diff --git a/src/bls12_381/fq.rs b/src/bls12_381/fq.rs
index e7be0ec59..a59d06851 100644
--- a/src/bls12_381/fq.rs
+++ b/src/bls12_381/fq.rs
@@ -25,7 +25,7 @@ const INV: u64 = 0x89f3fffcfffcfffd;
 const GENERATOR: FqRepr = FqRepr([0x321300000006554f, 0xb93c0018d6c40005, 0x57605e0db0ddbb51, 0x8b256521ed1f9bcb, 0x6cf28d7901622c03, 0x11ebab9dbb81e28c]);
 
 // 2^s * t = MODULUS - 1 with t odd
-const S: usize = 1;
+const S: u32 = 1;
 
 // 2^s root of unity computed by GENERATOR^t
 const ROOT_OF_UNITY: FqRepr = FqRepr([0x43f5fffffffcaaae, 0x32b7fff2ed47fffd, 0x7e83a49a2e99d69, 0xeca8f3318332bb7a, 0xef148d1ea0f4c069, 0x40ab3263eff0206]);
@@ -444,7 +444,7 @@ impl PrimeField for Fq {
         Fq(GENERATOR)
     }
 
-    fn s() -> usize {
+    fn s() -> u32 {
         S
     }
 
diff --git a/src/bls12_381/fr.rs b/src/bls12_381/fr.rs
index 63cc26476..d62f2659b 100644
--- a/src/bls12_381/fr.rs
+++ b/src/bls12_381/fr.rs
@@ -23,7 +23,7 @@ const INV: u64 = 0xfffffffeffffffff;
 const GENERATOR: FrRepr = FrRepr([0xefffffff1, 0x17e363d300189c0f, 0xff9c57876f8457b0, 0x351332208fc5a8c4]);
 
 // 2^s * t = MODULUS - 1 with t odd
-const S: usize = 32;
+const S: u32 = 32;
 
 // 2^s root of unity computed by GENERATOR^t
 const ROOT_OF_UNITY: FrRepr = FrRepr([0xb9b58d8c5f0e466a, 0x5b1b4c801819d7ec, 0xaf53ae352a31e64, 0x5bf3adda19e9b27b]);
@@ -264,7 +264,7 @@ impl PrimeField for Fr {
         Fr(GENERATOR)
     }
 
-    fn s() -> usize {
+    fn s() -> u32 {
         S
     }
 
diff --git a/src/lib.rs b/src/lib.rs
index 6e98aa6ec..12b4af6d0 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -496,7 +496,7 @@ pub trait PrimeField: Field
     fn multiplicative_generator() -> Self;
 
     /// Returns s such that 2^s * t = `char()` - 1 with t odd.
-    fn s() -> usize;
+    fn s() -> u32;
 
     /// Returns the 2^s root of unity computed by exponentiating the `multiplicative_generator()`
     /// by t.