diff --git a/src/lib.rs b/src/lib.rs
index cdfab0abb..a2aa913a2 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -117,7 +117,7 @@
 //! ### Random number generation
 //!
 //! When the `rand_core` or `rand` features of this crate are enabled, it's
-//! possible to generate random numbers using any CSRNG by using the
+//! possible to generate random numbers using any RNG by using the
 //! [`Random`] trait:
 //!
 //! ```
diff --git a/src/limb/rand.rs b/src/limb/rand.rs
index bfaf62ebe..96f384789 100644
--- a/src/limb/rand.rs
+++ b/src/limb/rand.rs
@@ -2,23 +2,23 @@
 
 use super::Limb;
 use crate::{Encoding, NonZero, Random, RandomMod};
-use rand_core::CryptoRngCore;
+use rand_core::RngCore;
 use subtle::ConstantTimeLess;
 
 impl Random for Limb {
     #[cfg(target_pointer_width = "32")]
-    fn random(rng: &mut impl CryptoRngCore) -> Self {
+    fn random(rng: &mut impl RngCore) -> Self {
         Self(rng.next_u32())
     }
 
     #[cfg(target_pointer_width = "64")]
-    fn random(rng: &mut impl CryptoRngCore) -> Self {
+    fn random(rng: &mut impl RngCore) -> Self {
         Self(rng.next_u64())
     }
 }
 
 impl RandomMod for Limb {
-    fn random_mod(rng: &mut impl CryptoRngCore, modulus: &NonZero<Self>) -> Self {
+    fn random_mod(rng: &mut impl RngCore, modulus: &NonZero<Self>) -> Self {
         let mut bytes = <Self as Encoding>::Repr::default();
 
         let n_bits = modulus.bits() as usize;
diff --git a/src/modular/const_monty_form.rs b/src/modular/const_monty_form.rs
index ab0efbc26..8ad6d40e8 100644
--- a/src/modular/const_monty_form.rs
+++ b/src/modular/const_monty_form.rs
@@ -15,7 +15,7 @@ use core::{fmt::Debug, marker::PhantomData};
 use subtle::{Choice, ConditionallySelectable, ConstantTimeEq};
 
 #[cfg(feature = "rand_core")]
-use crate::{rand_core::CryptoRngCore, Random, RandomMod};
+use crate::{rand_core::RngCore, Random, RandomMod};
 
 #[cfg(feature = "serde")]
 use {
@@ -207,7 +207,7 @@ where
     MOD: ConstMontyParams<LIMBS>,
 {
     #[inline]
-    fn random(rng: &mut impl CryptoRngCore) -> Self {
+    fn random(rng: &mut impl RngCore) -> Self {
         Self::new(&Uint::random_mod(rng, MOD::MODULUS.as_nz_ref()))
     }
 }
diff --git a/src/non_zero.rs b/src/non_zero.rs
index 3f280b301..7465ec6d9 100644
--- a/src/non_zero.rs
+++ b/src/non_zero.rs
@@ -12,7 +12,7 @@ use subtle::{Choice, ConditionallySelectable, ConstantTimeEq, CtOption};
 use crate::{ArrayEncoding, ByteArray};
 
 #[cfg(feature = "rand_core")]
-use {crate::Random, rand_core::CryptoRngCore};
+use {crate::Random, rand_core::RngCore};
 
 #[cfg(feature = "serde")]
 use serdect::serde::{
@@ -232,8 +232,7 @@ impl<T> Random for NonZero<T>
 where
     T: Random + Zero,
 {
-    /// Generate a random `NonZero<T>`.
-    fn random(mut rng: &mut impl CryptoRngCore) -> Self {
+    fn random(mut rng: &mut impl RngCore) -> Self {
         // Use rejection sampling to eliminate zero values.
         // While this method isn't constant-time, the attacker shouldn't learn
         // anything about unrelated outputs so long as `rng` is a CSRNG.
diff --git a/src/odd.rs b/src/odd.rs
index c8a11a712..a7995d027 100644
--- a/src/odd.rs
+++ b/src/odd.rs
@@ -8,7 +8,7 @@ use subtle::{Choice, ConditionallySelectable, ConstantTimeEq, CtOption};
 use crate::BoxedUint;
 
 #[cfg(feature = "rand_core")]
-use {crate::Random, rand_core::CryptoRngCore};
+use {crate::Random, rand_core::RngCore};
 
 #[cfg(all(feature = "alloc", feature = "rand_core"))]
 use crate::RandomBits;
@@ -153,7 +153,7 @@ impl PartialOrd<Odd<BoxedUint>> for BoxedUint {
 #[cfg(feature = "rand_core")]
 impl<const LIMBS: usize> Random for Odd<Uint<LIMBS>> {
     /// Generate a random `Odd<Uint<T>>`.
-    fn random(rng: &mut impl CryptoRngCore) -> Self {
+    fn random(rng: &mut impl RngCore) -> Self {
         let mut ret = Uint::random(rng);
         ret.limbs[0] |= Limb::ONE;
         Odd(ret)
@@ -163,7 +163,7 @@ impl<const LIMBS: usize> Random for Odd<Uint<LIMBS>> {
 #[cfg(all(feature = "alloc", feature = "rand_core"))]
 impl Odd<BoxedUint> {
     /// Generate a random `Odd<Uint<T>>`.
-    pub fn random(rng: &mut impl CryptoRngCore, bit_length: u32) -> Self {
+    pub fn random(rng: &mut impl RngCore, bit_length: u32) -> Self {
         let mut ret = BoxedUint::random_bits(rng, bit_length);
         ret.limbs[0] |= Limb::ONE;
         Odd(ret)
diff --git a/src/traits.rs b/src/traits.rs
index 54bfff62b..a33e5d8f0 100644
--- a/src/traits.rs
+++ b/src/traits.rs
@@ -20,7 +20,7 @@ use subtle::{
 };
 
 #[cfg(feature = "rand_core")]
-use rand_core::CryptoRngCore;
+use rand_core::RngCore;
 
 /// Integers whose representation takes a bounded amount of space.
 pub trait Bounded {
@@ -282,8 +282,10 @@ pub trait Constants: ConstZero {
 /// Random number generation support.
 #[cfg(feature = "rand_core")]
 pub trait Random: Sized {
-    /// Generate a cryptographically secure random value.
-    fn random(rng: &mut impl CryptoRngCore) -> Self;
+    /// Generate a random value.
+    ///
+    /// If `rng` is a CSRNG, the generation is cryptographically secure as well.
+    fn random(rng: &mut impl RngCore) -> Self;
 }
 
 /// Possible errors of the methods in [`RandomBits`] trait.
@@ -343,28 +345,27 @@ impl core::error::Error for RandomBitsError {}
 /// Random bits generation support.
 #[cfg(feature = "rand_core")]
 pub trait RandomBits: Sized {
-    /// Generate a cryptographically secure random value in range `[0, 2^bit_length)`.
+    /// Generate a random value in range `[0, 2^bit_length)`.
     ///
     /// A wrapper for [`RandomBits::try_random_bits`] that panics on error.
-    fn random_bits(rng: &mut impl CryptoRngCore, bit_length: u32) -> Self {
+    fn random_bits(rng: &mut impl RngCore, bit_length: u32) -> Self {
         Self::try_random_bits(rng, bit_length).expect("try_random_bits() failed")
     }
 
-    /// Generate a cryptographically secure random value in range `[0, 2^bit_length)`.
+    /// Generate a random value in range `[0, 2^bit_length)`.
     ///
     /// This method is variable time wrt `bit_length`.
-    fn try_random_bits(
-        rng: &mut impl CryptoRngCore,
-        bit_length: u32,
-    ) -> Result<Self, RandomBitsError>;
+    ///
+    /// If `rng` is a CSRNG, the generation is cryptographically secure as well.
+    fn try_random_bits(rng: &mut impl RngCore, bit_length: u32) -> Result<Self, RandomBitsError>;
 
-    /// Generate a cryptographically secure random value in range `[0, 2^bit_length)`,
+    /// Generate a random value in range `[0, 2^bit_length)`,
     /// returning an integer with the closest available size to `bits_precision`
     /// (if the implementing type supports runtime sizing).
     ///
     /// A wrapper for [`RandomBits::try_random_bits_with_precision`] that panics on error.
     fn random_bits_with_precision(
-        rng: &mut impl CryptoRngCore,
+        rng: &mut impl RngCore,
         bit_length: u32,
         bits_precision: u32,
     ) -> Self {
@@ -372,13 +373,15 @@ pub trait RandomBits: Sized {
             .expect("try_random_bits_with_precision() failed")
     }
 
-    /// Generate a cryptographically secure random value in range `[0, 2^bit_length)`,
+    /// Generate a random value in range `[0, 2^bit_length)`,
     /// returning an integer with the closest available size to `bits_precision`
     /// (if the implementing type supports runtime sizing).
     ///
     /// This method is variable time wrt `bit_length`.
+    ///
+    /// If `rng` is a CSRNG, the generation is cryptographically secure as well.
     fn try_random_bits_with_precision(
-        rng: &mut impl CryptoRngCore,
+        rng: &mut impl RngCore,
         bit_length: u32,
         bits_precision: u32,
     ) -> Result<Self, RandomBitsError>;
@@ -387,18 +390,17 @@ pub trait RandomBits: Sized {
 /// Modular random number generation support.
 #[cfg(feature = "rand_core")]
 pub trait RandomMod: Sized + Zero {
-    /// Generate a cryptographically secure random number which is less than
-    /// a given `modulus`.
+    /// Generate a random number 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.
+    /// RNG 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
+    /// issue so long as the underlying random number generator is 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;
+    fn random_mod(rng: &mut impl RngCore, modulus: &NonZero<Self>) -> Self;
 }
 
 /// Compute `self + rhs mod p`.
diff --git a/src/uint/boxed/rand.rs b/src/uint/boxed/rand.rs
index 6a2e73966..120aa1eac 100644
--- a/src/uint/boxed/rand.rs
+++ b/src/uint/boxed/rand.rs
@@ -5,18 +5,15 @@ use crate::{
     uint::rand::{random_bits_core, random_mod_core},
     NonZero, RandomBits, RandomBitsError, RandomMod,
 };
-use rand_core::CryptoRngCore;
+use rand_core::RngCore;
 
 impl RandomBits for BoxedUint {
-    fn try_random_bits(
-        rng: &mut impl CryptoRngCore,
-        bit_length: u32,
-    ) -> Result<Self, RandomBitsError> {
+    fn try_random_bits(rng: &mut impl RngCore, bit_length: u32) -> Result<Self, RandomBitsError> {
         Self::try_random_bits_with_precision(rng, bit_length, bit_length)
     }
 
     fn try_random_bits_with_precision(
-        rng: &mut impl CryptoRngCore,
+        rng: &mut impl RngCore,
         bit_length: u32,
         bits_precision: u32,
     ) -> Result<Self, RandomBitsError> {
@@ -34,16 +31,17 @@ impl RandomBits for BoxedUint {
 }
 
 impl RandomMod for BoxedUint {
-    /// Generate a cryptographically secure random [`BoxedUint`] which is less than a given
-    /// `modulus`.
+    /// Generate a 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.
+    /// This function uses rejection sampling, a method which produces an
+    /// unbiased distribution of in-range values provided the underlying
+    /// RNG 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 {
+    /// The variable-time nature of the algorithm should not pose a security
+    /// issue so long as the underlying random number generator is 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 RngCore, modulus: &NonZero<Self>) -> Self {
         let mut n = BoxedUint::zero_with_precision(modulus.bits_precision());
         random_mod_core(rng, &mut n, modulus, modulus.bits());
         n
diff --git a/src/uint/rand.rs b/src/uint/rand.rs
index ce6b41de8..b3ee11033 100644
--- a/src/uint/rand.rs
+++ b/src/uint/rand.rs
@@ -2,12 +2,11 @@
 
 use super::{Uint, Word};
 use crate::{Encoding, Limb, NonZero, Random, RandomBits, RandomBitsError, RandomMod, Zero};
-use rand_core::CryptoRngCore;
+use rand_core::RngCore;
 use subtle::ConstantTimeLess;
 
 impl<const LIMBS: usize> Random for Uint<LIMBS> {
-    /// Generate a cryptographically secure random [`Uint`].
-    fn random(mut rng: &mut impl CryptoRngCore) -> Self {
+    fn random(mut rng: &mut impl RngCore) -> Self {
         let mut limbs = [Limb::ZERO; LIMBS];
 
         for limb in &mut limbs {
@@ -22,7 +21,7 @@ impl<const LIMBS: usize> Random for Uint<LIMBS> {
 ///
 /// NOTE: Assumes that the limbs in the given slice are zeroed!
 pub(crate) fn random_bits_core(
-    rng: &mut impl CryptoRngCore,
+    rng: &mut impl RngCore,
     zeroed_limbs: &mut [Limb],
     bit_length: u32,
 ) -> Result<(), RandomBitsError> {
@@ -51,15 +50,12 @@ pub(crate) fn random_bits_core(
 }
 
 impl<const LIMBS: usize> RandomBits for Uint<LIMBS> {
-    fn try_random_bits(
-        rng: &mut impl CryptoRngCore,
-        bit_length: u32,
-    ) -> Result<Self, RandomBitsError> {
+    fn try_random_bits(rng: &mut impl RngCore, bit_length: u32) -> Result<Self, RandomBitsError> {
         Self::try_random_bits_with_precision(rng, bit_length, Self::BITS)
     }
 
     fn try_random_bits_with_precision(
-        rng: &mut impl CryptoRngCore,
+        rng: &mut impl RngCore,
         bit_length: u32,
         bits_precision: u32,
     ) -> Result<Self, RandomBitsError> {
@@ -82,18 +78,17 @@ impl<const LIMBS: usize> RandomBits for Uint<LIMBS> {
 }
 
 impl<const LIMBS: usize> RandomMod for Uint<LIMBS> {
-    /// Generate a cryptographically secure random [`Uint`] which is less than
-    /// a given `modulus`.
+    /// Generate a random number 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.
+    /// RNG 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
+    /// issue so long as the underlying random number generator is 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 {
+    fn random_mod(rng: &mut impl RngCore, modulus: &NonZero<Self>) -> Self {
         let mut n = Self::ZERO;
         random_mod_core(rng, &mut n, modulus, modulus.bits_vartime());
         n
@@ -103,7 +98,7 @@ impl<const LIMBS: usize> RandomMod for Uint<LIMBS> {
 /// 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,
+    rng: &mut impl RngCore,
     n: &mut T,
     modulus: &NonZero<T>,
     n_bits: u32,
diff --git a/src/wrapping.rs b/src/wrapping.rs
index 86640246c..c49378b0c 100644
--- a/src/wrapping.rs
+++ b/src/wrapping.rs
@@ -8,7 +8,7 @@ use core::{
 use subtle::{Choice, ConditionallySelectable, ConstantTimeEq};
 
 #[cfg(feature = "rand_core")]
-use {crate::Random, rand_core::CryptoRngCore};
+use {crate::Random, rand_core::RngCore};
 
 #[cfg(feature = "serde")]
 use serdect::serde::{Deserialize, Deserializer, Serialize, Serializer};
@@ -259,7 +259,7 @@ impl<T: fmt::UpperHex> fmt::UpperHex for Wrapping<T> {
 
 #[cfg(feature = "rand_core")]
 impl<T: Random> Random for Wrapping<T> {
-    fn random(rng: &mut impl CryptoRngCore) -> Self {
+    fn random(rng: &mut impl RngCore) -> Self {
         Wrapping(Random::random(rng))
     }
 }