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Diffstat (limited to 'openssl/crypto/bn/bn_sqrt.c')
-rw-r--r--openssl/crypto/bn/bn_sqrt.c393
1 files changed, 0 insertions, 393 deletions
diff --git a/openssl/crypto/bn/bn_sqrt.c b/openssl/crypto/bn/bn_sqrt.c
deleted file mode 100644
index 6beaf9e5..00000000
--- a/openssl/crypto/bn/bn_sqrt.c
+++ /dev/null
@@ -1,393 +0,0 @@
-/* crypto/bn/bn_sqrt.c */
-/* 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 "cryptlib.h"
-#include "bn_lcl.h"
-
-
-BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
-/* 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 *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;
- }
- bn_check_top(ret);
- return ret;
- }
-
- BNerr(BN_F_BN_MOD_SQRT, 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;
- }
- bn_check_top(ret);
- 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)) goto end;
- if (!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)) goto end;
- if (!BN_sub_word(t, 1)) goto end;
-
- /* x = a*b*t */
- if (!BN_mod_mul(x, A, b, p, ctx)) goto end;
- if (!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 */
- BNerr(BN_F_BN_MOD_SQRT, 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.
- */
- BNerr(BN_F_BN_MOD_SQRT, 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))
- {
- BNerr(BN_F_BN_MOD_SQRT, 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)) goto end;
- if (!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)
- {
- BNerr(BN_F_BN_MOD_SQRT, 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)) goto end;
- if (!BN_mod_mul(x, x, t, p, ctx)) goto end;
- if (!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))
- {
- BNerr(BN_F_BN_MOD_SQRT, BN_R_NOT_A_SQUARE);
- err = 1;
- }
- }
-
- end:
- if (err)
- {
- if (ret != NULL && ret != in)
- {
- BN_clear_free(ret);
- }
- ret = NULL;
- }
- BN_CTX_end(ctx);
- bn_check_top(ret);
- return ret;
- }
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