initial/final commitHEADmaster

1 files changed, 358 insertions, 0 deletions

diff --git a/openssl-1.1.0h/crypto/bn/bn_sqrt.c b/openssl-1.1.0h/crypto/bn/bn_sqrt.c
new file mode 100644
index 0000000..84376c7
--- /dev/null
+++ b/openssl-1.1.0h/crypto/bn/bn_sqrt.c
@@ -0,0 +1,358 @@
+/*
+ * Copyright 2000-2016 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"
+
+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 != in)
+            BN_clear_free(ret);
+        ret = NULL;
+    }
+    BN_CTX_end(ctx);
+    bn_check_top(ret);
+    return ret;
+}