diff --git a/crypto/bn/gcd.c b/crypto/bn/gcd.c
index c33a3cd5..e1061498 100644
--- a/crypto/bn/gcd.c
+++ b/crypto/bn/gcd.c
@@ -223,20 +223,23 @@ err:
 }
 
 /* solves ax == 1 (mod n) */
-static BIGNUM *BN_mod_inverse_no_branch(BIGNUM *out, const BIGNUM *a,
-                                        const BIGNUM *n, BN_CTX *ctx);
+static BIGNUM *BN_mod_inverse_no_branch(BIGNUM *out, int *out_no_inverse,
+                                        const BIGNUM *a, const BIGNUM *n,
+                                        BN_CTX *ctx);
 
-BIGNUM *BN_mod_inverse(BIGNUM *out, const BIGNUM *a, const BIGNUM *n,
-                       BN_CTX *ctx) {
+BIGNUM *BN_mod_inverse_ex(BIGNUM *out, int *out_no_inverse, const BIGNUM *a,
+                          const BIGNUM *n, BN_CTX *ctx) {
   BIGNUM *A, *B, *X, *Y, *M, *D, *T, *R = NULL;
   BIGNUM *ret = NULL;
   int sign;
 
   if ((a->flags & BN_FLG_CONSTTIME) != 0 ||
       (n->flags & BN_FLG_CONSTTIME) != 0) {
-    return BN_mod_inverse_no_branch(out, a, n, ctx);
+    return BN_mod_inverse_no_branch(out, out_no_inverse, a, n, ctx);
   }
 
+  *out_no_inverse = 0;
+
   BN_CTX_start(ctx);
   A = BN_CTX_get(ctx);
   B = BN_CTX_get(ctx);
@@ -522,6 +525,7 @@ BIGNUM *BN_mod_inverse(BIGNUM *out, const BIGNUM *a, const BIGNUM *n,
       }
     }
   } else {
+    *out_no_inverse = 1;
     OPENSSL_PUT_ERROR(BN, BN_R_NO_INVERSE);
     goto err;
   }
@@ -535,16 +539,25 @@ err:
   return ret;
 }
 
+BIGNUM *BN_mod_inverse(BIGNUM *out, const BIGNUM *a, const BIGNUM *n,
+                       BN_CTX *ctx) {
+  int no_inverse;
+  return BN_mod_inverse_ex(out, &no_inverse, a, n, ctx);
+}
+
 /* BN_mod_inverse_no_branch is a special version of BN_mod_inverse.
  * It does not contain branches that may leak sensitive information. */
-static BIGNUM *BN_mod_inverse_no_branch(BIGNUM *out, const BIGNUM *a,
-                                        const BIGNUM *n, BN_CTX *ctx) {
+static BIGNUM *BN_mod_inverse_no_branch(BIGNUM *out, int *out_no_inverse,
+                                        const BIGNUM *a, const BIGNUM *n,
+                                        BN_CTX *ctx) {
   BIGNUM *A, *B, *X, *Y, *M, *D, *T, *R = NULL;
   BIGNUM local_A, local_B;
   BIGNUM *pA, *pB;
   BIGNUM *ret = NULL;
   int sign;
 
+  *out_no_inverse = 0;
+
   BN_CTX_start(ctx);
   A = BN_CTX_get(ctx);
   B = BN_CTX_get(ctx);
@@ -682,6 +695,7 @@ static BIGNUM *BN_mod_inverse_no_branch(BIGNUM *out, const BIGNUM *a,
       }
     }
   } else {
+    *out_no_inverse = 1;
     OPENSSL_PUT_ERROR(BN, BN_R_NO_INVERSE);
     goto err;
   }
diff --git a/crypto/rsa/blinding.c b/crypto/rsa/blinding.c
index 75c34225..c93cee1b 100644
--- a/crypto/rsa/blinding.c
+++ b/crypto/rsa/blinding.c
@@ -325,10 +325,11 @@ BN_BLINDING *BN_BLINDING_create_param(
     if (!BN_rand_range(ret->A, ret->mod)) {
       goto err;
     }
-    if (BN_mod_inverse(ret->Ai, ret->A, ret->mod, ctx) == NULL) {
+
+    int no_inverse;
+    if (BN_mod_inverse_ex(ret->Ai, &no_inverse, ret->A, ret->mod, ctx) == NULL) {
       /* this should almost never happen for good RSA keys */
-      uint32_t error = ERR_peek_last_error();
-      if (ERR_GET_REASON(error) == BN_R_NO_INVERSE) {
+      if (no_inverse) {
         if (retry_counter-- == 0) {
           OPENSSL_PUT_ERROR(RSA, RSA_R_TOO_MANY_ITERATIONS);
           goto err;
diff --git a/include/openssl/bn.h b/include/openssl/bn.h
index 7edb7784..0a1f5e5f 100644
--- a/include/openssl/bn.h
+++ b/include/openssl/bn.h
@@ -706,6 +706,14 @@ OPENSSL_EXPORT int BN_gcd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
 OPENSSL_EXPORT BIGNUM *BN_mod_inverse(BIGNUM *out, const BIGNUM *a,
                                       const BIGNUM *n, BN_CTX *ctx);
 
+/* BN_mod_inverse_ex acts like |BN_mod_inverse| except that, when it returns
+ * zero, it will set |*out_no_inverse| to one if the failure was caused because
+ * |a| has no inverse mod |n|. Otherwise it will set |*out_no_inverse| to
+ * zero. */
+OPENSSL_EXPORT BIGNUM *BN_mod_inverse_ex(BIGNUM *out, int *out_no_inverse,
+                                         const BIGNUM *a, const BIGNUM *n,
+                                         BN_CTX *ctx);
+
 /* BN_kronecker returns the Kronecker symbol of |a| and |b| (which is -1, 0 or
  * 1), or -2 on error. */
 OPENSSL_EXPORT int BN_kronecker(const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);