diff --git a/crypto/bn/bn_blind.c b/crypto/bn/bn_blind.c
index 24d138309d47b..7a8237c43dd10 100644
--- a/crypto/bn/bn_blind.c
+++ b/crypto/bn/bn_blind.c
@@ -109,10 +109,15 @@ int BN_BLINDING_update(BN_BLINDING *b, BN_CTX *ctx)
         if (!BN_BLINDING_create_param(b, NULL, NULL, ctx, NULL, NULL))
             goto err;
     } else if (!(b->flags & BN_BLINDING_NO_UPDATE)) {
-        if (!BN_mod_mul(b->A, b->A, b->A, b->mod, ctx))
-            goto err;
-        if (!BN_mod_mul(b->Ai, b->Ai, b->Ai, b->mod, ctx))
-            goto err;
+        if (b->m_ctx != NULL) {
+            if (!bn_mul_mont_fixed_top(b->Ai, b->Ai, b->Ai, b->m_ctx, ctx)
+                || !bn_mul_mont_fixed_top(b->A, b->A, b->A, b->m_ctx, ctx))
+                goto err;
+        } else {
+            if (!BN_mod_mul(b->Ai, b->Ai, b->Ai, b->mod, ctx)
+                || !BN_mod_mul(b->A, b->A, b->A, b->mod, ctx))
+                goto err;
+        }
     }
 
     ret = 1;
@@ -144,13 +149,13 @@ int BN_BLINDING_convert_ex(BIGNUM *n, BIGNUM *r, BN_BLINDING *b, BN_CTX *ctx)
     else if (!BN_BLINDING_update(b, ctx))
         return (0);
 
-    if (r != NULL) {
-        if (!BN_copy(r, b->Ai))
-            ret = 0;
-    }
+    if (r != NULL && (BN_copy(r, b->Ai) == NULL))
+        return 0;
 
-    if (!BN_mod_mul(n, n, b->A, b->mod, ctx))
-        ret = 0;
+    if (b->m_ctx != NULL)
+        ret = BN_mod_mul_montgomery(n, n, b->A, b->m_ctx, ctx);
+    else
+        ret = BN_mod_mul(n, n, b->A, b->mod, ctx);
 
     return ret;
 }
@@ -167,14 +172,29 @@ int BN_BLINDING_invert_ex(BIGNUM *n, const BIGNUM *r, BN_BLINDING *b,
 
     bn_check_top(n);
 
-    if (r != NULL)
-        ret = BN_mod_mul(n, n, r, b->mod, ctx);
-    else {
-        if (b->Ai == NULL) {
-            BNerr(BN_F_BN_BLINDING_INVERT_EX, BN_R_NOT_INITIALIZED);
-            return (0);
+    if (r == NULL && (r = b->Ai) == NULL) {
+        BNerr(BN_F_BN_BLINDING_INVERT_EX, BN_R_NOT_INITIALIZED);
+        return 0;
+    }
+
+    if (b->m_ctx != NULL) {
+        /* ensure that BN_mod_mul_montgomery takes pre-defined path */
+        if (n->dmax >= r->top) {
+            size_t i, rtop = r->top, ntop = n->top;
+            BN_ULONG mask;
+
+            for (i = 0; i < rtop; i++) {
+                mask = (BN_ULONG)0 - ((i - ntop) >> (8 * sizeof(i) - 1));
+                n->d[i] &= mask;
+            }
+            mask = (BN_ULONG)0 - ((rtop - ntop) >> (8 * sizeof(ntop) - 1));
+            /* always true, if (rtop >= ntop) n->top = r->top; */
+            n->top = (int)(rtop & ~mask) | (ntop & mask);
+            n->flags |= (BN_FLG_FIXED_TOP & ~mask);
         }
-        ret = BN_mod_mul(n, n, b->Ai, b->mod, ctx);
+        ret = BN_mod_mul_montgomery(n, n, r, b->m_ctx, ctx);
+    } else {
+        ret = BN_mod_mul(n, n, r, b->mod, ctx);
     }
 
     bn_check_top(n);
@@ -253,31 +273,35 @@ BN_BLINDING *BN_BLINDING_create_param(BN_BLINDING *b,
         int rv;
         if (!BN_rand_range(ret->A, ret->mod))
             goto err;
-        if (!int_bn_mod_inverse(ret->Ai, ret->A, ret->mod, ctx, &rv)) {
-            /*
-             * this should almost never happen for good RSA keys
-             */
-            if (rv) {
-                if (retry_counter-- == 0) {
-                    BNerr(BN_F_BN_BLINDING_CREATE_PARAM,
-                          BN_R_TOO_MANY_ITERATIONS);
-                    goto err;
-                }
-            } else
-                goto err;
-        } else
+        if (int_bn_mod_inverse(ret->Ai, ret->A, ret->mod, ctx, &rv))
             break;
+
+        /*
+         * this should almost never happen for good RSA keys
+         */
+        if (!rv)
+            goto err;
+
+        if (retry_counter-- == 0) {
+            BNerr(BN_F_BN_BLINDING_CREATE_PARAM, BN_R_TOO_MANY_ITERATIONS);
+            goto err;
+        }
     } while (1);
 
     if (ret->bn_mod_exp != NULL && ret->m_ctx != NULL) {
-        if (!ret->bn_mod_exp
-            (ret->A, ret->A, ret->e, ret->mod, ctx, ret->m_ctx))
+        if (!ret->bn_mod_exp(ret->A, ret->A, ret->e, ret->mod, ctx, ret->m_ctx))
             goto err;
     } else {
         if (!BN_mod_exp(ret->A, ret->A, ret->e, ret->mod, ctx))
             goto err;
     }
 
+    if (ret->m_ctx != NULL) {
+        if (!bn_to_mont_fixed_top(ret->Ai, ret->Ai, ret->m_ctx, ctx)
+            || !bn_to_mont_fixed_top(ret->A, ret->A, ret->m_ctx, ctx))
+            goto err;
+    }
+
     return ret;
  err:
     if (b == NULL) {