### Files

``````From 23f1773ddf92979006d0f438523f3c73320c384f Mon Sep 17 00:00:00 2001
From: Tomas Mraz <tomas@openssl.org>
Date: Mon, 28 Feb 2022 18:26:30 +0100
Subject: [PATCH] Add documentation of BN_mod_sqrt()

---
util/missingcrypto.txt |  1 -
2 files changed, 13 insertions(+), 3 deletions(-)

index 62d3ee7205..cf6c49c0e3 100644
@@ -3,7 +3,7 @@

-BN_mod_sub, BN_mod_mul, BN_mod_sqr, BN_exp, BN_mod_exp, BN_gcd -
+BN_mod_sub, BN_mod_mul, BN_mod_sqr, BN_mod_sqrt, BN_exp, BN_mod_exp, BN_gcd -
arithmetic operations on BIGNUMs

@@ -36,6 +36,8 @@ arithmetic operations on BIGNUMs

int BN_mod_sqr(BIGNUM *r, BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);

+ BIGNUM *BN_mod_sqrt(BIGNUM *in, BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
+
int BN_exp(BIGNUM *r, BIGNUM *a, BIGNUM *p, BN_CTX *ctx);

int BN_mod_exp(BIGNUM *r, BIGNUM *a, const BIGNUM *p,
@@ -87,6 +89,12 @@ L<BN_mod_mul_reciprocal(3)>.
BN_mod_sqr() takes the square of I<a> modulo B<m> and places the
result in I<r>.

+BN_mod_sqrt() returns the modular square root of I<a> such that
+C<in^2 = a (mod p)>. The modulus I<p> must be a
+prime, otherwise an error or an incorrect "result" will be returned.
+The result is stored into I<in> which can be NULL. The result will be
+newly allocated in that case.
+
BN_exp() raises I<a> to the I<p>-th power and places the result in I<r>
(C<r=a^p>). This function is faster than repeated applications of
BN_mul().
@@ -108,7 +116,10 @@ the arguments.

-For all functions, 1 is returned for success, 0 on error. The return
+The BN_mod_sqrt() returns the result (possibly incorrect if I<p> is
+not a prime), or NULL.
+
+For all remaining functions, 1 is returned for success, 0 on error. The return
value should always be checked (e.g., C<if (!BN_add(r,a,b)) goto err;>).
The error codes can be obtained by L<ERR_get_error(3)>.

diff --git a/util/missingcrypto.txt b/util/missingcrypto.txt
index b61bdeb880..4d2fd7f6b7 100644
--- a/util/missingcrypto.txt
+++ b/util/missingcrypto.txt
@@ -264,7 +264,6 @@ BN_mod_lshift(3)
BN_mod_lshift1(3)
BN_mod_lshift1_quick(3)
BN_mod_lshift_quick(3)
-BN_mod_sqrt(3)
BN_mod_sub_quick(3)
BN_nist_mod_192(3)
BN_nist_mod_224(3)

From 46673310c9a755b2a56f53d115854983d6ada11a Mon Sep 17 00:00:00 2001
From: Tomas Mraz <tomas@openssl.org>
Date: Mon, 28 Feb 2022 18:26:35 +0100
Subject: [PATCH] Add a negative testcase for BN_mod_sqrt

---
test/bntest.c                          | 11 ++++++++++-
test/recipes/10-test_bn_data/bnmod.txt | 12 ++++++++++++
2 files changed, 22 insertions(+), 1 deletion(-)

diff --git a/test/bntest.c b/test/bntest.c
index efdb3ef963..d49f87373a 100644
--- a/test/bntest.c
+++ b/test/bntest.c
@@ -1732,8 +1732,17 @@ static int file_modsqrt(STANZA *s)
|| !TEST_ptr(ret2 = BN_new()))
goto err;

+    if (BN_is_negative(mod_sqrt)) {
+        /* A negative testcase */
+        if (!TEST_ptr_null(BN_mod_sqrt(ret, a, p, ctx)))
+            goto err;
+
+        st = 1;
+        goto err;
+    }
+
/* There are two possible answers. */
-    if (!TEST_true(BN_mod_sqrt(ret, a, p, ctx))
+    if (!TEST_ptr(BN_mod_sqrt(ret, a, p, ctx))
|| !TEST_true(BN_sub(ret2, p, ret)))
goto err;

diff --git a/test/recipes/10-test_bn_data/bnmod.txt b/test/recipes/10-test_bn_data/bnmod.txt
index e22d656091..bc8a434ea5 100644
--- a/test/recipes/10-test_bn_data/bnmod.txt
+++ b/test/recipes/10-test_bn_data/bnmod.txt
@@ -2799,3 +2799,15 @@ P = 9df9d6cc20b8540411af4e5357ef2b0353cb1f2ab5ffc3e246b41c32f71e951f
ModSqrt = a1d52989f12f204d3d2167d9b1e6c8a6174c0c786a979a5952383b7b8bd186
A = 2eee37cf06228a387788188e650bc6d8a2ff402931443f69156a29155eca07dcb45f3aac238d92943c0c25c896098716baa433f25bd696a142f5a69d5d937e81
P = 9df9d6cc20b8540411af4e5357ef2b0353cb1f2ab5ffc3e246b41c32f71e951f
+
+# Negative testcases for BN_mod_sqrt()
+
+# This one triggers an infinite loop with unfixed implementation
+# It should just fail.
+ModSqrt = -1
+A = 20a7ee
+P = 460201
+
+ModSqrt = -1
+A = 65bebdb00a96fc814ec44b81f98b59fba3c30203928fa5214c51e0a97091645280c947b005847f239758482b9bfc45b066fde340d1fe32fc9c1bf02e1b2d0ed
+P = 9df9d6cc20b8540411af4e5357ef2b0353cb1f2ab5ffc3e246b41c32f71e951f

From cafcc62d7719dea73f334c9ef763d1e215fcd94d Mon Sep 17 00:00:00 2001
From: Tomas Mraz <tomas@openssl.org>
Date: Mon, 28 Feb 2022 18:26:21 +0100
Subject: [PATCH] Fix possible infinite loop in BN_mod_sqrt()

The calculation in some cases does not finish for non-prime p.

This fixes CVE-2022-0778.

Based on patch by David Benjamin <davidben@google.com>.
---
crypto/bn/bn_sqrt.c | 30 ++++++++++++++++++------------
1 file changed, 18 insertions(+), 12 deletions(-)

diff --git a/crypto/bn/bn_sqrt.c b/crypto/bn/bn_sqrt.c
index b663ae5ec5..c5ea7ab194 100644
--- a/crypto/bn/bn_sqrt.c
+++ b/crypto/bn/bn_sqrt.c
@@ -14,7 +14,8 @@ BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
/*
* Returns 'ret' such that ret^2 == a (mod p), using the Tonelli/Shanks
* algorithm (cf. Henri Cohen, "A Course in Algebraic Computational Number
- * Theory", algorithm 1.5.1). 'p' must be prime!
+ * Theory", algorithm 1.5.1). 'p' must be prime, otherwise an error or
+ * an incorrect "result" will be returned.
*/
{
BIGNUM *ret = in;
@@ -303,18 +304,23 @@ BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
goto vrfy;
}

-        /* find smallest  i  such that  b^(2^i) = 1 */
-        i = 1;
-        if (!BN_mod_sqr(t, b, p, ctx))
-            goto end;
-        while (!BN_is_one(t)) {
-            i++;
-            if (i == e) {
-                ERR_raise(ERR_LIB_BN, BN_R_NOT_A_SQUARE);
-                goto end;
+        /* Find the smallest i, 0 < i < e, such that b^(2^i) = 1. */
+        for (i = 1; i < e; i++) {
+            if (i == 1) {
+                if (!BN_mod_sqr(t, b, p, ctx))
+                    goto end;
+
+            } else {
+                if (!BN_mod_mul(t, t, t, p, ctx))
+                    goto end;
}
-            if (!BN_mod_mul(t, t, t, p, ctx))
-                goto end;
+            if (BN_is_one(t))
+                break;
+        }
+        /* If not found, a is not a square or p is not prime. */
+        if (i >= e) {
+            ERR_raise(ERR_LIB_BN, BN_R_NOT_A_SQUARE);
+            goto end;
}

/* t := y^2^(e - i - 1) */

``````