diff --git a/umbral-pre-python/Cargo.toml b/umbral-pre-python/Cargo.toml
index 8b9f21ff..3b330329 100644
--- a/umbral-pre-python/Cargo.toml
+++ b/umbral-pre-python/Cargo.toml
@@ -11,3 +11,4 @@ crate-type = ["cdylib"]
 pyo3 = { version = "0.13", features = ["extension-module"] }
 umbral-pre = { path = "../umbral-pre" }
 generic-array = "0.14"
+hex = "0.4"
diff --git a/umbral-pre-python/src/lib.rs b/umbral-pre-python/src/lib.rs
index 990cdfef..2c463371 100644
--- a/umbral-pre-python/src/lib.rs
+++ b/umbral-pre-python/src/lib.rs
@@ -3,7 +3,7 @@ use pyo3::create_exception;
 use pyo3::exceptions::{PyException, PyTypeError, PyValueError};
 use pyo3::prelude::*;
 use pyo3::pyclass::PyClass;
-use pyo3::types::PyBytes;
+use pyo3::types::{PyBytes, PyUnicode};
 use pyo3::wrap_pyfunction;
 use pyo3::PyObjectProtocol;
 
@@ -42,6 +42,27 @@ fn from_bytes<T: HasSerializableBackend<U>, U: SerializableToArray>(bytes: &[u8]
         })
 }
 
+fn hash<T: HasSerializableBackend<U>, U: SerializableToArray>(obj: &T) -> PyResult<isize> {
+    let serialized = obj.as_backend().to_array();
+
+    // call `hash((class_name, bytes(obj)))`
+    Python::with_gil(|py| {
+        let builtins = PyModule::import(py, "builtins")?;
+        let arg1 = PyUnicode::new(py, T::name());
+        let arg2: PyObject = PyBytes::new(py, serialized.as_slice()).into();
+        builtins.getattr("hash")?.call1(((arg1, arg2),))?.extract()
+    })
+}
+
+// For some reason this lint is not recognized in Rust 1.46 (the one in CI)
+// remove when CI is updated to a newer Rust version.
+#[allow(clippy::unknown_clippy_lints)]
+#[allow(clippy::unnecessary_wraps)] // Don't want to wrap it in Ok() on every call
+fn hexstr<T: HasSerializableBackend<U>, U: SerializableToArray>(obj: &T) -> PyResult<String> {
+    let hex_str = hex::encode(obj.as_backend().to_array().as_slice());
+    Ok(format!("{}:{}", T::name(), &hex_str[0..16]))
+}
+
 fn richcmp<T: HasSerializableBackend<U> + PyClass + PartialEq, U>(
     obj: &T,
     other: PyRef<T>,
@@ -103,6 +124,10 @@ impl PyObjectProtocol for SecretKey {
     fn __bytes__(&self) -> PyResult<PyObject> {
         to_bytes(self)
     }
+
+    fn __str__(&self) -> PyResult<String> {
+        Ok(format!("{}:...", Self::name()))
+    }
 }
 
 #[pyclass(module = "umbral")]
@@ -163,6 +188,10 @@ impl PyObjectProtocol for SecretKeyFactory {
     fn __bytes__(&self) -> PyResult<PyObject> {
         to_bytes(self)
     }
+
+    fn __str__(&self) -> PyResult<String> {
+        Ok(format!("{}:...", Self::name()))
+    }
 }
 
 #[pyclass(module = "umbral")]
@@ -209,9 +238,18 @@ impl PyObjectProtocol for PublicKey {
     fn __bytes__(&self) -> PyResult<PyObject> {
         to_bytes(self)
     }
+
+    fn __hash__(&self) -> PyResult<isize> {
+        hash(self)
+    }
+
+    fn __str__(&self) -> PyResult<String> {
+        hexstr(self)
+    }
 }
 
 #[pyclass(module = "umbral")]
+#[derive(PartialEq)]
 pub struct Capsule {
     backend: umbral_pre::Capsule,
 }
@@ -240,9 +278,21 @@ impl Capsule {
 
 #[pyproto]
 impl PyObjectProtocol for Capsule {
+    fn __richcmp__(&self, other: PyRef<Capsule>, op: CompareOp) -> PyResult<bool> {
+        richcmp(self, other, op)
+    }
+
     fn __bytes__(&self) -> PyResult<PyObject> {
         to_bytes(self)
     }
+
+    fn __hash__(&self) -> PyResult<isize> {
+        hash(self)
+    }
+
+    fn __str__(&self) -> PyResult<String> {
+        hexstr(self)
+    }
 }
 
 #[pyfunction]
@@ -289,6 +339,7 @@ pub fn decrypt_original(
 }
 
 #[pyclass(module = "umbral")]
+#[derive(PartialEq)]
 pub struct KeyFrag {
     backend: umbral_pre::KeyFrag,
 }
@@ -330,9 +381,21 @@ impl KeyFrag {
 
 #[pyproto]
 impl PyObjectProtocol for KeyFrag {
+    fn __richcmp__(&self, other: PyRef<KeyFrag>, op: CompareOp) -> PyResult<bool> {
+        richcmp(self, other, op)
+    }
+
     fn __bytes__(&self) -> PyResult<PyObject> {
         to_bytes(self)
     }
+
+    fn __hash__(&self) -> PyResult<isize> {
+        hash(self)
+    }
+
+    fn __str__(&self) -> PyResult<String> {
+        hexstr(self)
+    }
 }
 
 #[allow(clippy::too_many_arguments)]
@@ -364,7 +427,7 @@ pub fn generate_kfrags(
 }
 
 #[pyclass(module = "umbral")]
-#[derive(Clone)]
+#[derive(Clone, PartialEq)]
 pub struct CapsuleFrag {
     backend: umbral_pre::CapsuleFrag,
 }
@@ -410,9 +473,21 @@ impl CapsuleFrag {
 
 #[pyproto]
 impl PyObjectProtocol for CapsuleFrag {
+    fn __richcmp__(&self, other: PyRef<CapsuleFrag>, op: CompareOp) -> PyResult<bool> {
+        richcmp(self, other, op)
+    }
+
     fn __bytes__(&self) -> PyResult<PyObject> {
         to_bytes(self)
     }
+
+    fn __hash__(&self) -> PyResult<isize> {
+        hash(self)
+    }
+
+    fn __str__(&self) -> PyResult<String> {
+        hexstr(self)
+    }
 }
 
 #[pyfunction]