RustCrypto: Signatures has timing side-channel in ML-DSA decomposition
Summary
A timing side-channel was discovered in the Decompose algorithm which is used during ML-DSA signing to generate hints for the signature.
Details
The analysis was performed using a constant-time analyzer that examines compiled assembly code for instructions with data-dependent timing behavior. The analyzer flags:
- UDIV/SDIV instructions: Hardware division instructions have early termination optimizations where execution time depends on operand values.
The decompose function used a hardware division instruction to compute r1.0 / TwoGamma2::U32. This function is called during signing through high_bits() and low_bits(), which process values derived from secret key components:
(&w - &cs2).low_bits() where cs2 is derived from secret key component s2Hint::new() calls high_bits() on values derived from secret key component t0
Original Code:
```rust
fn decompose<TwoGamma2: Unsigned>(self) -> (Elem, Elem) {
// ...
let mut r1 = r_plus - r0;
r1.0 /= TwoGamma2::U32; // Variable-time division on secret-derived data
(r1, r0)
}
```
PoC
I do not have an exploit written for this, currently.
Impact
The dividend (r1.0) is derived from secret key material. An attacker with precise timing measurements could extract information about the signing key by observing timing variations in the division operation.
Mitigation
Replacing division with constant-time Barrett reduction mitigates this risk. Since TwoGamma2 is a compile-time constant, we precompute the multiplicative inverse:
```patch
diff --git a/ml-dsa/src/algebra.rs b/ml-dsa/src/algebra.rs
index 559b68a..bb126ce 100644
--- a/ml-dsa/src/algebra.rs
+++ b/ml-dsa/src/algebra.rs
@@ -54,8 +54,50 @@ pub(crate) trait Decompose {
fn decompose<TwoGamma2: Unsigned>(self) -> (Elem, Elem);
}
+/// Constant-time division by a compile-time constant divisor.
+///
+/// This trait provides a constant-time alternative to the hardware division
+/// instruction, which has variable timing based on operand values.
+/// Uses Barrett reduction to compute x / M where M is a compile-time constant.
+pub(crate) trait ConstantTimeDiv: Unsigned {
+ /// Bit shift for Barrett reduction, chosen to provide sufficient precision
+ const CT_DIV_SHIFT: usize;
+ /// Precomputed multiplier: ceil(2^SHIFT / M)
+ const CT_DIV_MULTIPLIER: u64;
+
+ /// Perform constant-time division of x by Self::U32
+ /// Requires: x < Q (the field modulus, ~2^23)
+ #[inline(always)]
+ fn ct_div(x: u32) -> u32 {
+ // Barrett reduction: q = (x * MULTIPLIER) >> SHIFT
+ // This gives us floor(x / M) for x < 2^SHIFT / MULTIPLIER * M
+ let x64 = u64::from(x);
+ let quotient = (x64 * Self::CT_DIV_MULTIPLIER) >> Self::CT_DIV_SHIFT;
+ quotient as u32
+ }
+}
+
+impl<M> ConstantTimeDiv for M
+where
+ M: Unsigned,
+{
+ // Use a shift that provides enough precision for the ML-DSA field (Q ~ 2^23)
+ // We need SHIFT > log2(Q) + log2(M) to ensure accuracy
+ // With Q < 2^24 and M < 2^20, SHIFT = 48 is sufficient
+ const CT_DIV_SHIFT: usize = 48;
+
+ // Precompute the multiplier at compile time
+ // We add (M-1) before dividing to get ceiling division, ensuring we never underestimate
+ #[allow(clippy::integer_division_remainder_used)]
+ const CT_DIV_MULTIPLIER: u64 = ((1u64 << Self::CT_DIV_SHIFT) + M::U64 - 1) / M::U64;
+}
+
impl Decompose for Elem {
// Algorithm 36 Decompose
+ //
+ // This implementation uses constant-time division to avoid timing side-channels.
+ // The original algorithm used hardware division which has variable timing based
+ // on operand values, potentially leaking secret information during signing.
fn decompose<TwoGamma2: Unsigned>(self) -> (Elem, Elem) {
let r_plus = self.clone();
let r0 = r_plus.mod_plus_minus::<TwoGamma2>();
@@ -63,8 +105,9 @@ impl Decompose for Elem {
if r_plus - r0 == Elem::new(BaseField::Q - 1) {
(Elem::new(0), r0 - Elem::new(1))
} else {
- let mut r1 = r_plus - r0;
- r1.0 /= TwoGamma2::U32;
+ let diff = r_plus - r0;
+ // Use constant-time division instead of hardware division
+ let r1 = Elem::new(TwoGamma2::ct_div(diff.0));
(r1, r0)
}
}
```
See our blog post on [how we avoided side-channels in our Go implementation of ML-DSA](https://blog.trailofbits.com/2025/11/14/how-we-avoided-side-channels-in-our-new-post-quantum-go-cryptography-libraries/) for more information.
