X-Git-Url: https://git.librecmc.org/?a=blobdiff_plain;f=crypto%2Fbn%2Fbn_sqrt.c;h=6beaf9e5e5ddfd6da6942c67b045049a7c979ddb;hb=231a737a82cecde336ef4eeebdc26469f8c44e98;hp=2a72c189cbad97b99694f99635dd1b175212b4de;hpb=25439b76adb66fe0ce6e012a9af1e1ce969a1479;p=oweals%2Fopenssl.git diff --git a/crypto/bn/bn_sqrt.c b/crypto/bn/bn_sqrt.c index 2a72c189cb..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 * 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; } @@ -93,17 +95,24 @@ BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx) return(NULL); } -#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) + if (BN_is_zero(a) || BN_is_one(a)) { - BNerr(BN_F_BN_MOD_SQRT, BN_R_NOT_A_SQUARE); - return(NULL); + 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; } -#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); @@ -115,31 +124,88 @@ 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 (!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. (q+1)/2. + * 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_add_word(q,1)) goto end; - if (!BN_rshift1(q,q)) goto end; - if (!BN_mod_exp(ret, a, q, p, ctx)) goto end; + 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 end; + 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, + * , + * 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 > 1, so we really have to use the Tonelli/Shanks algorithm. + /* 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 { @@ -162,7 +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) { @@ -184,6 +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. */ @@ -218,11 +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; } @@ -231,11 +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; } @@ -243,10 +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) { @@ -263,7 +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; } @@ -294,6 +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) { @@ -304,5 +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; }