diff --git a/Cargo.lock b/Cargo.lock
index 49682ad..0d2a027 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -813,6 +813,7 @@ version = "0.1.0-rc.7"
 dependencies = [
  "const-oid 0.10.2",
  "criterion",
+ "ctutils",
  "getrandom 0.4.2",
  "hex",
  "hex-literal",
diff --git a/ml-dsa/Cargo.toml b/ml-dsa/Cargo.toml
index 55cac1b..b660cf5 100644
--- a/ml-dsa/Cargo.toml
+++ b/ml-dsa/Cargo.toml
@@ -36,6 +36,7 @@ hybrid-array = { version = "0.4", features = ["extra-sizes"] }
 module-lattice = "0.2.0-rc.0"
 sha3 = { version = "0.11.0-rc.8", default-features = false }
 signature = { version = "3.0.0-rc.10", default-features = false, features = ["digest"] }
+ctutils = { version = "0.4", default-features = false }
 
 # optional dependencies
 const-oid = { version = "0.10", features = ["db"], optional = true }
diff --git a/ml-dsa/src/algebra.rs b/ml-dsa/src/algebra.rs
index d3a9b02..68bbc98 100644
--- a/ml-dsa/src/algebra.rs
+++ b/ml-dsa/src/algebra.rs
@@ -1,3 +1,4 @@
+use ctutils::{CtEq, CtGt, CtLt, CtSelect};
 use hybrid_array::{
     ArraySize,
     typenum::{Shleft, U1, U13, Unsigned},
@@ -28,11 +29,9 @@ pub(crate) trait BarrettReduce: Unsigned {
         let quotient = (x * Self::MULTIPLIER) >> Self::SHIFT;
         let remainder = x - quotient * m;
 
-        if remainder < m {
-            Truncate::truncate(remainder)
-        } else {
-            Truncate::truncate(remainder - m)
-        }
+        let r_small: u32 = Truncate::truncate(remainder);
+        let r_large: u32 = Truncate::truncate(remainder.wrapping_sub(m));
+        u32::ct_select(&r_large, &r_small, remainder.ct_lt(&m))
     }
 }
 
@@ -103,14 +102,17 @@ impl Decompose for Elem {
         let r_plus = self.clone();
         let r0 = r_plus.mod_plus_minus::<TwoGamma2>();
 
-        if r_plus - r0 == Elem::new(BaseField::Q - 1) {
-            (Elem::new(0), r0 - Elem::new(1))
-        } else {
-            let diff = r_plus - r0;
-            // Use constant-time division instead of hardware division
-            let r1 = Elem::new(TwoGamma2::ct_div(diff.0));
-            (r1, r0)
-        }
+        let diff = r_plus - r0;
+        let is_edge = diff.0.ct_eq(&(BaseField::Q - 1));
+
+        // Compute both branches unconditionally
+        let edge = (Elem::new(0), r0 - Elem::new(1));
+        let r1 = Elem::new(TwoGamma2::ct_div(diff.0));
+        let normal = (r1, r0);
+
+        let r1_out = Elem::new(u32::ct_select(&normal.0.0, &edge.0.0, is_edge));
+        let r0_out = Elem::new(u32::ct_select(&normal.1.0, &edge.1.0, is_edge));
+        (r1_out, r0_out)
     }
 }
 
@@ -126,11 +128,12 @@ pub(crate) trait AlgebraExt: Sized {
 impl AlgebraExt for Elem {
     fn mod_plus_minus<M: Unsigned>(&self) -> Self {
         let raw_mod = Elem::new(M::reduce(self.0));
-        if raw_mod.0 <= M::U32 >> 1 {
-            raw_mod
-        } else {
-            raw_mod - Elem::new(M::U32)
-        }
+        let in_lower_half = !raw_mod.0.ct_gt(&(M::U32 >> 1));
+        Elem::new(u32::ct_select(
+            &(raw_mod - Elem::new(M::U32)).0,
+            &raw_mod.0,
+            in_lower_half,
+        ))
     }
 
     // FIPS 204 defines the infinity norm differently for signed vs. unsigned integers:
@@ -142,11 +145,8 @@ impl AlgebraExt for Elem {
     // the signed integers used in this crate, so we can safely use the unsigned version.  However,
     // since mod_plus_minus is also unsigned, we need to unwrap the "negative" values.
     fn infinity_norm(&self) -> u32 {
-        if self.0 <= BaseField::Q >> 1 {
-            self.0
-        } else {
-            BaseField::Q - self.0
-        }
+        let in_lower_half = !self.0.ct_gt(&(BaseField::Q >> 1));
+        u32::ct_select(&(BaseField::Q - self.0), &self.0, in_lower_half)
     }
 
     // Algorithm 35 Power2Round
diff --git a/ml-dsa/src/hint.rs b/ml-dsa/src/hint.rs
index e1d497f..c03ad1f 100644
--- a/ml-dsa/src/hint.rs
+++ b/ml-dsa/src/hint.rs
@@ -2,6 +2,7 @@ use crate::{
     algebra::{AlgebraExt, BaseField, Decompose, Elem, Polynomial, Vector},
     param::{EncodedHint, SignatureParams},
 };
+use ctutils::{Choice, CtEq, CtGt, CtSelect};
 use hybrid_array::{
     Array,
     typenum::{U256, Unsigned},
@@ -17,25 +18,29 @@ fn make_hint<TwoGamma2: Unsigned>(z: Elem, r: Elem) -> bool {
 }
 
 /// Algorithm 40 `UseHint`: returns the high bits of `r` adjusted according to hint `h`.
+///
+/// All branches are replaced with constant-time selection to avoid
+/// leaking information about `r0` through branch timing.
 #[allow(clippy::integer_division_remainder_used, reason = "params are public")]
 fn use_hint<TwoGamma2: Unsigned>(h: bool, r: Elem) -> Elem {
     let m: u32 = (BaseField::Q - 1) / TwoGamma2::U32;
     let (r1, r0) = r.decompose::<TwoGamma2>();
     let gamma2 = TwoGamma2::U32 / 2;
 
-    if h {
-        if r0.0 > 0 && r0.0 <= gamma2 {
-            Elem::new((r1.0 + 1) % m)
-        } else if (r0.0 == 0) || (r0.0 >= BaseField::Q - gamma2) {
-            Elem::new((r1.0 + m - 1) % m)
-        } else {
-            // We use the Elem encoding even for signed integers.  Since r0 is computed
-            // mod+- 2*gamma2 (possibly minus 1), it is guaranteed to be in [-gamma2, gamma2].
-            unreachable!();
-        }
-    } else {
-        r1
-    }
+    // Compute both possible hint-adjusted results unconditionally
+    let r1_inc = Elem::new((r1.0 + 1) % m);
+    let r1_dec = Elem::new((r1.0 + m - 1) % m);
+
+    // r0 is "positive" when r0 > 0 AND r0 <= gamma2
+    let r0_positive = !r0.0.ct_eq(&0) & !r0.0.ct_gt(&gamma2);
+    let hinted = Elem::new(u32::ct_select(&r1_dec.0, &r1_inc.0, r0_positive));
+
+    // Apply hint only when h is set
+    Elem::new(u32::ct_select(
+        &r1.0,
+        &hinted.0,
+        Choice::from_u8_lsb(u8::from(h)),
+    ))
 }
 
 #[derive(Clone, PartialEq, Debug)]