diff --git a/src/uint/boxed.rs b/src/uint/boxed.rs
index 1768b48f..fe779c43 100644
--- a/src/uint/boxed.rs
+++ b/src/uint/boxed.rs
@@ -17,6 +17,9 @@ mod shr;
 mod sub;
 mod sub_mod;
 
+#[cfg(feature = "rand_core")]
+mod rand;
+
 use crate::{Limb, NonZero, Uint, Word, Zero, U128, U64};
 use alloc::{boxed::Box, vec, vec::Vec};
 use core::fmt;
diff --git a/src/uint/boxed/rand.rs b/src/uint/boxed/rand.rs
new file mode 100644
index 00000000..74df0375
--- /dev/null
+++ b/src/uint/boxed/rand.rs
@@ -0,0 +1,63 @@
+//! Random number generator support.
+
+use super::BoxedUint;
+use crate::{uint::rand::random_mod_core, Limb, NonZero, Random, RandomMod};
+use rand_core::CryptoRngCore;
+
+impl BoxedUint {
+    /// Generate a cryptographically secure random [`BoxedUint`].
+    pub fn random(mut rng: &mut impl CryptoRngCore, bits_precision: usize) -> Self {
+        let mut ret = BoxedUint::zero_with_precision(bits_precision);
+
+        for limb in &mut *ret.limbs {
+            *limb = Limb::random(&mut rng)
+        }
+
+        ret
+    }
+}
+
+impl RandomMod for BoxedUint {
+    /// Generate a cryptographically secure random [`BoxedUint`] which is less than a given
+    /// `modulus`.
+    ///
+    /// This function uses rejection sampling, a method which produces an unbiased distribution of
+    /// in-range values provided the underlying CSRNG is unbiased, but runs in variable-time.
+    ///
+    /// The variable-time nature of the algorithm should not pose a security issue so long as the
+    /// underlying random number generator is truly a CSRNG, where previous outputs are unrelated to
+    /// subsequent outputs and do not reveal information about the RNG's internal state.
+    fn random_mod(rng: &mut impl CryptoRngCore, modulus: &NonZero<Self>) -> Self {
+        let mut n = BoxedUint::zero_with_precision(modulus.bits_precision());
+        random_mod_core(rng, &mut n, modulus, modulus.bits());
+        n
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use crate::{NonZero, RandomMod, U256};
+    use rand_core::SeedableRng;
+
+    #[test]
+    fn random_mod() {
+        let mut rng = rand_chacha::ChaCha8Rng::seed_from_u64(1);
+
+        // Ensure `random_mod` runs in a reasonable amount of time
+        let modulus = NonZero::new(U256::from(42u8)).unwrap();
+        let res = U256::random_mod(&mut rng, &modulus);
+
+        // Check that the value is in range
+        assert!(res >= U256::ZERO);
+        assert!(res < U256::from(42u8));
+
+        // Ensure `random_mod` runs in a reasonable amount of time
+        // when the modulus is larger than 1 limb
+        let modulus = NonZero::new(U256::from(0x10000000000000001u128)).unwrap();
+        let res = U256::random_mod(&mut rng, &modulus);
+
+        // Check that the value is in range
+        assert!(res >= U256::ZERO);
+        assert!(res < U256::from(0x10000000000000001u128));
+    }
+}
diff --git a/src/uint/rand.rs b/src/uint/rand.rs
index 80af3bb1..96e8ff56 100644
--- a/src/uint/rand.rs
+++ b/src/uint/rand.rs
@@ -1,7 +1,7 @@
 //! Random number generator support
 
 use super::Uint;
-use crate::{Encoding, Limb, NonZero, Random, RandomMod};
+use crate::{Encoding, Limb, NonZero, Random, RandomMod, Zero};
 use rand_core::CryptoRngCore;
 use subtle::ConstantTimeLess;
 
@@ -32,31 +32,43 @@ impl<const LIMBS: usize> RandomMod for Uint<LIMBS> {
     /// outputs and do not reveal information about the RNG's internal state.
     fn random_mod(rng: &mut impl CryptoRngCore, modulus: &NonZero<Self>) -> Self {
         let mut n = Self::ZERO;
+        random_mod_core(rng, &mut n, modulus, modulus.bits_vartime());
+        n
+    }
+}
+
+/// Generic implementation of `random_mod` which can be shared with `BoxedUint`.
+// TODO(tarcieri): obtain `n_bits` via a trait like `Integer`
+pub(super) fn random_mod_core<T>(
+    rng: &mut impl CryptoRngCore,
+    n: &mut T,
+    modulus: &NonZero<T>,
+    n_bits: usize,
+) where
+    T: AsMut<[Limb]> + ConstantTimeLess + Zero,
+{
+    let n_bytes = (n_bits + 7) / 8;
+    let n_limbs = (n_bits + Limb::BITS - 1) / Limb::BITS;
+    let hi_bytes = n_bytes - (n_limbs - 1) * Limb::BYTES;
+
+    let mut bytes = Limb::ZERO.to_le_bytes();
+
+    loop {
+        for i in 0..n_limbs - 1 {
+            rng.fill_bytes(bytes.as_mut());
+            // Need to deserialize from little-endian to make sure that two 32-bit limbs
+            // deserialized sequentially are equal to one 64-bit limb produced from the same
+            // byte stream.
+            n.as_mut()[i] = Limb::from_le_bytes(bytes);
+        }
+
+        // Generate the high limb which may need to only be filled partially.
+        bytes.as_mut().fill(0);
+        rng.fill_bytes(&mut (bytes.as_mut()[0..hi_bytes]));
+        n.as_mut()[n_limbs - 1] = Limb::from_le_bytes(bytes);
 
-        let n_bits = modulus.as_ref().bits_vartime();
-        let n_bytes = (n_bits + 7) / 8;
-        let n_limbs = (n_bits + Limb::BITS - 1) / Limb::BITS;
-        let hi_bytes = n_bytes - (n_limbs - 1) * Limb::BYTES;
-
-        let mut bytes = Limb::ZERO.to_le_bytes();
-
-        loop {
-            for i in 0..n_limbs - 1 {
-                rng.fill_bytes(bytes.as_mut());
-                // Need to deserialize from little-endian to make sure that two 32-bit limbs
-                // deserialized sequentially are equal to one 64-bit limb produced from the same
-                // byte stream.
-                n.limbs[i] = Limb::from_le_bytes(bytes);
-            }
-
-            // Generate the high limb which may need to only be filled partially.
-            bytes.as_mut().fill(0);
-            rng.fill_bytes(&mut (bytes.as_mut()[0..hi_bytes]));
-            n.limbs[n_limbs - 1] = Limb::from_le_bytes(bytes);
-
-            if n.ct_lt(modulus).into() {
-                return n;
-            }
+        if n.ct_lt(modulus).into() {
+            break;
         }
     }
 }