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-rw-r--r--thirdparty/openssl/crypto/bn/bn_gcd.c702
1 files changed, 702 insertions, 0 deletions
diff --git a/thirdparty/openssl/crypto/bn/bn_gcd.c b/thirdparty/openssl/crypto/bn/bn_gcd.c
new file mode 100644
index 0000000000..ce59fe701f
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+++ b/thirdparty/openssl/crypto/bn/bn_gcd.c
@@ -0,0 +1,702 @@
+/* crypto/bn/bn_gcd.c */
+/* 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.]
+ */
+/* ====================================================================
+ * Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved.
+ *
+ * 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 above 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 acknowledgment:
+ * "This product includes software developed by the OpenSSL Project
+ * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
+ *
+ * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
+ * endorse or promote products derived from this software without
+ * prior written permission. For written permission, please contact
+ * openssl-core@openssl.org.
+ *
+ * 5. Products derived from this software may not be called "OpenSSL"
+ * nor may "OpenSSL" appear in their names without prior written
+ * permission of the OpenSSL Project.
+ *
+ * 6. Redistributions of any form whatsoever must retain the following
+ * acknowledgment:
+ * "This product includes software developed by the OpenSSL Project
+ * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
+ * EXPRESSED 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 OpenSSL PROJECT OR
+ * ITS 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.
+ * ====================================================================
+ *
+ * This product includes cryptographic software written by Eric Young
+ * (eay@cryptsoft.com). This product includes software written by Tim
+ * Hudson (tjh@cryptsoft.com).
+ *
+ */
+
+#include "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 *A, *B, *X, *Y, *M, *D, *T, *R = NULL;
+ BIGNUM *ret = NULL;
+ int sign;
+
+ 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) <= (BN_BITS <= 32 ? 450 : 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 sytems, 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 {
+ BNerr(BN_F_BN_MOD_INVERSE, 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);
+}
+
+/*
+ * 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 local_A, local_B;
+ BIGNUM *pA, *pB;
+ 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.
+ */
+ pB = &local_B;
+ local_B.flags = 0;
+ BN_with_flags(pB, B, BN_FLG_CONSTTIME);
+ if (!BN_nnmod(B, pB, 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|).
+ */
+
+ 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.
+ */
+ pA = &local_A;
+ local_A.flags = 0;
+ BN_with_flags(pA, A, BN_FLG_CONSTTIME);
+
+ /* (D, M) := (A/B, A%B) ... */
+ if (!BN_div(D, M, pA, 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.
+ */
+
+ 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 v1.2.3 (git 2.25.1) at 2025-03-21 20:04:32 +0000