diff --git a/crypto/rsa/padding.c b/crypto/rsa/padding.c
index 5a42e248..40542923 100644
--- a/crypto/rsa/padding.c
+++ b/crypto/rsa/padding.c
@@ -56,6 +56,7 @@
 #include <openssl/rsa.h>
 
 #include <assert.h>
+#include <limits.h>
 #include <string.h>
 
 #include <openssl/digest.h>
@@ -65,6 +66,7 @@
 #include <openssl/sha.h>
 
 #include "internal.h"
+#include "../internal.h"
 
 /* TODO(fork): don't the check functions have to be constant time? */
 
@@ -191,51 +193,30 @@ int RSA_padding_add_PKCS1_type_2(uint8_t *to, unsigned tlen,
   return 1;
 }
 
-/* constant_time_byte_eq returns 1 if |x| == |y| and 0 otherwise. */
-static int constant_time_byte_eq(unsigned char a, unsigned char b) {
-  unsigned char z = ~(a ^ b);
-  z &= z >> 4;
-  z &= z >> 2;
-  z &= z >> 1;
-
-  return z;
-}
-
-/* constant_time_select returns |x| if |v| is 1 and |y| if |v| is 0.
- * Its behavior is undefined if |v| takes any other value. */
-static int constant_time_select(int v, int x, int y) {
-  return ((~(v - 1)) & x) | ((v - 1) & y);
-}
-
-/* constant_time_le returns 1 if |x| <= |y| and 0 otherwise.
- * |x| and |y| must be positive. */
-static int constant_time_le(int x, int y) {
-  return ((x - y - 1) >> (sizeof(int) * 8 - 1)) & 1;
-}
-
 int RSA_message_index_PKCS1_type_2(const uint8_t *from, size_t from_len,
                                    size_t *out_index) {
   size_t i;
-  int first_byte_is_zero, second_byte_is_two, looking_for_index;
-  int valid_index, zero_index = 0;
+  unsigned first_byte_is_zero, second_byte_is_two, looking_for_index;
+  unsigned valid_index, zero_index = 0;
 
   /* PKCS#1 v1.5 decryption. See "PKCS #1 v2.2: RSA Cryptography
    * Standard", section 7.2.2. */
-  if (from_len < RSA_PKCS1_PADDING_SIZE) {
+  if (from_len < RSA_PKCS1_PADDING_SIZE || from_len > UINT_MAX) {
     /* |from| is zero-padded to the size of the RSA modulus, a public value, so
-     * this can be rejected in non-constant time. */
+     * this can be rejected in non-constant time. This logic also requires
+     * |from_len| fit in an |unsigned|. */
     *out_index = 0;
     return 0;
   }
 
-  first_byte_is_zero = constant_time_byte_eq(from[0], 0);
-  second_byte_is_two = constant_time_byte_eq(from[1], 2);
+  first_byte_is_zero = constant_time_eq(from[0], 0);
+  second_byte_is_two = constant_time_eq(from[1], 2);
 
-  looking_for_index = 1;
+  looking_for_index = ~0u;
   for (i = 2; i < from_len; i++) {
-    int equals0 = constant_time_byte_eq(from[i], 0);
-    zero_index =
-        constant_time_select(looking_for_index & equals0, i, zero_index);
+    unsigned equals0 = constant_time_is_zero(from[i]);
+    zero_index = constant_time_select(looking_for_index & equals0, (unsigned)i,
+                                      zero_index);
     looking_for_index = constant_time_select(equals0, 0, looking_for_index);
   }
 
@@ -247,13 +228,13 @@ int RSA_message_index_PKCS1_type_2(const uint8_t *from, size_t from_len,
   valid_index &= ~looking_for_index;
 
   /* PS must be at least 8 bytes long, and it starts two bytes into |from|. */
-  valid_index &= constant_time_le(2 + 8, zero_index);
+  valid_index &= constant_time_ge(zero_index, 2 + 8);
 
   /* Skip the zero byte. */
   zero_index++;
 
   *out_index = constant_time_select(valid_index, zero_index, 0);
-  return valid_index;
+  return constant_time_select(valid_index, 1, 0);
 }
 
 int RSA_padding_check_PKCS1_type_2(uint8_t *to, unsigned tlen,
@@ -421,10 +402,9 @@ int RSA_padding_check_PKCS1_OAEP_mgf1(uint8_t *to, unsigned tlen,
                                       const uint8_t *from, unsigned flen,
                                       const uint8_t *param, unsigned plen,
                                       const EVP_MD *md, const EVP_MD *mgf1md) {
-  unsigned i, dblen, mlen = -1, mdlen;
+  unsigned i, dblen, mlen = -1, mdlen, bad, looking_for_one_byte, one_index;
   const uint8_t *maskeddb, *maskedseed;
   uint8_t *db = NULL, seed[EVP_MAX_MD_SIZE], phash[EVP_MAX_MD_SIZE];
-  int bad, looking_for_one_byte, one_index = 0;
 
   if (md == NULL) {
     md = EVP_sha1();
@@ -472,15 +452,14 @@ int RSA_padding_check_PKCS1_OAEP_mgf1(uint8_t *to, unsigned tlen,
     goto err;
   }
 
-  bad = CRYPTO_memcmp(db, phash, mdlen);
-  bad |= from[0];
+  bad = ~constant_time_is_zero(CRYPTO_memcmp(db, phash, mdlen));
+  bad |= ~constant_time_is_zero(from[0]);
 
-  looking_for_one_byte = 1;
+  looking_for_one_byte = ~0u;
   for (i = mdlen; i < dblen; i++) {
-    int equals1 = constant_time_byte_eq(db[i], 1);
-    int equals0 = constant_time_byte_eq(db[i], 0);
-    one_index =
-        constant_time_select(looking_for_one_byte & equals1, i, one_index);
+    unsigned equals1 = constant_time_eq(db[i], 1);
+    unsigned equals0 = constant_time_eq(db[i], 0);
+    one_index = constant_time_select(looking_for_one_byte & equals1, i, one_index);
     looking_for_one_byte =
         constant_time_select(equals1, 0, looking_for_one_byte);
     bad |= looking_for_one_byte & ~equals0;