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Fix a bug in BN_mod_sqrt() that can cause it to loop forever.
Obtained from: OpenSSL Project Security: CVE-2022-0778
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@ -14,7 +14,8 @@ BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
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/*
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* Returns 'ret' such that ret^2 == a (mod p), using the Tonelli/Shanks
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* algorithm (cf. Henri Cohen, "A Course in Algebraic Computational Number
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* Theory", algorithm 1.5.1). 'p' must be prime!
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* Theory", algorithm 1.5.1). 'p' must be prime, otherwise an error or
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* an incorrect "result" will be returned.
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*/
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{
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BIGNUM *ret = in;
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@ -301,18 +302,23 @@ BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
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goto vrfy;
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}
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/* find smallest i such that b^(2^i) = 1 */
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i = 1;
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if (!BN_mod_sqr(t, b, p, ctx))
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goto end;
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while (!BN_is_one(t)) {
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i++;
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if (i == e) {
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BNerr(BN_F_BN_MOD_SQRT, BN_R_NOT_A_SQUARE);
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goto end;
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/* Find the smallest i, 0 < i < e, such that b^(2^i) = 1. */
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for (i = 1; i < e; i++) {
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if (i == 1) {
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if (!BN_mod_sqr(t, b, p, ctx))
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goto end;
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} else {
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if (!BN_mod_mul(t, t, t, p, ctx))
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goto end;
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}
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if (!BN_mod_mul(t, t, t, p, ctx))
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goto end;
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if (BN_is_one(t))
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break;
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}
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/* If not found, a is not a square or p is not prime. */
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if (i >= e) {
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BNerr(BN_F_BN_MOD_SQRT, BN_R_NOT_A_SQUARE);
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goto end;
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}
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/* t := y^2^(e - i - 1) */
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@ -3,7 +3,7 @@
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=head1 NAME
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BN_add, BN_sub, BN_mul, BN_sqr, BN_div, BN_mod, BN_nnmod, BN_mod_add,
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BN_mod_sub, BN_mod_mul, BN_mod_sqr, BN_exp, BN_mod_exp, BN_gcd -
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BN_mod_sub, BN_mod_mul, BN_mod_sqr, BN_mod_sqrt, BN_exp, BN_mod_exp, BN_gcd -
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arithmetic operations on BIGNUMs
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=head1 SYNOPSIS
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@ -36,6 +36,8 @@ arithmetic operations on BIGNUMs
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int BN_mod_sqr(BIGNUM *r, BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
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BIGNUM *BN_mod_sqrt(BIGNUM *in, BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
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int BN_exp(BIGNUM *r, BIGNUM *a, BIGNUM *p, BN_CTX *ctx);
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int BN_mod_exp(BIGNUM *r, BIGNUM *a, const BIGNUM *p,
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@ -87,6 +89,12 @@ L<BN_mod_mul_reciprocal(3)>.
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BN_mod_sqr() takes the square of I<a> modulo B<m> and places the
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result in I<r>.
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BN_mod_sqrt() returns the modular square root of I<a> such that
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C<in^2 = a (mod p)>. The modulus I<p> must be a
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prime, otherwise an error or an incorrect "result" will be returned.
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The result is stored into I<in> which can be NULL. The result will be
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newly allocated in that case.
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BN_exp() raises I<a> to the I<p>-th power and places the result in I<r>
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(C<r=a^p>). This function is faster than repeated applications of
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BN_mul().
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@ -108,7 +116,10 @@ the arguments.
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=head1 RETURN VALUES
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For all functions, 1 is returned for success, 0 on error. The return
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The BN_mod_sqrt() returns the result (possibly incorrect if I<p> is
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not a prime), or NULL.
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For all remaining functions, 1 is returned for success, 0 on error. The return
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value should always be checked (e.g., C<if (!BN_add(r,a,b)) goto err;>).
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The error codes can be obtained by L<ERR_get_error(3)>.
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