diff --git a/polyfuzzy/src/fmd2.rs b/polyfuzzy/src/fmd2.rs
index 9cd0acc..4e4f766 100644
--- a/polyfuzzy/src/fmd2.rs
+++ b/polyfuzzy/src/fmd2.rs
@@ -16,7 +16,7 @@ use crate::{
     DetectionKey, FmdKeyGen, FmdSecretKey, MultiFmdScheme,
 };
 
-#[derive(Debug, Clone)]
+#[derive(Debug, Clone, PartialEq, Eq)]
 #[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
 /// γ public subkeys (points). The basepoint is hardcoded to the Ristretto basepoint.
 pub struct FmdPublicKey {
@@ -31,7 +31,7 @@ impl From<GenericFmdPublicKey> for FmdPublicKey {
     }
 }
 
-#[derive(Debug, Clone)]
+#[derive(Debug, Clone, PartialEq, Eq)]
 #[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
 /// A point `u`, a scalar `y`, and γ ciphertext bits `c`.
 pub struct FlagCiphertexts {
@@ -59,7 +59,7 @@ impl From<GenericFlagCiphertexts> for FlagCiphertexts {
 }
 
 /// The multi-key scheme.
-#[derive(Debug, Clone)]
+#[derive(Debug, Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Hash)]
 pub struct Fmd2MultikeyScheme {
     gamma: usize,
 }
diff --git a/polyfuzzy/src/fmd2_compact/mod.rs b/polyfuzzy/src/fmd2_compact/mod.rs
index 9338a71..111be85 100644
--- a/polyfuzzy/src/fmd2_compact/mod.rs
+++ b/polyfuzzy/src/fmd2_compact/mod.rs
@@ -19,6 +19,7 @@ use crate::{
 };
 
 /// A polynomial over the scalar field of Ristretto of degree = `t` (the threshold parameter).
+#[derive(Debug, Clone, PartialEq, Eq, Hash)]
 #[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
 pub struct CompactSecretKey(Polynomial);
 
@@ -33,7 +34,7 @@ impl CompactSecretKey {
 /// An encoded polynomial over Ristretto. t+2 points.
 /// The first point is the basepoint, the remaining
 /// t+1 points the encoded coefficients.
-#[derive(Debug, Clone)]
+#[derive(Debug, Clone, PartialEq, Eq)]
 pub struct CompactPublicKey {
     fingerprint: [u8; 20],
     polynomial: EncodedPolynomial,
@@ -73,7 +74,7 @@ impl CompactPublicKey {
 
 /// A compressed representation that drops the basepoint.
 #[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
-#[derive(Debug, Clone)]
+#[derive(Debug, Clone, PartialEq, Eq)]
 pub struct CompressedCompactPublicKey {
     coeffs: Vec<RistrettoPoint>,
 }
@@ -90,13 +91,13 @@ impl CompressedCompactPublicKey {
 
 /// The evaluations of the secret polynomial
 /// encoded using an arbitrary basepoint.
-#[derive(PartialEq, Debug, Clone)]
+#[derive(Debug, Clone, PartialEq, Eq)]
 pub struct FmdPublicKey(PointEvaluations);
 
 /// The basepoint for the chamaleon hash,
 /// and `u`, `y`, `c`.
 #[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
-#[derive(Debug, Clone)]
+#[derive(Debug, Clone, PartialEq, Eq)]
 pub struct FlagCiphertexts(GenericFlagCiphertexts);
 
 impl FlagCiphertexts {
@@ -108,7 +109,7 @@ impl FlagCiphertexts {
 }
 
 /// Cache of expanded FMD public keys.
-#[derive(Debug, Clone)]
+#[derive(Debug, Clone, PartialEq, Eq)]
 struct ExpandedKeyCache {
     /// Fingerprint of the [`CompactPublicKey`].
     fingerprint: [u8; 20],
@@ -134,7 +135,7 @@ impl ExpandedKeyCache {
 }
 
 /// The multi-key FMD scheme supporting key expansion and key randomization.
-#[derive(Debug, Clone)]
+#[derive(Debug, Clone, PartialEq, Eq)]
 pub struct MultiFmd2CompactScheme {
     /// The threshold parameter
     threshold: usize,
diff --git a/polyfuzzy/src/fmd2_compact/polynomial.rs b/polyfuzzy/src/fmd2_compact/polynomial.rs
index 4887fa3..aacafca 100644
--- a/polyfuzzy/src/fmd2_compact/polynomial.rs
+++ b/polyfuzzy/src/fmd2_compact/polynomial.rs
@@ -5,6 +5,7 @@ use curve25519_dalek::{RistrettoPoint, Scalar};
 use serde::{Deserialize, Serialize};
 
 /// A degree `t` polynomial p(X) in Z_q[X] given by its t+1 coefficients.
+#[derive(Debug, Clone, PartialEq, Eq, Hash)]
 #[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
 pub(crate) struct Polynomial {
     coeffs: Vec<Scalar>,
@@ -12,7 +13,7 @@ pub(crate) struct Polynomial {
 
 /// A degree t polynomial encoded in the exponent of a Ristretto point
 /// given by its t+1 points.
-#[derive(Debug, Clone)]
+#[derive(Debug, Clone, PartialEq, Eq)]
 pub(crate) struct EncodedPolynomial {
     pub(crate) basepoint: RistrettoPoint,
     pub(crate) coeffs: Vec<RistrettoPoint>,
@@ -20,13 +21,14 @@ pub(crate) struct EncodedPolynomial {
 
 /// γ scalar evaluations of the polynomial p(X) at public scalars.
 /// result[i] = p(public_scalar[i])
+#[derive(Debug, Clone, PartialEq, Eq, Hash)]
 pub(crate) struct ScalarEvaluations {
     pub(crate) results: Vec<Scalar>,
 }
 
 /// γ point evaluations of the polynomial p(X) at public scalars.
 /// result[i] = p(public_scalar[i]) * basepoint
-#[derive(PartialEq, Debug, Clone)]
+#[derive(Debug, Clone, PartialEq, Eq)]
 pub(crate) struct PointEvaluations {
     pub(crate) basepoint: RistrettoPoint,
     pub(crate) results: Vec<RistrettoPoint>,
diff --git a/polyfuzzy/src/fmd2_generic.rs b/polyfuzzy/src/fmd2_generic.rs
index f71b90a..f0ffa38 100644
--- a/polyfuzzy/src/fmd2_generic.rs
+++ b/polyfuzzy/src/fmd2_generic.rs
@@ -14,7 +14,7 @@ use serde::{Deserialize, Serialize};
 use sha2::{Digest, Sha256, Sha512};
 
 /// Compressed representation of the γ bit-ciphertexts of a [`GenericFlagCiphertexts`].
-#[derive(Debug, Clone, PartialEq, Eq)]
+#[derive(Debug, Clone, PartialEq, Eq, PartialOrd, Ord, Hash)]
 #[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
 pub(crate) struct CompressedCiphertextBits(pub(crate) Vec<u8>);
 
@@ -31,7 +31,7 @@ impl CompressedCiphertextBits {
 }
 
 /// Decompressed inner bit-ciphertexts of a [`GenericFlagCiphertexts`].
-#[derive(Debug, Clone)]
+#[derive(Debug, Clone, PartialEq, Eq, PartialOrd, Ord, Hash)]
 #[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
 pub(crate) struct CiphertextBits(pub(crate) Vec<bool>);
 
@@ -55,7 +55,7 @@ impl CiphertextBits {
     }
 }
 
-#[derive(Debug, Clone)]
+#[derive(Debug, Clone, PartialEq, Eq, Hash)]
 #[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
 /// γ secret subkeys (scalars). For minimum false-positive rate p:=2^{-γ}.
 pub struct FmdSecretKey(pub(crate) Vec<Scalar>);
@@ -135,7 +135,7 @@ impl FmdSecretKey {
     }
 }
 
-#[derive(Debug, Clone)]
+#[derive(Debug, Clone, PartialEq, Eq, Hash)]
 #[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
 /// A subset of n-out-γ secret subkeys, and the positions
 /// they occupy in [FmdSecretKey].
@@ -193,12 +193,13 @@ impl DetectionKey {
     }
 }
 
-#[derive(Debug, Clone)]
+#[derive(Debug, Clone, PartialEq, Eq)]
 pub(crate) struct GenericFmdPublicKey {
     pub(crate) basepoint_eg: RistrettoPoint, // Basepoint to generate the DDH mask (for ElGamal).
     pub(crate) keys: Vec<RistrettoPoint>,
 }
 
+#[derive(Debug, Clone, PartialEq, Eq)]
 pub(crate) struct ChamaleonHashBasepoint {
     base: RistrettoPoint, // Basepoint for the Chamaleon Hash.
     dlog: Scalar,         // Discrete log of `basepoint_ch` in base `GenericPublicKey.basepoint_eg`.
@@ -222,7 +223,7 @@ impl Default for ChamaleonHashBasepoint {
     }
 }
 
-#[derive(Debug, Clone)]
+#[derive(Debug, Clone, PartialEq, Eq)]
 #[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
 pub(crate) struct GenericFlagCiphertexts {
     pub(crate) basepoint_ch: RistrettoPoint, // Basepoint for the Chamaleon Hash.