diff --git a/Cargo.lock b/Cargo.lock
index f1320d9a..2fc5f8ec 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -1488,6 +1488,17 @@ dependencies = [
  "zeroize",
 ]
 
+[[package]]
+name = "crypto-bigint"
+version = "0.5.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "7c2538c4e68e52548bacb3e83ac549f903d44f011ac9d5abb5e132e67d0808f7"
+dependencies = [
+ "rand_core 0.6.4",
+ "subtle",
+ "zeroize",
+]
+
 [[package]]
 name = "crypto-common"
 version = "0.1.6"
@@ -1626,7 +1637,7 @@ dependencies = [
 name = "dalek-ff-group"
 version = "0.2.0"
 dependencies = [
- "crypto-bigint",
+ "crypto-bigint 0.5.1",
  "curve25519-dalek 3.2.0",
  "digest 0.10.6",
  "ff",
@@ -2089,7 +2100,7 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "e7bb888ab5300a19b8e5bceef25ac745ad065f3c9f7efc6de1b91958110891d3"
 dependencies = [
  "base16ct",
- "crypto-bigint",
+ "crypto-bigint 0.4.9",
  "der",
  "digest 0.10.6",
  "ff",
@@ -4925,7 +4936,7 @@ checksum = "2a60c7ce501c71e03a9c9c0d35b861413ae925bd979cc7a4e30d060069aaac8d"
 name = "minimal-ed448"
 version = "0.2.0"
 dependencies = [
- "crypto-bigint",
+ "crypto-bigint 0.5.1",
  "dalek-ff-group",
  "ff",
  "ff-group-tests",
@@ -6869,7 +6880,7 @@ version = "0.3.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "7743f17af12fa0b03b803ba12cd6a8d9483a587e89c69445e3909655c0b9fabb"
 dependencies = [
- "crypto-bigint",
+ "crypto-bigint 0.4.9",
  "hmac 0.12.1",
  "zeroize",
 ]
diff --git a/crypto/dalek-ff-group/Cargo.toml b/crypto/dalek-ff-group/Cargo.toml
index f500df34..93e798b7 100644
--- a/crypto/dalek-ff-group/Cargo.toml
+++ b/crypto/dalek-ff-group/Cargo.toml
@@ -22,7 +22,7 @@ subtle = "^2.4"
 ff = { version = "0.12", features = ["bits"] }
 group = "0.12"
 
-crypto-bigint = "0.4"
+crypto-bigint = "0.5"
 
 sha2 = "0.9"
 curve25519-dalek = "^3.2"
diff --git a/crypto/dalek-ff-group/src/field.rs b/crypto/dalek-ff-group/src/field.rs
index 2afe6396..f70fa40e 100644
--- a/crypto/dalek-ff-group/src/field.rs
+++ b/crypto/dalek-ff-group/src/field.rs
@@ -8,7 +8,7 @@ use subtle::{
   ConditionallySelectable,
 };
 
-use crypto_bigint::{Integer, Encoding, U256, U512};
+use crypto_bigint::{Integer, NonZero, Encoding, U256, U512};
 
 use group::ff::{Field, PrimeField, FieldBits, PrimeFieldBits};
 
@@ -78,7 +78,7 @@ const MOD_3_8: FieldElement =
 const MOD_5_8: FieldElement = FieldElement(MOD_3_8.0.saturating_sub(&U256::ONE));
 
 fn reduce(x: U512) -> U256 {
-  U256::from_le_slice(&x.reduce(&WIDE_MODULUS).unwrap().to_le_bytes()[.. 32])
+  U256::from_le_slice(&x.rem(&NonZero::new(WIDE_MODULUS).unwrap()).to_le_bytes()[.. 32])
 }
 
 constant_time!(FieldElement, U256);
@@ -87,10 +87,7 @@ math!(
   FieldElement,
   |x, y| U256::add_mod(&x, &y, &MODULUS),
   |x, y| U256::sub_mod(&x, &y, &MODULUS),
-  |x, y| {
-    let wide = U256::mul_wide(&x, &y);
-    reduce(U512::from((wide.1, wide.0)))
-  }
+  |x, y| reduce(U512::from(U256::mul_wide(&x, &y)))
 );
 from_uint!(FieldElement, U256);
 
@@ -125,7 +122,7 @@ impl Field for FieldElement {
     FieldElement(reduce(self.0.square()))
   }
   fn double(&self) -> Self {
-    FieldElement((self.0 << 1).reduce(&MODULUS).unwrap())
+    FieldElement((self.0 << 1).rem(&NonZero::new(MODULUS).unwrap()))
   }
 
   fn invert(&self) -> CtOption<Self> {
diff --git a/crypto/ed448/Cargo.toml b/crypto/ed448/Cargo.toml
index addc783c..807c125b 100644
--- a/crypto/ed448/Cargo.toml
+++ b/crypto/ed448/Cargo.toml
@@ -24,7 +24,7 @@ ff = { version = "0.12", features = ["bits"] }
 group = "0.12"
 
 generic-array = "0.14"
-crypto-bigint = { version = "0.4", features = ["zeroize"] }
+crypto-bigint = { version = "0.5", features = ["zeroize"] }
 
 dalek-ff-group = { path = "../dalek-ff-group", version = "0.2" }
 
diff --git a/crypto/ed448/src/backend.rs b/crypto/ed448/src/backend.rs
index 7daae853..5148cebf 100644
--- a/crypto/ed448/src/backend.rs
+++ b/crypto/ed448/src/backend.rs
@@ -33,7 +33,7 @@ macro_rules! field {
     use rand_core::RngCore;
 
     use generic_array::{typenum::U57, GenericArray};
-    use crypto_bigint::{Integer, Encoding};
+    use crypto_bigint::{Integer, NonZero, Encoding};
 
     use group::ff::{Field, PrimeField, FieldBits, PrimeFieldBits};
 
@@ -45,7 +45,7 @@ macro_rules! field {
     use $crate::backend::u8_from_bool;
 
     fn reduce(x: U1024) -> U512 {
-      U512::from_le_slice(&x.reduce(&$WIDE_MODULUS).unwrap().to_le_bytes()[.. 64])
+      U512::from_le_slice(&x.rem(&NonZero::new($WIDE_MODULUS).unwrap()).to_le_bytes()[.. 64])
     }
 
     constant_time!($FieldName, U512);
@@ -54,10 +54,7 @@ macro_rules! field {
       $FieldName,
       |x, y| U512::add_mod(&x, &y, &$MODULUS.0),
       |x, y| U512::sub_mod(&x, &y, &$MODULUS.0),
-      |x, y| {
-        let wide = U512::mul_wide(&x, &y);
-        reduce(U1024::from((wide.1, wide.0)))
-      }
+      |x, y| reduce(U1024::from(U512::mul_wide(&x, &y)))
     );
     from_uint!($FieldName, U512);
 
@@ -122,7 +119,7 @@ macro_rules! field {
         *self * self
       }
       fn double(&self) -> Self {
-        $FieldName((self.0 << 1).reduce(&$MODULUS.0).unwrap())
+        $FieldName((self.0 << 1).rem(&NonZero::new($MODULUS.0).unwrap()))
       }
 
       fn invert(&self) -> CtOption<Self> {