diff options
Diffstat (limited to 'crypto')
-rw-r--r-- | crypto/bn/bn_div.c | 2 | ||||
-rw-r--r-- | crypto/bn/bn_sqrt.c | 29 | ||||
-rw-r--r-- | crypto/bn/bntest.c | 16 |
3 files changed, 30 insertions, 17 deletions
diff --git a/crypto/bn/bn_div.c b/crypto/bn/bn_div.c index 2e600c7c54..64b84ac1a7 100644 --- 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 6959cc5f6f..6e70e5c541 100644 --- 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 f27087d59c..9f308b75a9 100644 --- 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; |