diff --git a/Cargo.toml b/Cargo.toml
index 7f2138e..a9fc68b 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -11,7 +11,8 @@ blake2b_simd = "0.5"
 jubjub = "0.3"
 
 [dev-dependencies]
-rand = "0.7"
+rand_chacha = "0.2"
+proptest = "0.9"
 
 [features]
 nightly = []
diff --git a/src/lib.rs b/src/lib.rs
index ca9fabd..ca02315 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -68,18 +68,3 @@ pub(crate) mod private {
         }
     }
 }
-
-#[cfg(test)]
-mod tests {
-    use super::*;
-
-    #[test]
-    fn sign_and_verify() {
-        let sk = SecretKey::<Binding>::new(rand::thread_rng());
-        let msg = b"test";
-        let sig = sk.sign(rand::thread_rng(), msg);
-        let pk = PublicKey::from(&sk);
-
-        assert_eq!(pk.verify(msg, &sig), Ok(()));
-    }
-}
diff --git a/tests/proptests.rs b/tests/proptests.rs
new file mode 100644
index 0000000..36692f5
--- /dev/null
+++ b/tests/proptests.rs
@@ -0,0 +1,127 @@
+use std::convert::TryFrom;
+
+use proptest::prelude::*;
+use rand_core::{CryptoRng, RngCore};
+
+use redjubjub_zebra as rjj;
+
+use rjj::{PublicKey, PublicKeyBytes, SecretKey, SigType, Signature};
+
+/// A signature test-case, containing signature data and expected validity.
+#[derive(Clone, Debug)]
+struct SignatureCase<T: SigType> {
+    msg: Vec<u8>,
+    sig: Signature<T>,
+    pk_bytes: PublicKeyBytes<T>,
+    is_valid: bool,
+}
+
+impl<T: SigType> SignatureCase<T> {
+    fn new<R: RngCore + CryptoRng>(mut rng: R, msg: Vec<u8>) -> Self {
+        let sk = SecretKey::new(&mut rng);
+        let sig = sk.sign(&mut rng, &msg);
+        let pk_bytes = PublicKey::from(&sk).into();
+        Self {
+            msg,
+            sig,
+            pk_bytes,
+            is_valid: true,
+        }
+    }
+
+    // Check that signature verification succeeds or fails, as expected.
+    fn check(&self) -> bool {
+        // The signature data is stored in (refined) byte types, but do a round trip
+        // conversion to raw bytes to exercise those code paths.
+        let sig = {
+            let bytes: [u8; 64] = self.sig.into();
+            Signature::<T>::from(bytes)
+        };
+        let pk_bytes = {
+            let bytes: [u8; 32] = self.pk_bytes.into();
+            PublicKeyBytes::<T>::from(bytes)
+        };
+
+        // Check that signature validation has the expected result.
+        self.is_valid
+            == PublicKey::try_from(pk_bytes)
+                .and_then(|pk| pk.verify(&self.msg, &sig))
+                .is_ok()
+    }
+}
+
+#[derive(Copy, Clone, Debug)]
+enum Tweak {
+    None,
+    ChangeMessage,
+}
+
+impl Tweak {
+    fn apply<T: SigType>(&self, case: SignatureCase<T>) -> SignatureCase<T> {
+        use Tweak::*;
+        let SignatureCase {
+            mut msg,
+            sig,
+            pk_bytes,
+            is_valid,
+        } = case;
+        match (self, is_valid) {
+            (None, is_valid) => {
+                // This is a no-op, so return the original case.
+                SignatureCase {
+                    msg,
+                    sig,
+                    pk_bytes,
+                    is_valid,
+                }
+            }
+            (ChangeMessage, _) => {
+                // Changing the message makes the signature invalid.
+                msg.push(90);
+                SignatureCase {
+                    msg,
+                    sig,
+                    pk_bytes,
+                    is_valid: false,
+                }
+            }
+        }
+    }
+}
+
+fn tweak_strategy() -> impl Strategy<Value = Tweak> {
+    prop_oneof![
+        10 => Just(Tweak::None),
+        1 => Just(Tweak::ChangeMessage),
+    ]
+}
+
+proptest! {
+    #[test]
+    fn tweak_signature(
+        tweaks in prop::collection::vec(tweak_strategy(), (0,5)),
+        rng_seed in any::<u64>(),
+    ) {
+        use rjj::{Binding, SpendAuth, };
+        use rand_core::SeedableRng;
+
+        // Use a deterministic RNG so that test failures can be reproduced.
+        // Seeding with 64 bits of entropy is INSECURE and this code should
+        // not be copied outside of this test!
+        let mut rng = rand_chacha::ChaChaRng::seed_from_u64(rng_seed);
+
+        // Create a test case for each signature type.
+        let msg = b"test message for proptests";
+        let mut binding = SignatureCase::<Binding>::new(&mut rng, msg.to_vec());
+        let mut spendauth = SignatureCase::<SpendAuth>::new(&mut rng, msg.to_vec());
+
+        // Apply tweaks to each case.
+        for tweak in &tweaks {
+            binding = tweak.apply(binding);
+            spendauth = tweak.apply(spendauth);
+        }
+
+        assert!(binding.check());
+        assert!(spendauth.check());
+    }
+}