diff --git a/src/libextra/crypto/cryptoutil.rs b/src/libextra/crypto/cryptoutil.rs
index b89f77ec5c1..9fd02baf541 100644
--- a/src/libextra/crypto/cryptoutil.rs
+++ b/src/libextra/crypto/cryptoutil.rs
@@ -8,7 +8,7 @@
 // option. This file may not be copied, modified, or distributed
 // except according to those terms.
 
-use std::num::One;
+use std::num::{One, Zero, CheckedAdd};
 use std::vec::bytes::{MutableByteVector, copy_memory};
 
 
@@ -97,50 +97,73 @@ pub fn read_u32v_le(dst: &mut[u32], input: &[u8]) {
 }
 
 
-/// Returns true if adding the two parameters will result in integer overflow
-pub fn will_add_overflow<T: Int + Unsigned>(x: T, y: T) -> bool {
-    // This doesn't handle negative values! Don't copy this code elsewhere without considering if
-    // negative values are important to you!
-    let max: T = Bounded::max_value();
-    return x > max - y;
+trait ToBits {
+    /// Convert the value in bytes to the number of bits, a tuple where the 1st item is the
+    /// high-order value and the 2nd item is the low order value.
+    fn to_bits(self) -> (Self, Self);
 }
 
-/// Shifts the second parameter and then adds it to the first. fails!() if there would be unsigned
-/// integer overflow.
-pub fn shift_add_check_overflow<T: Int + Unsigned + Clone>(x: T, mut y: T, shift: T) -> T {
-    if y.leading_zeros() < shift {
-        fail!("Could not add values - integer overflow.");
+impl ToBits for u64 {
+    fn to_bits(self) -> (u64, u64) {
+        return (self >> 61, self << 3);
     }
-    y = y << shift;
-
-    if will_add_overflow(x.clone(), y.clone()) {
-        fail!("Could not add values - integer overflow.");
-    }
-
-    return x + y;
 }
 
-/// Shifts the second parameter and then adds it to the first, which is a tuple where the first
-/// element is the high order value. fails!() if there would be unsigned integer overflow.
-pub fn shift_add_check_overflow_tuple
-        <T: Int + Unsigned + Clone>
-        (x: (T, T), mut y: T, shift: T) -> (T, T) {
-    if y.leading_zeros() < shift {
-        fail!("Could not add values - integer overflow.");
-    }
-    y = y << shift;
+/// Adds the specified number of bytes to the bit count. fail!() if this would cause numeric
+/// overflow.
+pub fn add_bytes_to_bits<T: Int + CheckedAdd + ToBits>(bits: T, bytes: T) -> T {
+    let (new_high_bits, new_low_bits) = bytes.to_bits();
 
-    match x {
-        (hi, low) => {
-            let one: T = One::one();
-            if will_add_overflow(low.clone(), y.clone()) {
-                if will_add_overflow(hi.clone(), one.clone()) {
-                    fail!("Could not add values - integer overflow.");
-                } else {
-                    return (hi + one, low + y);
-                }
+    if new_high_bits > Zero::zero() {
+        fail!("Numeric overflow occured.")
+    }
+
+    match bits.checked_add(&new_low_bits) {
+        Some(x) => return x,
+        None => fail!("Numeric overflow occured.")
+    }
+}
+
+/// Adds the specified number of bytes to the bit count, which is a tuple where the first element is
+/// the high order value. fail!() if this would cause numeric overflow.
+pub fn add_bytes_to_bits_tuple
+        <T: Int + Unsigned + CheckedAdd + ToBits>
+        (bits: (T, T), bytes: T) -> (T, T) {
+    let (new_high_bits, new_low_bits) = bytes.to_bits();
+    let (hi, low) = bits;
+
+    // Add the low order value - if there is no overflow, then add the high order values
+    // If the addition of the low order values causes overflow, add one to the high order values
+    // before adding them.
+    match low.checked_add(&new_low_bits) {
+        Some(x) => {
+            if new_high_bits == Zero::zero() {
+                // This is the fast path - every other alternative will rarely occur in practice
+                // considering how large an input would need to be for those paths to be used.
+                return (hi, x);
             } else {
-                return (hi, low + y);
+                match hi.checked_add(&new_high_bits) {
+                    Some(y) => return (y, x),
+                    None => fail!("Numeric overflow occured.")
+                }
+            }
+        },
+        None => {
+            let one: T = One::one();
+            let z = match new_high_bits.checked_add(&one) {
+                Some(w) => w,
+                None => fail!("Numeric overflow occured.")
+            };
+            match hi.checked_add(&z) {
+                // This re-executes the addition that was already performed earlier when overflow
+                // occured, this time allowing the overflow to happen. Technically, this could be
+                // avoided by using the checked add intrinsic directly, but that involves using
+                // unsafe code and is not really worthwhile considering how infrequently code will
+                // run in practice. This is the reason that this function requires that the type T
+                // be Unsigned - overflow is not defined for Signed types. This function could be
+                // implemented for signed types as well if that were needed.
+                Some(y) => return (y, low + new_low_bits),
+                None => fail!("Numeric overflow occured.")
             }
         }
     }
diff --git a/src/libextra/crypto/sha1.rs b/src/libextra/crypto/sha1.rs
index 8ee9006f613..4d4d47feee8 100644
--- a/src/libextra/crypto/sha1.rs
+++ b/src/libextra/crypto/sha1.rs
@@ -23,7 +23,7 @@
  */
 
 
-use cryptoutil::{write_u32_be, read_u32v_be, shift_add_check_overflow, FixedBuffer, FixedBuffer64,
+use cryptoutil::{write_u32_be, read_u32v_be, add_bytes_to_bits, FixedBuffer, FixedBuffer64,
     StandardPadding};
 use digest::Digest;
 
@@ -52,7 +52,7 @@ pub struct Sha1 {
 fn add_input(st: &mut Sha1, msg: &[u8]) {
     assert!((!st.computed));
     // Assumes that msg.len() can be converted to u64 without overflow
-    st.length_bits = shift_add_check_overflow(st.length_bits, msg.len() as u64, 3);
+    st.length_bits = add_bytes_to_bits(st.length_bits, msg.len() as u64);
     st.buffer.input(msg, |d: &[u8]| { process_msg_block(d, &mut st.h); });
 }
 
diff --git a/src/libextra/crypto/sha2.rs b/src/libextra/crypto/sha2.rs
index 47535d5103a..96f3e13eb22 100644
--- a/src/libextra/crypto/sha2.rs
+++ b/src/libextra/crypto/sha2.rs
@@ -10,8 +10,8 @@
 
 use std::uint;
 
-use cryptoutil::{write_u64_be, write_u32_be, read_u64v_be, read_u32v_be, shift_add_check_overflow,
-    shift_add_check_overflow_tuple, FixedBuffer, FixedBuffer128, FixedBuffer64, StandardPadding};
+use cryptoutil::{write_u64_be, write_u32_be, read_u64v_be, read_u32v_be, add_bytes_to_bits,
+    add_bytes_to_bits_tuple, FixedBuffer, FixedBuffer128, FixedBuffer64, StandardPadding};
 use digest::Digest;
 
 
@@ -210,7 +210,7 @@ impl Engine512 {
     fn input(&mut self, input: &[u8]) {
         assert!(!self.finished)
         // Assumes that input.len() can be converted to u64 without overflow
-        self.length_bits = shift_add_check_overflow_tuple(self.length_bits, input.len() as u64, 3);
+        self.length_bits = add_bytes_to_bits_tuple(self.length_bits, input.len() as u64);
         self.buffer.input(input, |input: &[u8]| { self.state.process_block(input) });
     }
 
@@ -602,7 +602,7 @@ impl Engine256 {
     fn input(&mut self, input: &[u8]) {
         assert!(!self.finished)
         // Assumes that input.len() can be converted to u64 without overflow
-        self.length_bits = shift_add_check_overflow(self.length_bits, input.len() as u64, 3);
+        self.length_bits = add_bytes_to_bits(self.length_bits, input.len() as u64);
         self.buffer.input(input, |input: &[u8]| { self.state.process_block(input) });
     }