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>.

Reviewed-by: Paul Dale <pauli@openssl.org>
Reviewed-by: Matt Caswell <matt@openssl.org>

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) */