diff --git a/build.rs b/build.rs
index f7b94108b7..ee5423c84c 100644
--- a/build.rs
+++ b/build.rs
@@ -34,6 +34,7 @@ const ARM: &str = "arm";
 
 #[rustfmt::skip]
 const RING_SRCS: &[(&[&str], &str)] = &[
+    (&[], "crypto/constant_time.c"),
     (&[], "crypto/curve25519/curve25519.c"),
     (&[], "crypto/fipsmodule/aes/aes_nohw.c"),
     (&[], "crypto/fipsmodule/bn/montgomery.c"),
@@ -885,7 +886,7 @@ fn prefix_all_symbols(pp: char, prefix_prefix: &str, prefix: &str) -> String {
     ];
 
     static SYMBOLS_TO_PREFIX: &[&str] = &[
-        "CRYPTO_memcmp",
+        "RING_value_barrier_w",
         "CRYPTO_poly1305_finish",
         "CRYPTO_poly1305_finish_neon",
         "CRYPTO_poly1305_init",
diff --git a/crypto/constant_time.c b/crypto/constant_time.c
new file mode 100644
index 0000000000..56bfef6288
--- /dev/null
+++ b/crypto/constant_time.c
@@ -0,0 +1,19 @@
+/* Copyright 2023 Brian Smith.
+ *
+ * Permission to use, copy, modify, and/or distribute this software for any
+ * purpose with or without fee is hereby granted, provided that the above
+ * copyright notice and this permission notice appear in all copies.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
+ * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
+ * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
+ * SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
+ * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
+ * OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
+ * CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */
+
+#include "internal.h"
+
+RING_NOINLINE crypto_word_t RING_value_barrier_w(crypto_word_t a) {
+  return value_barrier_w(a);
+}
diff --git a/src/constant_time.rs b/src/constant_time.rs
index 3ac6ad4c21..f780c572f8 100644
--- a/src/constant_time.rs
+++ b/src/constant_time.rs
@@ -14,25 +14,44 @@
 
 //! Constant-time operations.
 
-use crate::{c, error};
+use crate::error;
 
 /// Returns `Ok(())` if `a == b` and `Err(error::Unspecified)` otherwise.
 /// The comparison of `a` and `b` is done in constant time with respect to the
 /// contents of each, but NOT in constant time with respect to the lengths of
 /// `a` and `b`.
 pub fn verify_slices_are_equal(a: &[u8], b: &[u8]) -> Result<(), error::Unspecified> {
+    verify_all_bytes_are_equal(a.iter().copied(), b.iter().copied())
+}
+
+// TODO: Use this in internal callers, in favor of `verify_slices_are_equal`.
+#[inline]
+pub(crate) fn verify_all_bytes_are_equal(
+    a: impl ExactSizeIterator<Item = u8>,
+    b: impl ExactSizeIterator<Item = u8>,
+) -> Result<(), error::Unspecified> {
     if a.len() != b.len() {
         return Err(error::Unspecified);
     }
-    let result = unsafe { CRYPTO_memcmp(a.as_ptr(), b.as_ptr(), a.len()) };
-    match result {
+    let zero_if_equal = a.zip(b).fold(0, |accum, (a, b)| accum | (a ^ b));
+    let zero_if_equal = unsafe { RING_value_barrier_w(Word::from(zero_if_equal)) };
+    match zero_if_equal {
         0 => Ok(()),
         _ => Err(error::Unspecified),
     }
 }
 
+/// The integer type that's the "natural" unsigned machine word size.
+pub(crate) type Word = CryptoWord;
+
+// Keep in sync with `crypto_word_t` in crypto/internal.h.
+#[cfg(target_pointer_width = "32")]
+type CryptoWord = u32;
+#[cfg(target_pointer_width = "64")]
+type CryptoWord = u64;
+
 prefixed_extern! {
-    fn CRYPTO_memcmp(a: *const u8, b: *const u8, len: c::size_t) -> c::int;
+    fn RING_value_barrier_w(a: CryptoWord) -> CryptoWord;
 }
 
 #[cfg(test)]