diff options
Diffstat (limited to 'third_party/boringssl/src/crypto/bn/sqrt.c')
-rw-r--r-- | third_party/boringssl/src/crypto/bn/sqrt.c | 505 |
1 files changed, 0 insertions, 505 deletions
diff --git a/third_party/boringssl/src/crypto/bn/sqrt.c b/third_party/boringssl/src/crypto/bn/sqrt.c deleted file mode 100644 index 2ed66c22c7..0000000000 --- a/third_party/boringssl/src/crypto/bn/sqrt.c +++ /dev/null @@ -1,505 +0,0 @@ -/* Written by Lenka Fibikova <fibikova@exp-math.uni-essen.de> - * and Bodo Moeller for the OpenSSL project. */ -/* ==================================================================== - * Copyright (c) 1998-2000 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 <openssl/bn.h> - -#include <openssl/err.h> - - -/* Returns 'ret' such that - * ret^2 == a (mod p), - * using the Tonelli/Shanks algorithm (cf. Henri Cohen, "A Course - * in Algebraic Computational Number Theory", algorithm 1.5.1). - * 'p' must be prime! */ -BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx) { - BIGNUM *ret = in; - int err = 1; - int r; - BIGNUM *A, *b, *q, *t, *x, *y; - int e, i, j; - - if (!BN_is_odd(p) || BN_abs_is_word(p, 1)) { - if (BN_abs_is_word(p, 2)) { - if (ret == NULL) { - ret = BN_new(); - } - if (ret == NULL) { - goto end; - } - if (!BN_set_word(ret, BN_is_bit_set(a, 0))) { - if (ret != in) { - BN_free(ret); - } - return NULL; - } - return ret; - } - - OPENSSL_PUT_ERROR(BN, BN_R_P_IS_NOT_PRIME); - return (NULL); - } - - if (BN_is_zero(a) || BN_is_one(a)) { - if (ret == NULL) { - ret = BN_new(); - } - if (ret == NULL) { - goto end; - } - if (!BN_set_word(ret, BN_is_one(a))) { - if (ret != in) { - BN_free(ret); - } - return NULL; - } - return ret; - } - - BN_CTX_start(ctx); - A = BN_CTX_get(ctx); - b = BN_CTX_get(ctx); - q = BN_CTX_get(ctx); - t = BN_CTX_get(ctx); - x = BN_CTX_get(ctx); - y = BN_CTX_get(ctx); - if (y == NULL) { - goto end; - } - - if (ret == NULL) { - ret = BN_new(); - } - if (ret == NULL) { - goto end; - } - - /* A = a mod p */ - if (!BN_nnmod(A, a, p, ctx)) { - goto end; - } - - /* now write |p| - 1 as 2^e*q where q is odd */ - e = 1; - while (!BN_is_bit_set(p, e)) { - e++; - } - /* we'll set q later (if needed) */ - - if (e == 1) { - /* The easy case: (|p|-1)/2 is odd, so 2 has an inverse - * modulo (|p|-1)/2, and square roots can be computed - * directly by modular exponentiation. - * We have - * 2 * (|p|+1)/4 == 1 (mod (|p|-1)/2), - * so we can use exponent (|p|+1)/4, i.e. (|p|-3)/4 + 1. - */ - if (!BN_rshift(q, p, 2)) { - goto end; - } - q->neg = 0; - if (!BN_add_word(q, 1) || - !BN_mod_exp(ret, A, q, p, ctx)) { - goto end; - } - err = 0; - goto vrfy; - } - - if (e == 2) { - /* |p| == 5 (mod 8) - * - * In this case 2 is always a non-square since - * Legendre(2,p) = (-1)^((p^2-1)/8) for any odd prime. - * So if a really is a square, then 2*a is a non-square. - * Thus for - * b := (2*a)^((|p|-5)/8), - * i := (2*a)*b^2 - * we have - * i^2 = (2*a)^((1 + (|p|-5)/4)*2) - * = (2*a)^((p-1)/2) - * = -1; - * so if we set - * x := a*b*(i-1), - * then - * x^2 = a^2 * b^2 * (i^2 - 2*i + 1) - * = a^2 * b^2 * (-2*i) - * = a*(-i)*(2*a*b^2) - * = a*(-i)*i - * = a. - * - * (This is due to A.O.L. Atkin, - * <URL: - *http://listserv.nodak.edu/scripts/wa.exe?A2=ind9211&L=nmbrthry&O=T&P=562>, - * November 1992.) - */ - - /* t := 2*a */ - if (!BN_mod_lshift1_quick(t, A, p)) { - goto end; - } - - /* b := (2*a)^((|p|-5)/8) */ - if (!BN_rshift(q, p, 3)) { - goto end; - } - q->neg = 0; - if (!BN_mod_exp(b, t, q, p, ctx)) { - goto end; - } - - /* y := b^2 */ - if (!BN_mod_sqr(y, b, p, ctx)) { - goto end; - } - - /* t := (2*a)*b^2 - 1*/ - if (!BN_mod_mul(t, t, y, p, ctx) || - !BN_sub_word(t, 1)) { - goto end; - } - - /* x = a*b*t */ - if (!BN_mod_mul(x, A, b, p, ctx) || - !BN_mod_mul(x, x, t, p, ctx)) { - goto end; - } - - if (!BN_copy(ret, x)) { - goto end; - } - err = 0; - goto vrfy; - } - - /* e > 2, so we really have to use the Tonelli/Shanks algorithm. - * First, find some y that is not a square. */ - if (!BN_copy(q, p)) { - goto end; /* use 'q' as temp */ - } - q->neg = 0; - i = 2; - do { - /* For efficiency, try small numbers first; - * if this fails, try random numbers. - */ - if (i < 22) { - if (!BN_set_word(y, i)) { - goto end; - } - } else { - if (!BN_pseudo_rand(y, BN_num_bits(p), 0, 0)) { - goto end; - } - if (BN_ucmp(y, p) >= 0) { - if (!(p->neg ? BN_add : BN_sub)(y, y, p)) { - goto end; - } - } - /* now 0 <= y < |p| */ - if (BN_is_zero(y)) { - if (!BN_set_word(y, i)) { - goto end; - } - } - } - - r = BN_kronecker(y, q, ctx); /* here 'q' is |p| */ - if (r < -1) { - goto end; - } - if (r == 0) { - /* m divides p */ - OPENSSL_PUT_ERROR(BN, BN_R_P_IS_NOT_PRIME); - goto end; - } - } while (r == 1 && ++i < 82); - - if (r != -1) { - /* Many rounds and still no non-square -- this is more likely - * a bug than just bad luck. - * Even if p is not prime, we should have found some y - * such that r == -1. - */ - OPENSSL_PUT_ERROR(BN, BN_R_TOO_MANY_ITERATIONS); - goto end; - } - - /* Here's our actual 'q': */ - if (!BN_rshift(q, q, e)) { - goto end; - } - - /* Now that we have some non-square, we can find an element - * of order 2^e by computing its q'th power. */ - if (!BN_mod_exp(y, y, q, p, ctx)) { - goto end; - } - if (BN_is_one(y)) { - OPENSSL_PUT_ERROR(BN, BN_R_P_IS_NOT_PRIME); - goto end; - } - - /* Now we know that (if p is indeed prime) there is an integer - * k, 0 <= k < 2^e, such that - * - * a^q * y^k == 1 (mod p). - * - * As a^q is a square and y is not, k must be even. - * q+1 is even, too, so there is an element - * - * X := a^((q+1)/2) * y^(k/2), - * - * and it satisfies - * - * X^2 = a^q * a * y^k - * = a, - * - * so it is the square root that we are looking for. - */ - - /* t := (q-1)/2 (note that q is odd) */ - if (!BN_rshift1(t, q)) { - goto end; - } - - /* x := a^((q-1)/2) */ - if (BN_is_zero(t)) /* special case: p = 2^e + 1 */ - { - if (!BN_nnmod(t, A, p, ctx)) { - goto end; - } - if (BN_is_zero(t)) { - /* special case: a == 0 (mod p) */ - BN_zero(ret); - err = 0; - goto end; - } else if (!BN_one(x)) { - goto end; - } - } else { - if (!BN_mod_exp(x, A, t, p, ctx)) { - goto end; - } - if (BN_is_zero(x)) { - /* special case: a == 0 (mod p) */ - BN_zero(ret); - err = 0; - goto end; - } - } - - /* b := a*x^2 (= a^q) */ - if (!BN_mod_sqr(b, x, p, ctx) || - !BN_mod_mul(b, b, A, p, ctx)) { - goto end; - } - - /* x := a*x (= a^((q+1)/2)) */ - if (!BN_mod_mul(x, x, A, p, ctx)) { - goto end; - } - - while (1) { - /* Now b is a^q * y^k for some even k (0 <= k < 2^E - * where E refers to the original value of e, which we - * don't keep in a variable), and x is a^((q+1)/2) * y^(k/2). - * - * We have a*b = x^2, - * y^2^(e-1) = -1, - * b^2^(e-1) = 1. - */ - - if (BN_is_one(b)) { - if (!BN_copy(ret, x)) { - goto end; - } - err = 0; - goto vrfy; - } - - - /* find smallest i such that b^(2^i) = 1 */ - i = 1; - if (!BN_mod_sqr(t, b, p, ctx)) { - goto end; - } - while (!BN_is_one(t)) { - i++; - if (i == e) { - OPENSSL_PUT_ERROR(BN, BN_R_NOT_A_SQUARE); - goto end; - } - if (!BN_mod_mul(t, t, t, p, ctx)) { - goto end; - } - } - - - /* t := y^2^(e - i - 1) */ - if (!BN_copy(t, y)) { - goto end; - } - for (j = e - i - 1; j > 0; j--) { - if (!BN_mod_sqr(t, t, p, ctx)) { - goto end; - } - } - if (!BN_mod_mul(y, t, t, p, ctx) || - !BN_mod_mul(x, x, t, p, ctx) || - !BN_mod_mul(b, b, y, p, ctx)) { - goto end; - } - e = i; - } - -vrfy: - if (!err) { - /* verify the result -- the input might have been not a square - * (test added in 0.9.8) */ - - if (!BN_mod_sqr(x, ret, p, ctx)) { - err = 1; - } - - if (!err && 0 != BN_cmp(x, A)) { - OPENSSL_PUT_ERROR(BN, BN_R_NOT_A_SQUARE); - err = 1; - } - } - -end: - if (err) { - if (ret != in) { - BN_clear_free(ret); - } - ret = NULL; - } - BN_CTX_end(ctx); - return ret; -} - -int BN_sqrt(BIGNUM *out_sqrt, const BIGNUM *in, BN_CTX *ctx) { - BIGNUM *estimate, *tmp, *delta, *last_delta, *tmp2; - int ok = 0, last_delta_valid = 0; - - if (in->neg) { - OPENSSL_PUT_ERROR(BN, BN_R_NEGATIVE_NUMBER); - return 0; - } - if (BN_is_zero(in)) { - BN_zero(out_sqrt); - return 1; - } - - BN_CTX_start(ctx); - if (out_sqrt == in) { - estimate = BN_CTX_get(ctx); - } else { - estimate = out_sqrt; - } - tmp = BN_CTX_get(ctx); - last_delta = BN_CTX_get(ctx); - delta = BN_CTX_get(ctx); - if (estimate == NULL || tmp == NULL || last_delta == NULL || delta == NULL) { - OPENSSL_PUT_ERROR(BN, ERR_R_MALLOC_FAILURE); - goto err; - } - - /* We estimate that the square root of an n-bit number is 2^{n/2}. */ - BN_lshift(estimate, BN_value_one(), BN_num_bits(in)/2); - - /* This is Newton's method for finding a root of the equation |estimate|^2 - - * |in| = 0. */ - for (;;) { - /* |estimate| = 1/2 * (|estimate| + |in|/|estimate|) */ - if (!BN_div(tmp, NULL, in, estimate, ctx) || - !BN_add(tmp, tmp, estimate) || - !BN_rshift1(estimate, tmp) || - /* |tmp| = |estimate|^2 */ - !BN_sqr(tmp, estimate, ctx) || - /* |delta| = |in| - |tmp| */ - !BN_sub(delta, in, tmp)) { - OPENSSL_PUT_ERROR(BN, ERR_R_BN_LIB); - goto err; - } - - delta->neg = 0; - /* The difference between |in| and |estimate| squared is required to always - * decrease. This ensures that the loop always terminates, but I don't have - * a proof that it always finds the square root for a given square. */ - if (last_delta_valid && BN_cmp(delta, last_delta) >= 0) { - break; - } - - last_delta_valid = 1; - - tmp2 = last_delta; - last_delta = delta; - delta = tmp2; - } - - if (BN_cmp(tmp, in) != 0) { - OPENSSL_PUT_ERROR(BN, BN_R_NOT_A_SQUARE); - goto err; - } - - ok = 1; - -err: - if (ok && out_sqrt == in && !BN_copy(out_sqrt, estimate)) { - ok = 0; - } - BN_CTX_end(ctx); - return ok; -} |