diff --git a/Cargo.toml b/Cargo.toml
index f32957c59..f7dcd140c 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -52,6 +52,8 @@ serde = { version = "1.0", default-features = false, optional = true, features =
 packed_simd = { version = "0.3.4", package = "packed_simd_2", features = ["into_bits"], optional = true }
 zeroize = { version = ">=1, <1.4", default-features = false }
 fiat-crypto = { version = "0.1.6", optional = true}
+num-traits = "0.2"
+hex = "0.4.3"
 
 [features]
 nightly = ["subtle/nightly"]
diff --git a/src/lib.rs b/src/lib.rs
index f33ffded1..2b72678ff 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -264,7 +264,9 @@ extern crate packed_simd;
 extern crate byteorder;
 pub extern crate digest;
 extern crate rand_core;
+extern crate num_traits;
 extern crate zeroize;
+extern crate hex;
 
 #[cfg(any(feature = "fiat_u64_backend", feature = "fiat_u32_backend"))]
 extern crate fiat_crypto;
diff --git a/src/ristretto.rs b/src/ristretto.rs
index b9e37343b..b59e588e4 100644
--- a/src/ristretto.rs
+++ b/src/ristretto.rs
@@ -159,12 +159,14 @@
 //! https://ristretto.group/
 
 use core::borrow::Borrow;
-use core::fmt::Debug;
+use core::fmt::{Debug, Display};
 use core::iter::Sum;
 use core::ops::{Add, Neg, Sub};
 use core::ops::{AddAssign, SubAssign};
 use core::ops::{Mul, MulAssign};
 
+use::num_traits::Zero;
+
 use rand_core::{CryptoRng, RngCore};
 
 use digest::generic_array::typenum::U64;
@@ -422,6 +424,23 @@ impl<'de> Deserialize<'de> for CompressedRistretto {
     }
 }
 
+impl Zero for RistrettoPoint {
+    fn zero() -> Self {
+	RistrettoPoint::identity()
+    }
+    fn is_zero(&self) -> bool {
+	self == &RistrettoPoint::identity()
+    }
+}
+
+impl Display for RistrettoPoint {
+    fn fmt(&self, f: &mut ::core::fmt::Formatter) -> ::core::fmt::Result {
+	let data = hex::encode(self.compress().as_bytes());
+	write!(f, "{}", data)?;
+	Ok(())
+    }
+}
+
 // ------------------------------------------------------------------------
 // Internal point representations
 // ------------------------------------------------------------------------
diff --git a/src/scalar.rs b/src/scalar.rs
index 00de74081..f9e3abbf2 100644
--- a/src/scalar.rs
+++ b/src/scalar.rs
@@ -138,16 +138,18 @@
 //!
 //! The resulting `Scalar` has exactly the specified bit pattern,
 //! **except for the highest bit, which will be set to 0**.
-
 use core::borrow::Borrow;
-use core::cmp::{Eq, PartialEq};
-use core::fmt::Debug;
+use core::cmp::{Eq, Ord, PartialEq};
+use core::fmt::{Debug, Display};
 use core::iter::{Product, Sum};
 use core::ops::Index;
 use core::ops::Neg;
 use core::ops::{Add, AddAssign};
 use core::ops::{Mul, MulAssign};
 use core::ops::{Sub, SubAssign};
+use core::ops::{Div, DivAssign};
+
+use::num_traits::{Zero, One};
 
 #[allow(unused_imports)]
 use prelude::*;
@@ -192,7 +194,7 @@ type UnpackedScalar = backend::serial::u32::scalar::Scalar29;
 
 /// The `Scalar` struct holds an integer \\(s < 2\^{255} \\) which
 /// represents an element of \\(\mathbb Z / \ell\\).
-#[derive(Copy, Clone, Hash)]
+#[derive(Copy, Clone, Hash, Ord, PartialOrd)]
 pub struct Scalar {
     /// `bytes` is a little-endian byte encoding of an integer representing a scalar modulo the
     /// group order.
@@ -268,6 +270,14 @@ impl Debug for Scalar {
     }
 }
 
+impl Display for Scalar {
+    fn fmt(&self, f: &mut ::core::fmt::Formatter) -> ::core::fmt::Result {
+	let data = hex::encode(self.bytes);
+        write!(f, "{}", data)?;
+	Ok(())
+    }
+}
+
 impl Eq for Scalar {}
 impl PartialEq for Scalar {
     fn eq(&self, other: &Self) -> bool {
@@ -290,6 +300,39 @@ impl Index<usize> for Scalar {
     }
 }
 
+impl Zero for Scalar {
+    fn zero() -> Self {
+	Scalar::zero()
+    }
+    fn is_zero(&self) -> bool {
+	self == &Scalar::zero()
+    }
+}
+
+impl One for Scalar {
+    fn one() -> Self {
+	Scalar::one()
+    }
+    fn is_one(&self) -> bool {
+	self == &Scalar::one()
+    }
+}
+
+impl Div<Scalar> for Scalar {
+    type Output = Scalar;
+    fn div(self, q: Scalar) -> Self::Output {
+	let q1 = q.invert();
+	self * q1
+    }
+}
+
+impl DivAssign<Scalar> for Scalar {
+    fn div_assign(&mut self, q: Scalar) {
+	let q1 = q.invert();
+	*self = *self * q1;
+    }
+}
+
 impl<'b> MulAssign<&'b Scalar> for Scalar {
     fn mul_assign(&mut self, _rhs: &'b Scalar) {
         *self = UnpackedScalar::mul(&self.unpack(), &_rhs.unpack()).pack();