Add ConstantTimeSelect trait (#454)

We can't impl `subtle::ConditionallySelectable` for `Boxed*` types due
to a bound on `Copy`.

I've proposed various ways to try to fix this upstream, e.g.
dalek-cryptography/subtle#118, from which the `ConstantTimeSelect` trait
has been extracted. It provides the same API as
`ConditionallySelectable` but without the `Copy` bound.

A blanket impl of `ConstantTimeSelect` for all `ConditionallySelectable`
types means that all stack allocated types can continue to use
`ConditionallySelectable` and will receive an impl of
`ConstantTimeSelect` as well.

A bound on `ConstantTimeSelect` has been added to the `Integer` trait as
well, allowing it to be used on all `*Uint` types in this crate with
`Integer` as the trait abstraction.

src/modular/boxed_residue.rs

@@ -12,7 +12,7 @@ use super::{
     reduction::{montgomery_reduction_boxed, montgomery_reduction_boxed_mut},
     Retrieve,
 };
-use crate::{BoxedUint, Integer, Limb, NonZero, Word};
+use crate::{BoxedUint, ConstantTimeSelect, Integer, Limb, NonZero, Word};
 use subtle::CtOption;
 
 #[cfg(feature = "std")]
@@ -49,7 +49,7 @@ impl BoxedResidueParams {
 
         // Use a surrogate value of `1` in case a modulus of `0` is passed.
         // This will be rejected by the `is_odd` check above, which will fail and return `None`.
-        let modulus_nz = NonZero::new(BoxedUint::conditional_select(
+        let modulus_nz = NonZero::new(BoxedUint::ct_select(
             &modulus,
             &BoxedUint::one_with_precision(bits_precision),
             modulus.is_zero(),
@@ -82,7 +82,7 @@ impl BoxedResidueParams {
 
         // Use a surrogate value of `1` in case a modulus of `0` is passed.
         // This will be rejected by the `is_odd` check above, which will fail and return `None`.
-        let modulus_nz = NonZero::new(BoxedUint::conditional_select(
+        let modulus_nz = NonZero::new(BoxedUint::ct_select(
             &modulus,
             &BoxedUint::one_with_precision(bits_precision),
             modulus.is_zero(),

src/modular/boxed_residue/pow.rs

@@ -1,7 +1,7 @@
 //! Modular exponentiation support for [`BoxedResidue`].
 
 use super::{mul::MontgomeryMultiplier, BoxedResidue};
-use crate::{BoxedUint, Limb, PowBoundedExp, Word};
+use crate::{BoxedUint, ConstantTimeSelect, Limb, PowBoundedExp, Word};
 use alloc::vec::Vec;
 use subtle::{ConstantTimeEq, ConstantTimeLess};
 
@@ -103,7 +103,7 @@ fn pow_montgomery_form(
             // Constant-time lookup in the array of powers
             power.limbs.copy_from_slice(&powers[0].limbs);
             for i in 1..(1 << WINDOW) {
-                power.conditional_assign(&powers[i as usize], i.ct_eq(&idx));
+                power.ct_assign(&powers[i as usize], i.ct_eq(&idx));
             }
 
             multiplier.mul_amm_assign(&mut z, &power);

src/traits.rs

@@ -31,6 +31,51 @@ pub trait Bounded {
     const BYTES: usize;
 }
 
+/// Trait for types which are conditionally selectable in constant time, similar to (and blanket impl'd for) `subtle`'s
+/// [`ConditionallySelectable`] trait, but without the `Copy` bound which allows it to be impl'd for heap allocated
+/// types such as `BoxedUint`.
+///
+/// It also provides generic implementations of conditional assignment and conditional swaps.
+pub trait ConstantTimeSelect: Clone {
+    /// Select `a` or `b` according to `choice`.
+    ///
+    /// # Returns
+    /// - `a` if `choice == Choice(0)`;
+    /// - `b` if `choice == Choice(1)`.
+    fn ct_select(a: &Self, b: &Self, choice: Choice) -> Self;
+
+    /// Conditionally assign `other` to `self`, according to `choice`.
+    #[inline]
+    fn ct_assign(&mut self, other: &Self, choice: Choice) {
+        *self = Self::ct_select(self, other, choice);
+    }
+
+    /// Conditionally swap `self` and `other` if `choice == 1`; otherwise, reassign both unto themselves.
+    #[inline]
+    fn ct_swap(a: &mut Self, b: &mut Self, choice: Choice) {
+        let t: Self = a.clone();
+        a.ct_assign(b, choice);
+        b.ct_assign(&t, choice);
+    }
+}
+
+impl<T: ConditionallySelectable> ConstantTimeSelect for T {
+    #[inline(always)]
+    fn ct_select(a: &Self, b: &Self, choice: Choice) -> Self {
+        T::conditional_select(a, b, choice)
+    }
+
+    #[inline(always)]
+    fn ct_assign(&mut self, other: &Self, choice: Choice) {
+        self.conditional_assign(other, choice)
+    }
+
+    #[inline(always)]
+    fn ct_swap(a: &mut Self, b: &mut Self, choice: Choice) {
+        T::conditional_swap(a, b, choice)
+    }
+}
+
 /// Integer trait: represents common functionality of integer types provided by this crate.
 pub trait Integer:
     'static
@@ -55,10 +100,10 @@ pub trait Integer:
     + CheckedMul
     + CheckedDiv
     + Clone
-    // + ConditionallySelectable (see dalek-cryptography/subtle#94)
     + ConstantTimeEq
     + ConstantTimeGreater
     + ConstantTimeLess
+    + ConstantTimeSelect
     + Debug
     + Default
     + Div<NonZero<Self>, Output = Self>
@@ -113,7 +158,7 @@ pub trait Integer:
     fn bytes_precision(&self) -> usize;
 
     /// Calculate the number of leading zeros in the binary representation of this number.
-    fn leading_zeros(&self) -> u32  {
+    fn leading_zeros(&self) -> u32 {
         self.bits_precision() - self.bits()
     }
 

src/uint/boxed/ct.rs

@@ -1,17 +1,13 @@
 //! Constant-time helper functions.
 
 use super::BoxedUint;
-use crate::Limb;
-use subtle::{Choice, ConditionallySelectable, CtOption};
+use crate::{ConstantTimeSelect, Limb};
+use subtle::{Choice, ConditionallySelectable};
 
-impl BoxedUint {
-    /// Conditionally select `a` or `b` in constant time depending on [`Choice`].
-    ///
-    /// NOTE: can't impl `subtle`'s [`ConditionallySelectable`] trait due to its `Copy` bound, so
-    /// this is an inherent function instead.
-    ///
-    /// Panics if `a` and `b` don't have the same precision.
-    pub fn conditional_select(a: &Self, b: &Self, choice: Choice) -> Self {
+/// NOTE: can't impl `subtle`'s [`ConditionallySelectable`] trait due to its `Copy` bound
+impl ConstantTimeSelect for BoxedUint {
+    #[inline]
+    fn ct_select(a: &Self, b: &Self, choice: Choice) -> Self {
         debug_assert_eq!(a.bits_precision(), b.bits_precision());
         let mut limbs = vec![Limb::ZERO; a.nlimbs()].into_boxed_slice();
 
@@ -22,161 +18,37 @@ impl BoxedUint {
         Self { limbs }
     }
 
-    /// Conditionally assign `other` to `self`, according to `choice`.
-    ///
-    /// NOTE: can't impl `subtle`'s [`ConditionallySelectable`] trait due to its `Copy` bound, so
-    /// this is an inherent function instead.
-    ///
-    /// Panics if `a` and `b` don't have the same precision.
     #[inline]
-    pub fn conditional_assign(&mut self, other: &Self, choice: Choice) {
+    fn ct_assign(&mut self, other: &Self, choice: Choice) {
         debug_assert_eq!(self.bits_precision(), other.bits_precision());
 
         for i in 0..self.nlimbs() {
             self.limbs[i].conditional_assign(&other.limbs[i], choice);
         }
     }
 
-    /// Conditionally swap `self` and `other` if `choice == 1`; otherwise,
-    /// reassign both unto themselves.
-    ///
-    /// NOTE: can't impl `subtle`'s [`ConditionallySelectable`] trait due to its `Copy` bound, so
-    /// this is an inherent function instead.
-    ///
-    /// Panics if `a` and `b` don't have the same precision.
     #[inline]
-    pub fn conditional_swap(a: &mut Self, b: &mut Self, choice: Choice) {
+    fn ct_swap(a: &mut Self, b: &mut Self, choice: Choice) {
         debug_assert_eq!(a.bits_precision(), b.bits_precision());
 
         for i in 0..a.nlimbs() {
             Limb::conditional_swap(&mut a.limbs[i], &mut b.limbs[i], choice);
         }
     }
-
-    /// Conditional `map`: workaround which provides a [`CtOption::map`]-like API.
-    ///
-    /// Ensures both functions are called regardless of whether the first returns some/none with an
-    /// argument whose precision matches `self`. Note this still requires branching on the
-    /// intermediate [`CtOption`] value and therefore isn't fully constant time, but the best we can
-    /// do without upstream changes to `subtle` (see dalek-cryptography/subtle#94).
-    ///
-    /// Workaround due to `Copy` in [`ConditionallySelectable`] supertrait bounds.
-    pub fn conditional_map<C, F, T>(&self, condition: C, f: F) -> CtOption<T>
-    where
-        C: Fn(&Self) -> CtOption<Self>,
-        F: Fn(Self) -> T,
-    {
-        let conditional_val = condition(self);
-        let is_some = conditional_val.is_some();
-
-        let placeholder = Self::zero_with_precision(self.bits_precision());
-        let value = Option::<Self>::from(conditional_val).unwrap_or(placeholder);
-        debug_assert_eq!(self.bits_precision(), value.bits_precision());
-        CtOption::new(f(value), is_some)
-    }
-
-    /// Conditional `and_then`: workaround which provides a [`CtOption::and_then`]-like API.
-    ///
-    /// Ensures both functions are called regardless of whether the first returns some/none with an
-    /// argument whose precision matches `self`. Note this still requires branching on the
-    /// intermediate [`CtOption`] value and therefore isn't fully constant time, but the best we can
-    /// do without upstream changes to `subtle` (see dalek-cryptography/subtle#94).
-    ///
-    /// Workaround due to `Copy` in [`ConditionallySelectable`] supertrait bounds.
-    pub fn conditional_and_then<C, F>(&self, condition: C, f: F) -> CtOption<Self>
-    where
-        C: Fn(&Self) -> CtOption<Self>,
-        F: Fn(Self) -> CtOption<Self>,
-    {
-        let conditional_val = condition(self);
-        let mut is_some = conditional_val.is_some();
-
-        let placeholder = Self::zero_with_precision(self.bits_precision());
-        let value = Option::<Self>::from(conditional_val).unwrap_or(placeholder);
-        debug_assert_eq!(self.bits_precision(), value.bits_precision());
-
-        let conditional_val = f(value);
-        is_some &= conditional_val.is_some();
-
-        let placeholder = Self::zero_with_precision(self.bits_precision());
-        let value = Option::from(conditional_val).unwrap_or(placeholder);
-        debug_assert_eq!(self.bits_precision(), value.bits_precision());
-
-        CtOption::new(value, is_some)
-    }
 }
 
 #[cfg(test)]
 mod tests {
     use super::BoxedUint;
-    use subtle::{Choice, CtOption};
+    use crate::ConstantTimeSelect;
+    use subtle::Choice;
 
     #[test]
     fn conditional_select() {
         let a = BoxedUint::zero_with_precision(128);
         let b = BoxedUint::max(128);
 
-        assert_eq!(a, BoxedUint::conditional_select(&a, &b, Choice::from(0)));
-        assert_eq!(b, BoxedUint::conditional_select(&a, &b, Choice::from(1)));
-    }
-
-    #[test]
-    fn conditional_map_some() {
-        let n = BoxedUint::one();
-
-        let ret = n
-            .conditional_map(
-                |n| CtOption::new(n.clone(), 1u8.into()),
-                |n| n.wrapping_add(&BoxedUint::one()),
-            )
-            .unwrap();
-
-        assert_eq!(ret, BoxedUint::from(2u8));
+        assert_eq!(a, BoxedUint::ct_select(&a, &b, Choice::from(0)));
+        assert_eq!(b, BoxedUint::ct_select(&a, &b, Choice::from(1)));
     }
-
-    #[test]
-    fn conditional_map_none() {
-        let n = BoxedUint::one();
-
-        let ret = n.conditional_map(
-            |n| CtOption::new(n.clone(), 0u8.into()),
-            |n| n.wrapping_add(&BoxedUint::one()),
-        );
-
-        assert!(bool::from(ret.is_none()));
-    }
-
-    #[test]
-    fn conditional_and_then_all_some() {
-        let n = BoxedUint::one();
-
-        let ret = n
-            .conditional_and_then(
-                |n| CtOption::new(n.clone(), 1u8.into()),
-                |n| CtOption::new(n.wrapping_add(&BoxedUint::one()), 1u8.into()),
-            )
-            .unwrap();
-
-        assert_eq!(ret, BoxedUint::from(2u8));
-    }
-
-    macro_rules! conditional_and_then_none_test {
-        ($name:ident, $a:expr, $b:expr) => {
-            #[test]
-            fn $name() {
-                let n = BoxedUint::one();
-
-                let ret = n.conditional_and_then(
-                    |n| CtOption::new(n.clone(), $a.into()),
-                    |n| CtOption::new(n.wrapping_add(&BoxedUint::one()), $b.into()),
-                );
-
-                assert!(bool::from(ret.is_none()));
-            }
-        };
-    }
-
-    conditional_and_then_none_test!(conditional_and_then_none_some, 0, 1);
-    conditional_and_then_none_test!(conditional_and_then_some_none, 1, 0);
-    conditional_and_then_none_test!(conditional_and_then_none_none, 0, 0);
 }

src/uint/boxed/div.rs

@@ -1,6 +1,6 @@
 //! [`BoxedUint`] division operations.
 
-use crate::{BoxedUint, CheckedDiv, Limb, NonZero, Wrapping};
+use crate::{BoxedUint, CheckedDiv, ConstantTimeSelect, Limb, NonZero, Wrapping};
 use core::ops::{Div, DivAssign, Rem, RemAssign};
 use subtle::{Choice, ConstantTimeEq, ConstantTimeLess, CtOption};
 
@@ -42,7 +42,7 @@ impl BoxedUint {
 
         loop {
             let (r, borrow) = rem.sbb(&c, Limb::ZERO);
-            rem = Self::conditional_select(&r, &rem, !borrow.ct_eq(&Limb::ZERO));
+            rem = Self::ct_select(&r, &rem, !borrow.ct_eq(&Limb::ZERO));
             if bd == 0 {
                 break rem;
             }
@@ -84,9 +84,9 @@ impl BoxedUint {
 
         loop {
             let (mut r, borrow) = rem.sbb(&c, Limb::ZERO);
-            rem.conditional_assign(&r, !(Choice::from((borrow.0 & 1) as u8) | done));
+            rem.ct_assign(&r, !(Choice::from((borrow.0 & 1) as u8) | done));
             r = quo.bitor(&Self::one());
-            quo.conditional_assign(&r, !(Choice::from((borrow.0 & 1) as u8) | done));
+            quo.ct_assign(&r, !(Choice::from((borrow.0 & 1) as u8) | done));
             if i == 0 {
                 break;
             }
@@ -95,7 +95,7 @@ impl BoxedUint {
             // aren't modified further (but do the remaining iterations anyway to be constant-time)
             done = i.ct_lt(&mb);
             c.shr1_assign();
-            quo.conditional_assign(&quo.shl1(), !done);
+            quo.ct_assign(&quo.shl1(), !done);
         }
 
         (quo, rem)
@@ -117,9 +117,9 @@ impl BoxedUint {
         loop {
             let (mut r, borrow) = remainder.sbb(&c, Limb::ZERO);
             let borrow = Choice::from(borrow.0 as u8 & 1);
-            remainder = Self::conditional_select(&r, &remainder, borrow);
+            remainder = Self::ct_select(&r, &remainder, borrow);
             r = &quotient | Self::one();
-            quotient = Self::conditional_select(&r, &quotient, borrow);
+            quotient = Self::ct_select(&r, &quotient, borrow);
             if bd == 0 {
                 break;
             }

src/uint/boxed/inv_mod.rs

@@ -1,6 +1,6 @@
 //! [`BoxedUint`] modular inverse (i.e. reciprocal) operations.
 
-use crate::{BoxedUint, Integer};
+use crate::{BoxedUint, ConstantTimeSelect, Integer};
 use subtle::{Choice, ConstantTimeEq, ConstantTimeLess, CtOption};
 
 impl BoxedUint {
@@ -56,7 +56,7 @@ impl BoxedUint {
             let x_i = b.limbs[0].0 & 1;
             let x_i_choice = Choice::from(x_i as u8);
             // b_{i+1} = (b_i - a * X_i) / 2
-            b = Self::conditional_select(&b, &b.wrapping_sub(self), x_i_choice).shr1();
+            b = Self::ct_select(&b, &b.wrapping_sub(self), x_i_choice).shr1();
 
             // Store the X_i bit in the result (x = x | (1 << X_i))
             // Don't change the result in dummy iterations.
@@ -115,13 +115,13 @@ impl BoxedUint {
             // Set `self -= b` if `self` is odd.
             let swap = a.conditional_sbb_assign(&b, self_odd);
             // Set `b += self` if `swap` is true.
-            b = Self::conditional_select(&b, &b.wrapping_add(&a), swap);
+            b = Self::ct_select(&b, &b.wrapping_add(&a), swap);
             // Negate `self` if `swap` is true.
             a = a.conditional_wrapping_neg(swap);
 
             let mut new_u = u.clone();
             let mut new_v = v.clone();
-            Self::conditional_swap(&mut new_u, &mut new_v, swap);
+            Self::ct_swap(&mut new_u, &mut new_v, swap);
             let cy = new_u.conditional_sbb_assign(&new_v, self_odd);
             let cyy = new_u.conditional_adc_assign(modulus, cy);
             debug_assert!(bool::from(cy.ct_eq(&cyy)));