
+ }
+ }
+ a += 4;
+ r += 4;
+ }
+ }
+
+ if (dl > 0) {
+ for (;;) {
+ r[0] = a[0];
+ if (--dl <= 0) {
+ break;
+ }
+ r[1] = a[1];
+ if (--dl <= 0) {
+ break;
+ }
+ r[2] = a[2];
+ if (--dl <= 0) {
+ break;
+ }
+ r[3] = a[3];
+ if (--dl <= 0) {
+ break;
+ }
+
+ a += 4;
+ r += 4;
+ }
+ }
+ }
+
+ return c;
+}
+#else
+// On other platforms the function is defined in asm.
+BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
+ int cl, int dl);
+#endif
+
+// bn_abs_sub_part_words computes |r| = |a| - |b|, storing the absolute value
+// and returning a mask of all ones if the result was negative and all zeros if
+// the result was positive. |cl| and |dl| follow the |bn_sub_part_words| calling
+// convention.
+//
+// TODO(davidben): Make this take |size_t|. The |cl| + |dl| calling convention
+// is confusing. The trouble is 32-bit x86 implements |bn_sub_part_words| in
+// assembly, but we can probably just delete it?
+static BN_ULONG bn_abs_sub_part_words(BN_ULONG *r, const BN_ULONG *a,
+ const BN_ULONG *b, int cl, int dl,
+ BN_ULONG *tmp) {
+ BN_ULONG borrow = bn_sub_part_words(tmp, a, b, cl, dl);
+ bn_sub_part_words(r, b, a, cl, -dl);
+ int r_len = cl + (dl < 0 ? -dl : dl);
+ borrow = 0 - borrow;
+ bn_select_words(r, borrow, r /* tmp < 0 */, tmp /* tmp >= 0 */, r_len);
+ return borrow;
+}
+
+int bn_abs_sub_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
+ BN_CTX *ctx) {
+ int cl = a->width < b->width ? a->width : b->width;
+ int dl = a->width - b->width;
+ int r_len = a->width < b->width ? b->width : a->width;
+ BN_CTX_start(ctx);
+ BIGNUM *tmp = BN_CTX_get(ctx);
+ int ok = tmp != NULL &&
+ bn_wexpand(r, r_len) &&
+ bn_wexpand(tmp, r_len);
+ if (ok) {
+ bn_abs_sub_part_words(r->d, a->d, b->d, cl, dl, tmp->d);
+ r->width = r_len;
+ }
+ BN_CTX_end(ctx);
+ return ok;
+}
+
+// Karatsuba recursive multiplication algorithm
+// (cf. Knuth, The Art of Computer Programming, Vol. 2)
+
+// bn_mul_recursive sets |r| to |a| * |b|, using |t| as scratch space. |r| has
+// length 2*|n2|, |a| has length |n2| + |dna|, |b| has length |n2| + |dnb|, and
+// |t| has length 4*|n2|. |n2| must be a power of two. Finally, we must have
+// -|BN_MUL_RECURSIVE_SIZE_NORMAL|/2 <= |dna| <= 0 and
+// -|BN_MUL_RECURSIVE_SIZE_NORMAL|/2 <= |dnb| <= 0.
+//
+// TODO(davidben): Simplify and |size_t| the calling convention around lengths
+// here.
+static void bn_mul_recursive(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
+ int n2, int dna, int dnb, BN_ULONG *t) {
+ // |n2| is a power of two.
+ assert(n2 != 0 && (n2 & (n2 - 1)) == 0);
+ // Check |dna| and |dnb| are in range.
+ assert(-BN_MUL_RECURSIVE_SIZE_NORMAL/2 <= dna && dna <= 0);
+ assert(-BN_MUL_RECURSIVE_SIZE_NORMAL/2 <= dnb && dnb <= 0);
+
+ // Only call bn_mul_comba 8 if n2 == 8 and the
+ // two arrays are complete [steve]
+ if (n2 == 8 && dna == 0 && dnb == 0) {
+ bn_mul_comba8(r, a, b);
+ return;
+ }
+
+ // Else do normal multiply
+ if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL) {
+ bn_mul_normal(r, a, n2 + dna, b, n2 + dnb);
+ if (dna + dnb < 0) {
+ OPENSSL_memset(&r[2 * n2 + dna + dnb], 0,
+ sizeof(BN_ULONG) * -(dna + dnb));
+ }
+ return;
+ }
+
+ // Split |a| and |b| into a0,a1 and b0,b1, where a0 and b0 have size |n|.
+ // Split |t| into t0,t1,t2,t3, each of size |n|, with the remaining 4*|n| used
+ // for recursive calls.
+ // Split |r| into r0,r1,r2,r3. We must contribute a0*b0 to r0,r1, a0*a1+b0*b1
+ // to r1,r2, and a1*b1 to r2,r3. The middle term we will compute as:
+ //
+ // a0*a1 + b0*b1 = (a0 - a1)*(b1 - b0) + a1*b1 + a0*b0
+ //
+ // Note that we know |n| >= |BN_MUL_RECURSIVE_SIZE_NORMAL|/2 above, so
+ // |tna| and |tnb| are non-negative.
+ int n = n2 / 2, tna = n + dna, tnb = n + dnb;
+
+ // t0 = a0 - a1 and t1 = b1 - b0. The result will be multiplied, so we XOR
+ // their sign masks, giving the sign of (a0 - a1)*(b1 - b0). t0 and t1
+ // themselves store the absolute value.
+ BN_ULONG neg = bn_abs_sub_part_words(t, a, &a[n], tna, n - tna, &t[n2]);
+ neg ^= bn_abs_sub_part_words(&t[n], &b[n], b, tnb, tnb - n, &t[n2]);
+
+ // Compute:
+ // t2,t3 = t0 * t1 = |(a0 - a1)*(b1 - b0)|
+ // r0,r1 = a0 * b0
+ // r2,r3 = a1 * b1
+ if (n == 4 && dna == 0 && dnb == 0) {
+ bn_mul_comba4(&t[n2], t, &t[n]);
+
+ bn_mul_comba4(r, a, b);
+ bn_mul_comba4(&r[n2], &a[n], &b[n]);
+ } else if (n == 8 && dna == 0 && dnb == 0) {
+ bn_mul_comba8(&t[n2], t, &t[n]);
+
+ bn_mul_comba8(r, a, b);
+ bn_mul_comba8(&r[n2], &a[n], &b[n]);
+ } else {
+ BN_ULONG *p = &t[n2 * 2];
+ bn_mul_recursive(&t[n2], t, &t[n], n, 0, 0, p);
+ bn_mul_recursive(r, a, b, n, 0, 0, p);
+ bn_mul_recursive(&r[n2], &a[n], &b[n], n, dna, dnb, p);
+ }
+
+ // t0,t1,c = r0,r1 + r2,r3 = a0*b0 + a1*b1
+ BN_ULONG c = bn_add_words(t, r, &r[n2], n2);
+
+ // t2,t3,c = t0,t1,c + neg*t2,t3 = (a0 - a1)*(b1 - b0) + a1*b1 + a0*b0.
+ // The second term is stored as the absolute value, so we do this with a
+ // constant-time select.
+ BN_ULONG c_neg = c - bn_sub_words(&t[n2 * 2], t, &t[n2], n2);
+ BN_ULONG c_pos = c + bn_add_words(&t[n2], t, &t[n2], n2);
+ bn_select_words(&t[n2], neg, &t[n2 * 2], &t[n2], n2);
+ OPENSSL_COMPILE_ASSERT(sizeof(BN_ULONG) <= sizeof(crypto_word_t),
+ crypto_word_t_too_small);
+ c = constant_time_select_w(neg, c_neg, c_pos);
+
+ // We now have our three components. Add them together.
+ // r1,r2,c = r1,r2 + t2,t3,c
+ c += bn_add_words(&r[n], &r[n], &t[n2], n2);
+
+ // Propagate the carry bit to the end.
+ for (int i = n + n2; i < n2 + n2; i++) {
+ BN_ULONG old = r[i];
+ r[i] = old + c;
+ c = r[i] < old;
+ }
+
+ // The product should fit without carries.
+ assert(c == 0);
+}
+
+// bn_mul_part_recursive sets |r| to |a| * |b|, using |t| as scratch space. |r|
+// has length 4*|n|, |a| has length |n| + |tna|, |b| has length |n| + |tnb|, and
+// |t| has length 8*|n|. |n| must be a power of two. Additionally, we must have
+// 0 <= tna < n and 0 <= tnb < n, and |tna| and |tnb| must differ by at most
+// one.
+//
+// TODO(davidben): Make this take |size_t| and perhaps the actual lengths of |a|
+// and |b|.
+static void bn_mul_part_recursive(BN_ULONG *r, const BN_ULONG *a,
+ const BN_ULONG *b, int n, int tna, int tnb,
+ BN_ULONG *t) {
+ // |n| is a power of two.
+ assert(n != 0 && (n & (n - 1)) == 0);
+ // Check |tna| and |tnb| are in range.
+ assert(0 <= tna && tna < n);
+ assert(0 <= tnb && tnb < n);
+ assert(-1 <= tna - tnb && tna - tnb <= 1);
+
+ int n2 = n * 2;
+ if (n < 8) {
+ bn_mul_normal(r, a, n + tna, b, n + tnb);
+ OPENSSL_memset(r + n2 + tna + tnb, 0, n2 - tna - tnb);
+ return;
+ }
+
+ // Split |a| and |b| into a0,a1 and b0,b1, where a0 and b0 have size |n|. |a1|
+ // and |b1| have size |tna| and |tnb|, respectively.
+ // Split |t| into t0,t1,t2,t3, each of size |n|, with the remaining 4*|n| used
+ // for recursive calls.
+ // Split |r| into r0,r1,r2,r3. We must contribute a0*b0 to r0,r1, a0*a1+b0*b1
+ // to r1,r2, and a1*b1 to r2,r3. The middle term we will compute as:
+ //
+ // a0*a1 + b0*b1 = (a0 - a1)*(b1 - b0) + a1*b1 + a0*b0
+
+ // t0 = a0 - a1 and t1 = b1 - b0. The result will be multiplied, so we XOR
+ // their sign masks, giving the sign of (a0 - a1)*(b1 - b0). t0 and t1
+ // themselves store the absolute value.
+ BN_ULONG neg = bn_abs_sub_part_words(t, a, &a[n], tna, n - tna, &t[n2]);
+ neg ^= bn_abs_sub_part_words(&t[n], &b[n], b, tnb, tnb - n, &t[n2]);
+
+ // Compute:
+ // t2,t3 = t0 * t1 = |(a0 - a1)*(b1 - b0)|
+ // r0,r1 = a0 * b0
+ // r2,r3 = a1 * b1
+ if (n == 8) {
+ bn_mul_comba8(&t[n2], t, &t[n]);
+ bn_mul_comba8(r, a, b);
+
+ bn_mul_normal(&r[n2], &a[n], tna, &b[n], tnb);
+ // |bn_mul_normal| only writes |tna| + |tna| words. Zero the rest.
+ OPENSSL_memset(&r[n2 + tna + tnb], 0, sizeof(BN_ULONG) * (n2 - tna - tnb));
+ } else {
+ BN_ULONG *p = &t[n2 * 2];
+ bn_mul_recursive(&t[n2], t, &t[n], n, 0, 0, p);
+ bn_mul_recursive(r, a, b, n, 0, 0, p);
+
+ OPENSSL_memset(&r[n2], 0, sizeof(BN_ULONG) * n2);
+ if (tna < BN_MUL_RECURSIVE_SIZE_NORMAL &&
+ tnb < BN_MUL_RECURSIVE_SIZE_NORMAL) {
+ bn_mul_normal(&r[n2], &a[n], tna, &b[n], tnb);
+ } else {
+ int i = n;
+ for (;;) {
+ i /= 2;
+ if (i < tna || i < tnb) {
+ // E.g., n == 16, i == 8 and tna == 11. |tna| and |tnb| are within one
+ // of each other, so if |tna| is larger and tna > i, then we know
+ // tnb >= i, and this call is valid.
+ bn_mul_part_recursive(&r[n2], &a[n], &b[n], i, tna - i, tnb - i, p);
+ break;
+ }
+ if (i == tna || i == tnb) {
+ // If there is only a bottom half to the number, just do it. We know
+ // the larger of |tna - i| and |tnb - i| is zero. The other is zero or
+ // -1 by because of |tna| and |tnb| differ by at most one.
+ bn_mul_recursive(&r[n2], &a[n], &b[n], i, tna - i, tnb - i, p);
+ break;
+ }
+
+ // This loop will eventually terminate when |i| falls below
+ // |BN_MUL_RECURSIVE_SIZE_NORMAL| because we know one of |tna| and |tnb|
+ // exceeds that.
+ }
+ }
+ }
+
+ // t0,t1,c = r0,r1 + r2,r3 = a0*b0 + a1*b1
+ BN_ULONG c = bn_add_words(t, r, &r[n2], n2);
+
+ // t2,t3,c = t0,t1,c + neg*t2,t3 = (a0 - a1)*(b1 - b0) + a1*b1 + a0*b0.
+ // The second term is stored as the absolute value, so we do this with a
+ // constant-time select.
+ BN_ULONG c_neg = c - bn_sub_words(&t[n2 * 2], t, &t[n2], n2);
+ BN_ULONG c_pos = c + bn_add_words(&t[n2], t, &t[n2], n2);
+ bn_select_words(&t[n2], neg, &t[n2 * 2], &t[n2], n2);
+ OPENSSL_COMPILE_ASSERT(sizeof(BN_ULONG) <= sizeof(crypto_word_t),
+ crypto_word_t_too_small);
+ c = constant_time_select_w(neg, c_neg, c_pos);
+
+ // We now have our three components. Add them together.
+ // r1,r2,c = r1,r2 + t2,t3,c
+ c += bn_add_words(&r[n], &r[n], &t[n2], n2);
+
+ // Propagate the carry bit to the end.
+ for (int i = n + n2; i < n2 + n2; i++) {
+ BN_ULONG old = r[i];
+ r[i] = old + c;
+ c = r[i] < old;
+ }
+
+ // The product should fit without carries.
+ assert(c == 0);
+}
+
+// bn_mul_impl implements |BN_mul| and |bn_mul_consttime|. Note this function
+// breaks |BIGNUM| invariants and may return a negative zero. This is handled by
+// the callers.
+static int bn_mul_impl(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
+ BN_CTX *ctx) {
+ int al = a->width;
+ int bl = b->width;
+ if (al == 0 || bl == 0) {
+ BN_zero(r);
+ return 1;
+ }
+
+ int ret = 0;
+ BIGNUM *rr;
+ BN_CTX_start(ctx);
+ if (r == a || r == b) {
+ rr = BN_CTX_get(ctx);
+ if (r == NULL) {
+ goto err;
+ }
+ } else {
+ rr = r;
+ }
+ rr->neg = a->neg ^ b->neg;
+
+ int i = al - bl;
+ if (i == 0) {
+ if (al == 8) {
+ if (!bn_wexpand(rr, 16)) {
+ goto err;
+ }
+ rr->width = 16;
+ bn_mul_comba8(rr->d, a->d, b->d);
+ goto end;
+ }
+ }
+
+ int top = al + bl;
+ static const int kMulNormalSize = 16;
+ if (al >= kMulNormalSize && bl >= kMulNormalSize) {
+ if (-1 <= i && i <= 1) {
+ // Find the larger power of two less than or equal to the larger length.
+ int j;
+ if (i >= 0) {
+ j = BN_num_bits_word((BN_ULONG)al);
+ } else {
+ j = BN_num_bits_word((BN_ULONG)bl);
+ }
+ j = 1 << (j - 1);
+ assert(j <= al || j <= bl);
+ BIGNUM *t = BN_CTX_get(ctx);
+ if (t == NULL) {
+ goto err;
+ }
+ if (al > j || bl > j) {
+ // We know |al| and |bl| are at most one from each other, so if al > j,
+ // bl >= j, and vice versa. Thus we can use |bn_mul_part_recursive|.
+ assert(al >= j && bl >= j);
+ if (!bn_wexpand(t, j * 8) ||
+ !bn_wexpand(rr, j * 4)) {
+ goto err;
+ }
+ bn_mul_part_recursive(rr->d, a->d, b->d, j, al - j, bl - j, t->d);
+ } else {
+ // al <= j && bl <= j. Additionally, we know j <= al or j <= bl, so one
+ // of al - j or bl - j is zero. The other, by the bound on |i| above, is
+ // zero or -1. Thus, we can use |bn_mul_recursive|.
+ if (!bn_wexpand(t, j * 4) ||
+ !bn_wexpand(rr, j * 2)) {
+ goto err;
+ }
+ bn_mul_recursive(rr->d, a->d, b->d, j, al - j, bl - j, t->d);
+ }
+ rr->width = top;
+ goto end;
+ }
+ }
+
+ if (!bn_wexpand(rr, top)) {
+ goto err;
+ }
+ rr->width = top;
+ bn_mul_normal(rr->d, a->d, al, b->d, bl);
+
+end:
+ if (r != rr && !BN_copy(r, rr)) {
+ goto err;
+ }
+ ret = 1;
+
+err:
+ BN_CTX_end(ctx);
+ return ret;
+}
+
+int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) {
+ if (!bn_mul_impl(r, a, b, ctx)) {
+ return 0;
+ }
+
+ // This additionally fixes any negative zeros created by |bn_mul_impl|.
+ bn_set_minimal_width(r);
+ return 1;
+}
+
+int bn_mul_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) {
+ // Prevent negative zeros.
+ if (a->neg || b->neg) {
+ OPENSSL_PUT_ERROR(BN, BN_R_NEGATIVE_NUMBER);
+ return 0;
+ }
+
+ return bn_mul_impl(r, a, b, ctx);
+}
+
+int bn_mul_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a, size_t num_a,
+ const BN_ULONG *b, size_t num_b) {
+ if (num_r != num_a + num_b) {
+ OPENSSL_PUT_ERROR(BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
+ return 0;
+ }
+ // TODO(davidben): Should this call |bn_mul_comba4| too? |BN_mul| does not
+ // hit that code.
+ if (num_a == 8 && num_b == 8) {
+ bn_mul_comba8(r, a, b);
+ } else {
+ bn_mul_normal(r, a, num_a, b, num_b);
+ }
+ return 1;
+}
+
+// tmp must have 2*n words
+static void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, size_t n,
+ BN_ULONG *tmp) {
+ if (n == 0) {
+ return;
+ }
+
+ size_t max = n * 2;
+ const BN_ULONG *ap = a;
+ BN_ULONG *rp = r;
+ rp[0] = rp[max - 1] = 0;
+ rp++;
+
+ // Compute the contribution of a[i] * a[j] for all i < j.
+ if (n > 1) {
+ ap++;
+ rp[n - 1] = bn_mul_words(rp, ap, n - 1, ap[-1]);
+ rp += 2;
+ }
+ if (n > 2) {
+ for (size_t i = n - 2; i > 0; i--) {
+ ap++;
+ rp[i] = bn_mul_add_words(rp, ap, i, ap[-1]);
+ rp += 2;
+ }
+ }
+
+ // The final result fits in |max| words, so none of the following operations
+ // will overflow.
+
+ // Double |r|, giving the contribution of a[i] * a[j] for all i != j.
+ bn_add_words(r, r, r, max);
+
+ // Add in the contribution of a[i] * a[i] for all i.
+ bn_sqr_words(tmp, a, n);
+ bn_add_words(r, r, tmp, max);
+}
+
+// bn_sqr_recursive sets |r| to |a|^2, using |t| as scratch space. |r| has
+// length 2*|n2|, |a| has length |n2|, and |t| has length 4*|n2|. |n2| must be
+// a power of two.
+static void bn_sqr_recursive(BN_ULONG *r, const BN_ULONG *a, size_t n2,
+ BN_ULONG *t) {
+ // |n2| is a power of two.
+ assert(n2 != 0 && (n2 & (n2 - 1)) == 0);
+
+ if (n2 == 4) {
+ bn_sqr_comba4(r, a);
+ return;
+ }
+ if (n2 == 8) {
+ bn_sqr_comba8(r, a);
+ return;
+ }
+ if (n2 < BN_SQR_RECURSIVE_SIZE_NORMAL) {
+ bn_sqr_normal(r, a, n2, t);
+ return;
+ }
+
+ // Split |a| into a0,a1, each of size |n|.
+ // Split |t| into t0,t1,t2,t3, each of size |n|, with the remaining 4*|n| used
+ // for recursive calls.
+ // Split |r| into r0,r1,r2,r3. We must contribute a0^2 to r0,r1, 2*a0*a1 to
+ // r1,r2, and a1^2 to r2,r3.
+ size_t n = n2 / 2;
+ BN_ULONG *t_recursive = &t[n2 * 2];
+
+ // t0 = |a0 - a1|.
+ bn_abs_sub_words(t, a, &a[n], n, &t[n]);
+ // t2,t3 = t0^2 = |a0 - a1|^2 = a0^2 - 2*a0*a1 + a1^2
+ bn_sqr_recursive(&t[n2], t, n, t_recursive);
+
+ // r0,r1 = a0^2
+ bn_sqr_recursive(r, a, n, t_recursive);
+
+ // r2,r3 = a1^2
+ bn_sqr_recursive(&r[n2], &a[n], n, t_recursive);
+
+ // t0,t1,c = r0,r1 + r2,r3 = a0^2 + a1^2
+ BN_ULONG c = bn_add_words(t, r, &r[n2], n2);
+ // t2,t3,c = t0,t1,c - t2,t3 = 2*a0*a1
+ c -= bn_sub_words(&t[n2], t, &t[n2], n2);
+
+ // We now have our three components. Add them together.
+ // r1,r2,c = r1,r2 + t2,t3,c
+ c += bn_add_words(&r[n], &r[n], &t[n2], n2);
+
+ // Propagate the carry bit to the end.
+ for (size_t i = n + n2; i < n2 + n2; i++) {
+ BN_ULONG old = r[i];
+ r[i] = old + c;
+ c = r[i] < old;
+ }
+
+ // The square should fit without carries.
+ assert(c == 0);
+}
+
+int BN_mul_word(BIGNUM *bn, BN_ULONG w) {
+ if (!bn->width) {
+ return 1;
+ }
+
+ if (w == 0) {
+ BN_zero(bn);
+ return 1;
+ }
+
+ BN_ULONG ll = bn_mul_words(bn->d, bn->d, bn->width, w);
+ if (ll) {
+ if (!bn_wexpand(bn, bn->width + 1)) {
+ return 0;
+ }
+ bn->d[bn->width++] = ll;
+ }
+
+ return 1;
+}
+
+int bn_sqr_consttime(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx) {
+ int al = a->width;
+ if (al <= 0) {
+ r->width = 0;
+ r->neg = 0;
+ return 1;
+ }
+
+ int ret = 0;
+ BN_CTX_start(ctx);
+ BIGNUM *rr = (a != r) ? r : BN_CTX_get(ctx);
+ BIGNUM *tmp = BN_CTX_get(ctx);
+ if (!rr || !tmp) {
+ goto err;
+ }
+
+ int max = 2 * al; // Non-zero (from above)
+ if (!bn_wexpand(rr, max)) {
+ goto err;
+ }
+
+ if (al == 4) {
+ bn_sqr_comba4(rr->d, a->d);
+ } else if (al == 8) {
+ bn_sqr_comba8(rr->d, a->d);
+ } else {
+ if (al < BN_SQR_RECURSIVE_SIZE_NORMAL) {
+ BN_ULONG t[BN_SQR_RECURSIVE_SIZE_NORMAL * 2];
+ bn_sqr_normal(rr->d, a->d, al, t);
+ } else {
+ // If |al| is a power of two, we can use |bn_sqr_recursive|.
+ if (al != 0 && (al & (al - 1)) == 0) {
+ if (!bn_wexpand(tmp, al * 4)) {
+ goto err;
+ }
+ bn_sqr_recursive(rr->d, a->d, al, tmp->d);
+ } else {
+ if (!bn_wexpand(tmp, max)) {
+ goto err;
+ }
+ bn_sqr_normal(rr->d, a->d, al, tmp->d);
+ }
+ }
+ }
+
+ rr->neg = 0;
+ rr->width = max;
+
+ if (rr != r && !BN_copy(r, rr)) {
+ goto err;
+ }
+ ret = 1;
+
+err:
+ BN_CTX_end(ctx);
+ return ret;
+}
+
+int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx) {
+ if (!bn_sqr_consttime(r, a, ctx)) {
+ return 0;
+ }
+
+ bn_set_minimal_width(r);
+ return 1;
+}
+
+int bn_sqr_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a, size_t num_a) {
+ if (num_r != 2 * num_a || num_a > BN_SMALL_MAX_WORDS) {
+ OPENSSL_PUT_ERROR(BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
+ return 0;
+ }
+ if (num_a == 4) {
+ bn_sqr_comba4(r, a);
+ } else if (num_a == 8) {
+ bn_sqr_comba8(r, a);
+ } else {
+ BN_ULONG tmp[2 * BN_SMALL_MAX_WORDS];
+ bn_sqr_normal(r, a, num_a, tmp);
+ OPENSSL_cleanse(tmp, 2 * num_a * sizeof(BN_ULONG));
+ }
+ return 1;
+}
git://repos.xcallymotion.com / motion2.git / blobdiff