Sign-related fixes (and tests).

BN_mod_exp_mont does not work properly yet if modulus m
is negative (we want computations to be carried out
modulo |m|).

diff --git a/CHANGES b/CHANGES
index 9a1ad16fe38201888a277d060f631a1557d79765..107c31bf564fc1c2800274bcebf9d468df252e0c 100644 (file)
--- a/CHANGES
+++ b/CHANGES
@@ -3,6 +3,10 @@
 
  Changes between 0.9.6 and 0.9.7  [xx XXX 2000]
 
+  *) BN_div bugfix: If the result is 0, the sign (res->neg) must not be
+     set.
+     [Bodo Moeller]
+
   *) Changed the LHASH code to use prototypes for callbacks, and created
      macros to declare and implement thin (optionally static) functions
      that provide type-safety and avoid function pointer casting for the

diff --git a/crypto/bn/bn_div.c b/crypto/bn/bn_div.c
index 2e600c7c5426ef3a00566ca5ab89c35454bf9491..64b84ac1a76d06f294cae875b44f9578f3bc6fa8 100644 (file)
--- a/crypto/bn/bn_div.c
+++ b/crypto/bn/bn_div.c
@@ -241,6 +241,8 @@ int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
                }
        else
                res->top--;
+       if (res->top == 0)
+               res->neg = 0;
        resp--;
 
        for (i=0; i<loop-1; i++)

diff --git a/crypto/bn/bn_sqrt.c b/crypto/bn/bn_sqrt.c
index 6959cc5f6f8324c033138ea1663e5072bc18bbe1..6e70e5c54140fd3d4060a05c196ebfb39ca5f60f 100644 (file)
--- a/crypto/bn/bn_sqrt.c
+++ b/crypto/bn/bn_sqrt.c
@@ -133,21 +133,16 @@ BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
        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;
@@ -159,16 +154,16 @@ BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
        
        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
@@ -195,7 +190,7 @@ BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
                /* t := 2*a */
                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;
@@ -218,6 +213,8 @@ BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
        
        /* 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
                {
@@ -240,7 +237,7 @@ 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)
                        {
@@ -262,6 +259,8 @@ 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. */

diff --git a/crypto/bn/bntest.c b/crypto/bn/bntest.c
index f27087d59c3dccc62e41e94793ece0524c1414f2..9f308b75a9e6a3a53a73ac2ef1742ef22f03e086 100644 (file)
--- a/crypto/bn/bntest.c
+++ b/crypto/bn/bntest.c
@@ -907,6 +907,7 @@ int test_kron(BIO *bp, BN_CTX *ctx)
         * works.) */
 
        if (!BN_generate_prime(b, 512, 0, NULL, NULL, genprime_cb, NULL)) goto err;
+       b->neg = rand_neg();
        putc('\n', stderr);
 
        for (i = 0; i < num0; i++)
@@ -914,12 +915,17 @@ int test_kron(BIO *bp, BN_CTX *ctx)
                if (!BN_bntest_rand(a, 512, 0, 0)) goto err;
                a->neg = rand_neg();
 
-               /* t := (b-1)/2  (note that b is odd) */
+               /* t := (|b|-1)/2  (note that b is odd) */
                if (!BN_copy(t, b)) goto err;
+               t->neg = 0;
                if (!BN_sub_word(t, 1)) goto err;
                if (!BN_rshift1(t, t)) goto err;
                /* r := a^t mod b */
-               if (!BN_mod_exp(r, a, t, b, ctx)) goto err;
+               /* FIXME: Using BN_mod_exp (Montgomery variant) leads to
+                * incorrect results if  b  is negative ("Legendre symbol
+                * computation failed").
+                * We want computations to be carried out modulo |b|. */
+               if (!BN_mod_exp_simple(r, a, t, b, ctx)) goto err;
 
                if (BN_is_word(r, 1))
                        legendre = 1;
@@ -938,6 +944,9 @@ int test_kron(BIO *bp, BN_CTX *ctx)
                
                kronecker = BN_kronecker(a, b, ctx);
                if (kronecker < -1) goto err;
+               /* we actually need BN_kronecker(a, |b|) */
+               if (a->neg && b->neg)
+                       kronecker = -kronecker;
                
                if (legendre != kronecker)
                        {
@@ -991,6 +1000,7 @@ int test_sqrt(BIO *bp, BN_CTX *ctx)
                        if (!BN_generate_prime(p, 256, 0, a, r, genprime_cb, NULL)) goto err;
                        putc('\n', stderr);
                        }
+               p->neg = rand_neg();
 
                for (j = 0; j < num2; j++)
                        {
@@ -1003,6 +1013,8 @@ int test_sqrt(BIO *bp, BN_CTX *ctx)
                        if (!BN_nnmod(a, a, p, ctx)) goto err;
                        if (!BN_mod_sqr(a, a, p, ctx)) goto err;
                        if (!BN_mul(a, a, r, ctx)) goto err;
+                       if (rand_neg())
+                               if (!BN_sub(a, a, p)) goto err;
 
                        if (!BN_mod_sqrt(r, a, p, ctx)) goto err;
                        if (!BN_mod_sqr(r, r, p, ctx)) goto err;