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Diffstat (limited to 'openssl-1.1.0h/crypto/bn/bn_gcd.c')
-rw-r--r--openssl-1.1.0h/crypto/bn/bn_gcd.c616
1 files changed, 616 insertions, 0 deletions
diff --git a/openssl-1.1.0h/crypto/bn/bn_gcd.c b/openssl-1.1.0h/crypto/bn/bn_gcd.c
new file mode 100644
index 0000000..0676426
--- /dev/null
+++ b/openssl-1.1.0h/crypto/bn/bn_gcd.c
@@ -0,0 +1,616 @@
+/*
+ * Copyright 1995-2016 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
+ * in the file LICENSE in the source distribution or at
+ * https://www.openssl.org/source/license.html
+ */
+
+#include "internal/cryptlib.h"
+#include "bn_lcl.h"
+
+static BIGNUM *euclid(BIGNUM *a, BIGNUM *b);
+
+int BN_gcd(BIGNUM *r, const BIGNUM *in_a, const BIGNUM *in_b, BN_CTX *ctx)
+{
+ BIGNUM *a, *b, *t;
+ int ret = 0;
+
+ bn_check_top(in_a);
+ bn_check_top(in_b);
+
+ BN_CTX_start(ctx);
+ a = BN_CTX_get(ctx);
+ b = BN_CTX_get(ctx);
+ if (a == NULL || b == NULL)
+ goto err;
+
+ if (BN_copy(a, in_a) == NULL)
+ goto err;
+ if (BN_copy(b, in_b) == NULL)
+ goto err;
+ a->neg = 0;
+ b->neg = 0;
+
+ if (BN_cmp(a, b) < 0) {
+ t = a;
+ a = b;
+ b = t;
+ }
+ t = euclid(a, b);
+ if (t == NULL)
+ goto err;
+
+ if (BN_copy(r, t) == NULL)
+ goto err;
+ ret = 1;
+ err:
+ BN_CTX_end(ctx);
+ bn_check_top(r);
+ return (ret);
+}
+
+static BIGNUM *euclid(BIGNUM *a, BIGNUM *b)
+{
+ BIGNUM *t;
+ int shifts = 0;
+
+ bn_check_top(a);
+ bn_check_top(b);
+
+ /* 0 <= b <= a */
+ while (!BN_is_zero(b)) {
+ /* 0 < b <= a */
+
+ if (BN_is_odd(a)) {
+ if (BN_is_odd(b)) {
+ if (!BN_sub(a, a, b))
+ goto err;
+ if (!BN_rshift1(a, a))
+ goto err;
+ if (BN_cmp(a, b) < 0) {
+ t = a;
+ a = b;
+ b = t;
+ }
+ } else { /* a odd - b even */
+
+ if (!BN_rshift1(b, b))
+ goto err;
+ if (BN_cmp(a, b) < 0) {
+ t = a;
+ a = b;
+ b = t;
+ }
+ }
+ } else { /* a is even */
+
+ if (BN_is_odd(b)) {
+ if (!BN_rshift1(a, a))
+ goto err;
+ if (BN_cmp(a, b) < 0) {
+ t = a;
+ a = b;
+ b = t;
+ }
+ } else { /* a even - b even */
+
+ if (!BN_rshift1(a, a))
+ goto err;
+ if (!BN_rshift1(b, b))
+ goto err;
+ shifts++;
+ }
+ }
+ /* 0 <= b <= a */
+ }
+
+ if (shifts) {
+ if (!BN_lshift(a, a, shifts))
+ goto err;
+ }
+ bn_check_top(a);
+ return (a);
+ err:
+ return (NULL);
+}
+
+/* solves ax == 1 (mod n) */
+static BIGNUM *BN_mod_inverse_no_branch(BIGNUM *in,
+ const BIGNUM *a, const BIGNUM *n,
+ BN_CTX *ctx);
+
+BIGNUM *BN_mod_inverse(BIGNUM *in,
+ const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx)
+{
+ BIGNUM *rv;
+ int noinv;
+ rv = int_bn_mod_inverse(in, a, n, ctx, &noinv);
+ if (noinv)
+ BNerr(BN_F_BN_MOD_INVERSE, BN_R_NO_INVERSE);
+ return rv;
+}
+
+BIGNUM *int_bn_mod_inverse(BIGNUM *in,
+ const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx,
+ int *pnoinv)
+{
+ BIGNUM *A, *B, *X, *Y, *M, *D, *T, *R = NULL;
+ BIGNUM *ret = NULL;
+ int sign;
+
+ if (pnoinv)
+ *pnoinv = 0;
+
+ if ((BN_get_flags(a, BN_FLG_CONSTTIME) != 0)
+ || (BN_get_flags(n, BN_FLG_CONSTTIME) != 0)) {
+ return BN_mod_inverse_no_branch(in, a, n, ctx);
+ }
+
+ bn_check_top(a);
+ bn_check_top(n);
+
+ BN_CTX_start(ctx);
+ A = BN_CTX_get(ctx);
+ B = BN_CTX_get(ctx);
+ X = BN_CTX_get(ctx);
+ D = BN_CTX_get(ctx);
+ M = BN_CTX_get(ctx);
+ Y = BN_CTX_get(ctx);
+ T = BN_CTX_get(ctx);
+ if (T == NULL)
+ goto err;
+
+ if (in == NULL)
+ R = BN_new();
+ else
+ R = in;
+ if (R == NULL)
+ goto err;
+
+ BN_one(X);
+ BN_zero(Y);
+ if (BN_copy(B, a) == NULL)
+ goto err;
+ if (BN_copy(A, n) == NULL)
+ goto err;
+ A->neg = 0;
+ if (B->neg || (BN_ucmp(B, A) >= 0)) {
+ if (!BN_nnmod(B, B, A, ctx))
+ goto err;
+ }
+ sign = -1;
+ /*-
+ * From B = a mod |n|, A = |n| it follows that
+ *
+ * 0 <= B < A,
+ * -sign*X*a == B (mod |n|),
+ * sign*Y*a == A (mod |n|).
+ */
+
+ if (BN_is_odd(n) && (BN_num_bits(n) <= 2048)) {
+ /*
+ * Binary inversion algorithm; requires odd modulus. This is faster
+ * than the general algorithm if the modulus is sufficiently small
+ * (about 400 .. 500 bits on 32-bit systems, but much more on 64-bit
+ * systems)
+ */
+ int shift;
+
+ while (!BN_is_zero(B)) {
+ /*-
+ * 0 < B < |n|,
+ * 0 < A <= |n|,
+ * (1) -sign*X*a == B (mod |n|),
+ * (2) sign*Y*a == A (mod |n|)
+ */
+
+ /*
+ * Now divide B by the maximum possible power of two in the
+ * integers, and divide X by the same value mod |n|. When we're
+ * done, (1) still holds.
+ */
+ shift = 0;
+ while (!BN_is_bit_set(B, shift)) { /* note that 0 < B */
+ shift++;
+
+ if (BN_is_odd(X)) {
+ if (!BN_uadd(X, X, n))
+ goto err;
+ }
+ /*
+ * now X is even, so we can easily divide it by two
+ */
+ if (!BN_rshift1(X, X))
+ goto err;
+ }
+ if (shift > 0) {
+ if (!BN_rshift(B, B, shift))
+ goto err;
+ }
+
+ /*
+ * Same for A and Y. Afterwards, (2) still holds.
+ */
+ shift = 0;
+ while (!BN_is_bit_set(A, shift)) { /* note that 0 < A */
+ shift++;
+
+ if (BN_is_odd(Y)) {
+ if (!BN_uadd(Y, Y, n))
+ goto err;
+ }
+ /* now Y is even */
+ if (!BN_rshift1(Y, Y))
+ goto err;
+ }
+ if (shift > 0) {
+ if (!BN_rshift(A, A, shift))
+ goto err;
+ }
+
+ /*-
+ * We still have (1) and (2).
+ * Both A and B are odd.
+ * The following computations ensure that
+ *
+ * 0 <= B < |n|,
+ * 0 < A < |n|,
+ * (1) -sign*X*a == B (mod |n|),
+ * (2) sign*Y*a == A (mod |n|),
+ *
+ * and that either A or B is even in the next iteration.
+ */
+ if (BN_ucmp(B, A) >= 0) {
+ /* -sign*(X + Y)*a == B - A (mod |n|) */
+ if (!BN_uadd(X, X, Y))
+ goto err;
+ /*
+ * NB: we could use BN_mod_add_quick(X, X, Y, n), but that
+ * actually makes the algorithm slower
+ */
+ if (!BN_usub(B, B, A))
+ goto err;
+ } else {
+ /* sign*(X + Y)*a == A - B (mod |n|) */
+ if (!BN_uadd(Y, Y, X))
+ goto err;
+ /*
+ * as above, BN_mod_add_quick(Y, Y, X, n) would slow things down
+ */
+ if (!BN_usub(A, A, B))
+ goto err;
+ }
+ }
+ } else {
+ /* general inversion algorithm */
+
+ while (!BN_is_zero(B)) {
+ BIGNUM *tmp;
+
+ /*-
+ * 0 < B < A,
+ * (*) -sign*X*a == B (mod |n|),
+ * sign*Y*a == A (mod |n|)
+ */
+
+ /* (D, M) := (A/B, A%B) ... */
+ if (BN_num_bits(A) == BN_num_bits(B)) {
+ if (!BN_one(D))
+ goto err;
+ if (!BN_sub(M, A, B))
+ goto err;
+ } else if (BN_num_bits(A) == BN_num_bits(B) + 1) {
+ /* A/B is 1, 2, or 3 */
+ if (!BN_lshift1(T, B))
+ goto err;
+ if (BN_ucmp(A, T) < 0) {
+ /* A < 2*B, so D=1 */
+ if (!BN_one(D))
+ goto err;
+ if (!BN_sub(M, A, B))
+ goto err;
+ } else {
+ /* A >= 2*B, so D=2 or D=3 */
+ if (!BN_sub(M, A, T))
+ goto err;
+ if (!BN_add(D, T, B))
+ goto err; /* use D (:= 3*B) as temp */
+ if (BN_ucmp(A, D) < 0) {
+ /* A < 3*B, so D=2 */
+ if (!BN_set_word(D, 2))
+ goto err;
+ /*
+ * M (= A - 2*B) already has the correct value
+ */
+ } else {
+ /* only D=3 remains */
+ if (!BN_set_word(D, 3))
+ goto err;
+ /*
+ * currently M = A - 2*B, but we need M = A - 3*B
+ */
+ if (!BN_sub(M, M, B))
+ goto err;
+ }
+ }
+ } else {
+ if (!BN_div(D, M, A, B, ctx))
+ goto err;
+ }
+
+ /*-
+ * Now
+ * A = D*B + M;
+ * thus we have
+ * (**) sign*Y*a == D*B + M (mod |n|).
+ */
+
+ tmp = A; /* keep the BIGNUM object, the value does not matter */
+
+ /* (A, B) := (B, A mod B) ... */
+ A = B;
+ B = M;
+ /* ... so we have 0 <= B < A again */
+
+ /*-
+ * Since the former M is now B and the former B is now A,
+ * (**) translates into
+ * sign*Y*a == D*A + B (mod |n|),
+ * i.e.
+ * sign*Y*a - D*A == B (mod |n|).
+ * Similarly, (*) translates into
+ * -sign*X*a == A (mod |n|).
+ *
+ * Thus,
+ * sign*Y*a + D*sign*X*a == B (mod |n|),
+ * i.e.
+ * sign*(Y + D*X)*a == B (mod |n|).
+ *
+ * So if we set (X, Y, sign) := (Y + D*X, X, -sign), we arrive back at
+ * -sign*X*a == B (mod |n|),
+ * sign*Y*a == A (mod |n|).
+ * Note that X and Y stay non-negative all the time.
+ */
+
+ /*
+ * most of the time D is very small, so we can optimize tmp := D*X+Y
+ */
+ if (BN_is_one(D)) {
+ if (!BN_add(tmp, X, Y))
+ goto err;
+ } else {
+ if (BN_is_word(D, 2)) {
+ if (!BN_lshift1(tmp, X))
+ goto err;
+ } else if (BN_is_word(D, 4)) {
+ if (!BN_lshift(tmp, X, 2))
+ goto err;
+ } else if (D->top == 1) {
+ if (!BN_copy(tmp, X))
+ goto err;
+ if (!BN_mul_word(tmp, D->d[0]))
+ goto err;
+ } else {
+ if (!BN_mul(tmp, D, X, ctx))
+ goto err;
+ }
+ if (!BN_add(tmp, tmp, Y))
+ goto err;
+ }
+
+ M = Y; /* keep the BIGNUM object, the value does not matter */
+ Y = X;
+ X = tmp;
+ sign = -sign;
+ }
+ }
+
+ /*-
+ * The while loop (Euclid's algorithm) ends when
+ * A == gcd(a,n);
+ * we have
+ * sign*Y*a == A (mod |n|),
+ * where Y is non-negative.
+ */
+
+ if (sign < 0) {
+ if (!BN_sub(Y, n, Y))
+ goto err;
+ }
+ /* Now Y*a == A (mod |n|). */
+
+ if (BN_is_one(A)) {
+ /* Y*a == 1 (mod |n|) */
+ if (!Y->neg && BN_ucmp(Y, n) < 0) {
+ if (!BN_copy(R, Y))
+ goto err;
+ } else {
+ if (!BN_nnmod(R, Y, n, ctx))
+ goto err;
+ }
+ } else {
+ if (pnoinv)
+ *pnoinv = 1;
+ goto err;
+ }
+ ret = R;
+ err:
+ if ((ret == NULL) && (in == NULL))
+ BN_free(R);
+ BN_CTX_end(ctx);
+ bn_check_top(ret);
+ return (ret);
+}
+
+/*
+ * BN_mod_inverse_no_branch is a special version of BN_mod_inverse. It does
+ * not contain branches that may leak sensitive information.
+ */
+static BIGNUM *BN_mod_inverse_no_branch(BIGNUM *in,
+ const BIGNUM *a, const BIGNUM *n,
+ BN_CTX *ctx)
+{
+ BIGNUM *A, *B, *X, *Y, *M, *D, *T, *R = NULL;
+ BIGNUM *ret = NULL;
+ int sign;
+
+ bn_check_top(a);
+ bn_check_top(n);
+
+ BN_CTX_start(ctx);
+ A = BN_CTX_get(ctx);
+ B = BN_CTX_get(ctx);
+ X = BN_CTX_get(ctx);
+ D = BN_CTX_get(ctx);
+ M = BN_CTX_get(ctx);
+ Y = BN_CTX_get(ctx);
+ T = BN_CTX_get(ctx);
+ if (T == NULL)
+ goto err;
+
+ if (in == NULL)
+ R = BN_new();
+ else
+ R = in;
+ if (R == NULL)
+ goto err;
+
+ BN_one(X);
+ BN_zero(Y);
+ if (BN_copy(B, a) == NULL)
+ goto err;
+ if (BN_copy(A, n) == NULL)
+ goto err;
+ A->neg = 0;
+
+ if (B->neg || (BN_ucmp(B, A) >= 0)) {
+ /*
+ * Turn BN_FLG_CONSTTIME flag on, so that when BN_div is invoked,
+ * BN_div_no_branch will be called eventually.
+ */
+ {
+ BIGNUM local_B;
+ bn_init(&local_B);
+ BN_with_flags(&local_B, B, BN_FLG_CONSTTIME);
+ if (!BN_nnmod(B, &local_B, A, ctx))
+ goto err;
+ /* Ensure local_B goes out of scope before any further use of B */
+ }
+ }
+ sign = -1;
+ /*-
+ * From B = a mod |n|, A = |n| it follows that
+ *
+ * 0 <= B < A,
+ * -sign*X*a == B (mod |n|),
+ * sign*Y*a == A (mod |n|).
+ */
+
+ while (!BN_is_zero(B)) {
+ BIGNUM *tmp;
+
+ /*-
+ * 0 < B < A,
+ * (*) -sign*X*a == B (mod |n|),
+ * sign*Y*a == A (mod |n|)
+ */
+
+ /*
+ * Turn BN_FLG_CONSTTIME flag on, so that when BN_div is invoked,
+ * BN_div_no_branch will be called eventually.
+ */
+ {
+ BIGNUM local_A;
+ bn_init(&local_A);
+ BN_with_flags(&local_A, A, BN_FLG_CONSTTIME);
+
+ /* (D, M) := (A/B, A%B) ... */
+ if (!BN_div(D, M, &local_A, B, ctx))
+ goto err;
+ /* Ensure local_A goes out of scope before any further use of A */
+ }
+
+ /*-
+ * Now
+ * A = D*B + M;
+ * thus we have
+ * (**) sign*Y*a == D*B + M (mod |n|).
+ */
+
+ tmp = A; /* keep the BIGNUM object, the value does not
+ * matter */
+
+ /* (A, B) := (B, A mod B) ... */
+ A = B;
+ B = M;
+ /* ... so we have 0 <= B < A again */
+
+ /*-
+ * Since the former M is now B and the former B is now A,
+ * (**) translates into
+ * sign*Y*a == D*A + B (mod |n|),
+ * i.e.
+ * sign*Y*a - D*A == B (mod |n|).
+ * Similarly, (*) translates into
+ * -sign*X*a == A (mod |n|).
+ *
+ * Thus,
+ * sign*Y*a + D*sign*X*a == B (mod |n|),
+ * i.e.
+ * sign*(Y + D*X)*a == B (mod |n|).
+ *
+ * So if we set (X, Y, sign) := (Y + D*X, X, -sign), we arrive back at
+ * -sign*X*a == B (mod |n|),
+ * sign*Y*a == A (mod |n|).
+ * Note that X and Y stay non-negative all the time.
+ */
+
+ if (!BN_mul(tmp, D, X, ctx))
+ goto err;
+ if (!BN_add(tmp, tmp, Y))
+ goto err;
+
+ M = Y; /* keep the BIGNUM object, the value does not
+ * matter */
+ Y = X;
+ X = tmp;
+ sign = -sign;
+ }
+
+ /*-
+ * The while loop (Euclid's algorithm) ends when
+ * A == gcd(a,n);
+ * we have
+ * sign*Y*a == A (mod |n|),
+ * where Y is non-negative.
+ */
+
+ if (sign < 0) {
+ if (!BN_sub(Y, n, Y))
+ goto err;
+ }
+ /* Now Y*a == A (mod |n|). */
+
+ if (BN_is_one(A)) {
+ /* Y*a == 1 (mod |n|) */
+ if (!Y->neg && BN_ucmp(Y, n) < 0) {
+ if (!BN_copy(R, Y))
+ goto err;
+ } else {
+ if (!BN_nnmod(R, Y, n, ctx))
+ goto err;
+ }
+ } else {
+ BNerr(BN_F_BN_MOD_INVERSE_NO_BRANCH, BN_R_NO_INVERSE);
+ goto err;
+ }
+ ret = R;
+ err:
+ if ((ret == NULL) && (in == NULL))
+ BN_free(R);
+ BN_CTX_end(ctx);
+ bn_check_top(ret);
+ return (ret);
+}
generated by cgit