diff --git a/CHANGELOG.md b/CHANGELOG.md
index 01e044f4..9d53f78b 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -45,6 +45,8 @@
 
 # 0.49.0 - [unreleased]
 
+- Update to [`libp2p-core` `v0.36.1`](core/CHANGELOG.md#0361).
+
 - Update to [`libp2p-tcp` `v0.37.0`](transports/tcp/CHANGELOG.md#0370).
 - Update individual crates.
     - Update to [`libp2p-ping` `v0.39.1`](protocols/ping/CHANGELOG.md#0391).
diff --git a/Cargo.toml b/Cargo.toml
index 0a4344d1..e3e2283b 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -81,7 +81,7 @@ instant = "0.1.11" # Explicit dependency to be used in `wasm-bindgen` feature
 lazy_static = "1.2"
 
 libp2p-autonat = { version = "0.7.0", path = "protocols/autonat", optional = true }
-libp2p-core = { version = "0.36.0", path = "core",  default-features = false }
+libp2p-core = { version = "0.36.1", path = "core",  default-features = false }
 libp2p-dcutr = { version = "0.6.0", path = "protocols/dcutr",  optional = true }
 libp2p-floodsub = { version = "0.39.1", path = "protocols/floodsub", optional = true }
 libp2p-identify = { version = "0.39.0", path = "protocols/identify", optional = true }
diff --git a/core/CHANGELOG.md b/core/CHANGELOG.md
index 4a5e07f1..deb921e9 100644
--- a/core/CHANGELOG.md
+++ b/core/CHANGELOG.md
@@ -1,3 +1,9 @@
+# 0.36.1 - [unreleased]
+
+- Implement `Hash` and `Ord` for `PublicKey`. See [PR 2915].
+
+[PR 2915]: https://github.com/libp2p/rust-libp2p/pull/2915
+
 # 0.36.0
 
 - Make RSA keypair support optional. To enable RSA support, `rsa` feature should be enabled.
diff --git a/core/Cargo.toml b/core/Cargo.toml
index 8390c758..201f5220 100644
--- a/core/Cargo.toml
+++ b/core/Cargo.toml
@@ -3,7 +3,7 @@ name = "libp2p-core"
 edition = "2021"
 rust-version = "1.56.1"
 description = "Core traits and structs of libp2p"
-version = "0.36.0"
+version = "0.36.1"
 authors = ["Parity Technologies <admin@parity.io>"]
 license = "MIT"
 repository = "https://github.com/libp2p/rust-libp2p"
diff --git a/core/src/identity.rs b/core/src/identity.rs
index 73be1c78..af5dceb6 100644
--- a/core/src/identity.rs
+++ b/core/src/identity.rs
@@ -214,7 +214,7 @@ impl zeroize::Zeroize for keys_proto::PrivateKey {
 }
 
 /// The public key of a node's identity keypair.
-#[derive(Clone, Debug, PartialEq, Eq)]
+#[derive(Clone, Debug, PartialEq, Eq, Hash, PartialOrd, Ord)]
 pub enum PublicKey {
     /// A public Ed25519 key.
     Ed25519(ed25519::PublicKey),
@@ -379,4 +379,22 @@ mod tests {
 
         assert_eq!(expected_peer_id, peer_id);
     }
+
+    #[test]
+    fn public_key_implements_hash() {
+        use std::hash::Hash;
+
+        fn assert_implements_hash<T: Hash>() {}
+
+        assert_implements_hash::<PublicKey>();
+    }
+
+    #[test]
+    fn public_key_implements_ord() {
+        use std::cmp::Ord;
+
+        fn assert_implements_ord<T: Ord>() {}
+
+        assert_implements_ord::<PublicKey>();
+    }
 }
diff --git a/core/src/identity/ecdsa.rs b/core/src/identity/ecdsa.rs
index 81dfec4b..88411b23 100644
--- a/core/src/identity/ecdsa.rs
+++ b/core/src/identity/ecdsa.rs
@@ -21,7 +21,9 @@
 //! ECDSA keys with secp256r1 curve support.
 
 use super::error::DecodingError;
+use core::cmp;
 use core::fmt;
+use core::hash;
 use p256::{
     ecdsa::{
         signature::{Signer, Verifier},
@@ -117,7 +119,7 @@ impl fmt::Debug for SecretKey {
 }
 
 /// An ECDSA public key.
-#[derive(Clone, PartialEq, Eq)]
+#[derive(Clone, Eq, PartialOrd, Ord)]
 pub struct PublicKey(VerifyingKey);
 
 impl PublicKey {
@@ -222,6 +224,18 @@ impl fmt::Debug for PublicKey {
     }
 }
 
+impl cmp::PartialEq for PublicKey {
+    fn eq(&self, other: &Self) -> bool {
+        self.to_bytes().eq(&other.to_bytes())
+    }
+}
+
+impl hash::Hash for PublicKey {
+    fn hash<H: hash::Hasher>(&self, state: &mut H) {
+        self.to_bytes().hash(state);
+    }
+}
+
 #[cfg(test)]
 mod tests {
     use super::*;
diff --git a/core/src/identity/ed25519.rs b/core/src/identity/ed25519.rs
index 5782ac78..eef934d4 100644
--- a/core/src/identity/ed25519.rs
+++ b/core/src/identity/ed25519.rs
@@ -21,7 +21,9 @@
 //! Ed25519 keys.
 
 use super::error::DecodingError;
+use core::cmp;
 use core::fmt;
+use core::hash;
 use ed25519_dalek::{self as ed25519, Signer as _, Verifier as _};
 use rand::RngCore;
 use std::convert::TryFrom;
@@ -113,7 +115,7 @@ impl From<SecretKey> for Keypair {
 }
 
 /// An Ed25519 public key.
-#[derive(PartialEq, Eq, Clone)]
+#[derive(Eq, Clone)]
 pub struct PublicKey(ed25519::PublicKey);
 
 impl fmt::Debug for PublicKey {
@@ -126,6 +128,30 @@ impl fmt::Debug for PublicKey {
     }
 }
 
+impl cmp::PartialEq for PublicKey {
+    fn eq(&self, other: &Self) -> bool {
+        self.0.as_bytes().eq(other.0.as_bytes())
+    }
+}
+
+impl hash::Hash for PublicKey {
+    fn hash<H: hash::Hasher>(&self, state: &mut H) {
+        self.0.as_bytes().hash(state);
+    }
+}
+
+impl cmp::PartialOrd for PublicKey {
+    fn partial_cmp(&self, other: &Self) -> Option<cmp::Ordering> {
+        self.0.as_bytes().partial_cmp(other.0.as_bytes())
+    }
+}
+
+impl cmp::Ord for PublicKey {
+    fn cmp(&self, other: &Self) -> cmp::Ordering {
+        self.0.as_bytes().cmp(other.0.as_bytes())
+    }
+}
+
 impl PublicKey {
     /// Verify the Ed25519 signature on a message using the public key.
     pub fn verify(&self, msg: &[u8], sig: &[u8]) -> bool {
diff --git a/core/src/identity/rsa.rs b/core/src/identity/rsa.rs
index 1d20f00a..497dca40 100644
--- a/core/src/identity/rsa.rs
+++ b/core/src/identity/rsa.rs
@@ -70,7 +70,7 @@ impl Keypair {
 }
 
 /// An RSA public key.
-#[derive(Clone, PartialEq, Eq)]
+#[derive(Clone, PartialEq, Eq, Hash, PartialOrd, Ord)]
 pub struct PublicKey(Vec<u8>);
 
 impl PublicKey {
@@ -306,21 +306,14 @@ impl DerDecodable<'_> for Asn1SubjectPublicKeyInfo {
 mod tests {
     use super::*;
     use quickcheck::*;
-    use std::fmt;
 
     const KEY1: &'static [u8] = include_bytes!("test/rsa-2048.pk8");
     const KEY2: &'static [u8] = include_bytes!("test/rsa-3072.pk8");
     const KEY3: &'static [u8] = include_bytes!("test/rsa-4096.pk8");
 
-    #[derive(Clone)]
+    #[derive(Clone, Debug)]
     struct SomeKeypair(Keypair);
 
-    impl fmt::Debug for SomeKeypair {
-        fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
-            write!(f, "SomeKeypair")
-        }
-    }
-
     impl Arbitrary for SomeKeypair {
         fn arbitrary(g: &mut Gen) -> SomeKeypair {
             let mut key = g.choose(&[KEY1, KEY2, KEY3]).unwrap().to_vec();
diff --git a/core/src/identity/secp256k1.rs b/core/src/identity/secp256k1.rs
index 2c3aaf89..bfecc33e 100644
--- a/core/src/identity/secp256k1.rs
+++ b/core/src/identity/secp256k1.rs
@@ -22,7 +22,9 @@
 
 use super::error::{DecodingError, SigningError};
 use asn1_der::typed::{DerDecodable, Sequence};
+use core::cmp;
 use core::fmt;
+use core::hash;
 use libsecp256k1::{Message, Signature};
 use sha2::{Digest as ShaDigestTrait, Sha256};
 use zeroize::Zeroize;
@@ -150,7 +152,7 @@ impl SecretKey {
 }
 
 /// A Secp256k1 public key.
-#[derive(PartialEq, Eq, Clone)]
+#[derive(Eq, Clone)]
 pub struct PublicKey(libsecp256k1::PublicKey);
 
 impl fmt::Debug for PublicKey {
@@ -163,6 +165,30 @@ impl fmt::Debug for PublicKey {
     }
 }
 
+impl cmp::PartialEq for PublicKey {
+    fn eq(&self, other: &Self) -> bool {
+        self.encode().eq(&other.encode())
+    }
+}
+
+impl hash::Hash for PublicKey {
+    fn hash<H: hash::Hasher>(&self, state: &mut H) {
+        self.encode().hash(state);
+    }
+}
+
+impl cmp::PartialOrd for PublicKey {
+    fn partial_cmp(&self, other: &Self) -> Option<cmp::Ordering> {
+        self.encode().partial_cmp(&other.encode())
+    }
+}
+
+impl cmp::Ord for PublicKey {
+    fn cmp(&self, other: &Self) -> cmp::Ordering {
+        self.encode().cmp(&other.encode())
+    }
+}
+
 impl PublicKey {
     /// Verify the Secp256k1 signature on a message using the public key.
     pub fn verify(&self, msg: &[u8], sig: &[u8]) -> bool {