X-Git-Url: https://git.librecmc.org/?a=blobdiff_plain;f=crypto%2Fbn%2Fbn_sqrt.c;h=6beaf9e5e5ddfd6da6942c67b045049a7c979ddb;hb=19398a175a7dc36b66f9494d5ebfb85d2e6ac1d6;hp=6d50b5d895bc56e09ecaddd613f83f7f2c24a100;hpb=aa66eba7c8c7496db92b80da19688d6f96a40b96;p=oweals%2Fopenssl.git

diff --git a/crypto/bn/bn_sqrt.c b/crypto/bn/bn_sqrt.c
index 6d50b5d895..6beaf9e5e5 100644
--- a/crypto/bn/bn_sqrt.c
+++ b/crypto/bn/bn_sqrt.c
@@ -1,4 +1,4 @@
-/* crypto/bn/bn_mod.c */
+/* crypto/bn/bn_sqrt.c */
 /* Written by Lenka Fibikova <fibikova@exp-math.uni-essen.de>
  * and Bodo Moeller for the OpenSSL project. */
 /* ====================================================================
@@ -70,7 +70,7 @@ BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
 	BIGNUM *ret = in;
 	int err = 1;
 	int r;
-	BIGNUM *b, *q, *t, *x, *y;
+	BIGNUM *A, *b, *q, *t, *x, *y;
 	int e, i, j;
 	
 	if (!BN_is_odd(p) || BN_abs_is_word(p, 1))
@@ -83,9 +83,11 @@ BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
 				goto end;
 			if (!BN_set_word(ret, BN_is_bit_set(a, 0)))
 				{
-				BN_free(ret);
+				if (ret != in)
+					BN_free(ret);
 				return NULL;
 				}
+			bn_check_top(ret);
 			return ret;
 			}
 
@@ -101,23 +103,16 @@ BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
 			goto end;
 		if (!BN_set_word(ret, BN_is_one(a)))
 			{
-			BN_free(ret);
+			if (ret != in)
+				BN_free(ret);
 			return NULL;
 			}
+		bn_check_top(ret);
 		return ret;
 		}
 
-#if 0 /* if BN_mod_sqrt is used with correct input, this just wastes time */
-	r = BN_kronecker(a, p, ctx);
-	if (r < -1) return NULL;
-	if (r == -1)
-		{
-		BNerr(BN_F_BN_MOD_SQRT, BN_R_NOT_A_SQUARE);
-		return(NULL);
-		}
-#endif
-
 	BN_CTX_start(ctx);
+	A = BN_CTX_get(ctx);
 	b = BN_CTX_get(ctx);
 	q = BN_CTX_get(ctx);
 	t = BN_CTX_get(ctx);
@@ -129,43 +124,44 @@ BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
 		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++;
-	if (e > 2)
-		/* we don't need this  q  if  e = 1 or 2 */
-		if (!BN_rshift(q, p, e)) goto end;
-	q->neg = 0;
+	/* 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
+		/* 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.
+		 *     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;
+		if (!BN_mod_exp(ret, A, q, p, ctx)) goto end;
 		err = 0;
-		goto end;
+		goto vrfy;
 		}
 	
 	if (e == 2)
 		{
-		/* p == 5  (mod 8)
+		/* |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),
+		 *      b := (2*a)^((|p|-5)/8),
 		 *      i := (2*a)*b^2
 		 * we have
-		 *     i^2 = (2*a)^((1 + (p-5)/4)*2)
+		 *     i^2 = (2*a)^((1 + (|p|-5)/4)*2)
 		 *         = (2*a)^((p-1)/2)
 		 *         = -1;
 		 * so if we set
@@ -182,18 +178,12 @@ BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
 		 * November 1992.)
 		 */
 
-		/* make sure that  a  is reduced modulo p */
-		if (a->neg || BN_ucmp(a, p) >= 0)
-			{
-			if (!BN_nnmod(x, a, p, ctx)) goto end;
-			a = x; /* use x as temporary variable */
-			}
-
 		/* t := 2*a */
-		if (!BN_mod_lshift1_quick(t, a, p)) goto end;
+		if (!BN_mod_lshift1_quick(t, A, p)) goto end;
 
-		/* b := (2*a)^((p-5)/8) */
+		/* 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 */
@@ -204,16 +194,18 @@ BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
 		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, 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 end;
+		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
 		{
@@ -236,7 +228,7 @@ BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
 				if (!BN_set_word(y, i)) goto end;
 			}
 		
-		r = BN_kronecker(y, p, ctx);
+		r = BN_kronecker(y, q, ctx); /* here 'q' is |p| */
 		if (r < -1) goto end;
 		if (r == 0)
 			{
@@ -258,6 +250,8 @@ BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
 		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. */
@@ -292,11 +286,11 @@ BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
 	/* 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_nnmod(t, A, p, ctx)) goto end;
 		if (BN_is_zero(t))
 			{
 			/* special case: a == 0  (mod p) */
-			if (!BN_zero(ret)) goto end;
+			BN_zero(ret);
 			err = 0;
 			goto end;
 			}
@@ -305,11 +299,11 @@ BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
 		}
 	else
 		{
-		if (!BN_mod_exp(x, a, t, p, ctx)) goto end;
+		if (!BN_mod_exp(x, A, t, p, ctx)) goto end;
 		if (BN_is_zero(x))
 			{
 			/* special case: a == 0  (mod p) */
-			if (!BN_zero(ret)) goto end;
+			BN_zero(ret);
 			err = 0;
 			goto end;
 			}
@@ -317,10 +311,10 @@ BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
 
 	/* 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;
+	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;
+	if (!BN_mod_mul(x, x, A, p, ctx)) goto end;
 
 	while (1)
 		{
@@ -337,7 +331,7 @@ BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
 			{
 			if (!BN_copy(ret, x)) goto end;
 			err = 0;
-			goto end;
+			goto vrfy;
 			}
 
 
@@ -368,6 +362,22 @@ BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
 		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)
 		{
@@ -378,5 +388,6 @@ BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
 		ret = NULL;
 		}
 	BN_CTX_end(ctx);
+	bn_check_top(ret);
 	return ret;
 	}