diff --git a/README.md b/README.md
index 71df845a6..20852e034 100644
--- a/README.md
+++ b/README.md
@@ -27,7 +27,7 @@ In addition, the [`curves`](https://github.com/arkworks-rs/curves) repository co
 
 ## Build guide
 
-The library compiles on the `stable` toolchain of the Rust compiler. To install the latest version of Rust, first install `rustup` by following the instructions [here](https://rustup.rs/), or via your platform's package manager. Once `rustup` is installed, install the Rust toolchain by invoking:
+The library compiles on the `stable (1.46+)` toolchain of the Rust compiler. To install the latest version of Rust, first install `rustup` by following the instructions [here](https://rustup.rs/), or via your platform's package manager. Once `rustup` is installed, install the Rust toolchain by invoking:
 ```bash
 rustup install stable
 ```
diff --git a/ec/src/lib.rs b/ec/src/lib.rs
index 64dff019c..18127521d 100644
--- a/ec/src/lib.rs
+++ b/ec/src/lib.rs
@@ -330,6 +330,8 @@ where
 
 pub trait CurveCycle
 where
+    <Self::E1 as AffineCurve>::BaseField: PrimeField + SquareRootField,
+    <Self::E2 as AffineCurve>::BaseField: PrimeField + SquareRootField,
     <Self::E1 as AffineCurve>::Projective: MulAssign<<Self::E2 as AffineCurve>::BaseField>,
     <Self::E2 as AffineCurve>::Projective: MulAssign<<Self::E1 as AffineCurve>::BaseField>,
 {
@@ -340,7 +342,19 @@ where
     type E2: AffineCurve;
 }
 
-pub trait PairingFriendlyCycle: CurveCycle {
+pub trait PairingFriendlyCycle: CurveCycle
+where
+    <Self::E1 as AffineCurve>::BaseField: PrimeField + SquareRootField,
+    <Self::E2 as AffineCurve>::BaseField: PrimeField + SquareRootField,
+    <Self::E1 as AffineCurve>::Projective: MulAssign<<Self::E2 as AffineCurve>::BaseField>,
+    <Self::E2 as AffineCurve>::Projective: MulAssign<<Self::E1 as AffineCurve>::BaseField>,
+    <Self::Engine1 as PairingEngine>::G1Prepared: From<Self::E1>,
+    <Self::Engine2 as PairingEngine>::G1Prepared: From<Self::E2>,
+    <Self::Engine1 as PairingEngine>::G2Projective:
+        MulAssign<<Self::E1 as AffineCurve>::ScalarField>,
+    <Self::Engine2 as PairingEngine>::G2Projective:
+        MulAssign<<Self::E2 as AffineCurve>::ScalarField>,
+{
     type Engine1: PairingEngine<
         G1Affine = Self::E1,
         G1Projective = <Self::E1 as AffineCurve>::Projective,