Scalar::div_by_2 (#805)

* [WIP] Scalar::div_by_2

* debug_assert that carry is 0

* revise tests

* Test multiply by half scalar, double and compress (#804)

* Test `div_by_2` with `proptest` (#806)

---------

Co-authored-by: daxpedda <[email protected]>

Author: tarcieri

curve25519-dalek/Cargo.toml

@@ -41,6 +41,7 @@ sha2 = { version = "0.11.0-rc.0", default-features = false }
 bincode = "1"
 criterion = { version = "0.5", features = ["html_reports"] }
 hex = "0.4.2"
+proptest = "1"
 rand = "0.9"
 rand_core = { version = "0.9", default-features = false, features = ["os_rng"] }
 

curve25519-dalek/src/backend/serial/u32/scalar.rs

@@ -197,15 +197,33 @@ impl Scalar29 {
         }
 
         // conditionally add l if the difference is negative
+        difference.conditional_add_l(Choice::from((borrow >> 31) as u8));
+        difference
+    }
+
+    pub(crate) fn conditional_add_l(&mut self, condition: Choice) -> u32 {
         let mut carry: u32 = 0;
+        let mask = (1u32 << 29) - 1;
+
         for i in 0..9 {
-            let underflow = Choice::from((borrow >> 31) as u8);
-            let addend = u32::conditional_select(&0, &constants::L[i], underflow);
-            carry = (carry >> 29) + difference[i] + addend;
-            difference[i] = carry & mask;
+            let addend = u32::conditional_select(&0, &constants::L[i], condition);
+            carry = (carry >> 29) + self[i] + addend;
+            self[i] = carry & mask;
         }
+        carry
+    }
 
-        difference
+    /// Compute a raw in-place carrying right shift over the limbs.
+    #[inline(always)]
+    pub(crate) fn shr1_assign(&mut self) -> u32 {
+        let mut carry: u32 = 0;
+        for i in (0..9).rev() {
+            let limb = self[i];
+            let next_carry = limb & 1;
+            self[i] = (limb >> 1) | (carry << 28);
+            carry = next_carry;
+        }
+        carry
     }
 
     /// Compute `a * b`.

curve25519-dalek/src/backend/serial/u64/scalar.rs

@@ -186,15 +186,34 @@ impl Scalar52 {
         }
 
         // conditionally add l if the difference is negative
+        difference.conditional_add_l(Choice::from((borrow >> 63) as u8));
+        difference
+    }
+
+    pub(crate) fn conditional_add_l(&mut self, condition: Choice) -> u64 {
         let mut carry: u64 = 0;
+        let mask = (1u64 << 52) - 1;
+
         for i in 0..5 {
-            let underflow = Choice::from((borrow >> 63) as u8);
-            let addend = u64::conditional_select(&0, &constants::L[i], underflow);
-            carry = (carry >> 52) + difference[i] + addend;
-            difference[i] = carry & mask;
+            let addend = u64::conditional_select(&0, &constants::L[i], condition);
+            carry = (carry >> 52) + self[i] + addend;
+            self[i] = carry & mask;
         }
 
-        difference
+        carry
+    }
+
+    /// Compute a raw in-place carrying right shift over the limbs.
+    #[inline(always)]
+    pub(crate) fn shr1_assign(&mut self) -> u64 {
+        let mut carry: u64 = 0;
+        for i in (0..5).rev() {
+            let limb = self[i];
+            let next_carry = limb & 1;
+            self[i] = (limb >> 1) | (carry << 51);
+            carry = next_carry;
+        }
+        carry
     }
 
     /// Compute `a * b`

curve25519-dalek/src/ristretto.rs

@@ -1321,6 +1321,8 @@ impl Zeroize for RistrettoPoint {
 mod test {
     use super::*;
     use crate::edwards::CompressedEdwardsY;
+    #[cfg(feature = "group")]
+    use proptest::prelude::*;
 
     use rand_core::{OsRng, TryRngCore};
 
@@ -1867,6 +1869,39 @@ mod test {
         }
     }
 
+    #[cfg(feature = "group")]
+    proptest! {
+        #[test]
+        fn multiply_double_and_compress_random_points(
+            p1 in any::<[u8; 64]>(),
+            p2 in any::<[u8; 64]>(),
+            s1 in any::<[u8; 32]>(),
+            s2 in any::<[u8; 32]>(),
+        ) {
+            use group::Group;
+
+            let scalars = [
+                Scalar::from_bytes_mod_order(s1),
+                Scalar::ZERO,
+                Scalar::from_bytes_mod_order(s2),
+            ];
+
+            let points = [
+                RistrettoPoint::from_uniform_bytes(&p1),
+                <RistrettoPoint as Group>::identity(),
+                RistrettoPoint::from_uniform_bytes(&p2),
+            ];
+
+            let multiplied_points: [_; 3] =
+                core::array::from_fn(|i| scalars[i].div_by_2() * points[i]);
+            let compressed = RistrettoPoint::double_and_compress_batch(&multiplied_points);
+
+            for ((s, P), P2_compressed) in scalars.iter().zip(points).zip(compressed) {
+                prop_assert_eq!(P2_compressed, (s * P).compress());
+            }
+        }
+    }
+
     #[test]
     #[cfg(feature = "alloc")]
     fn vartime_precomputed_vs_nonprecomputed_multiscalar() {

curve25519-dalek/src/scalar.rs

@@ -831,6 +831,22 @@ impl Scalar {
         ret
     }
 
+    /// Compute `b` such that `b + b = a mod modulus`.
+    pub fn div_by_2(&self) -> Self {
+        // We are looking for such `b` that `b + b = a mod modulus`.
+        // Two possibilities:
+        // - if `a` is even, we can just divide by 2;
+        // - if `a` is odd, we divide `(a + modulus)` by 2.
+        let is_odd = Choice::from(self.as_bytes()[0] & 1);
+        let mut scalar = self.unpack();
+        scalar.conditional_add_l(is_odd);
+
+        let carry = scalar.shr1_assign();
+        debug_assert_eq!(carry, 0);
+
+        scalar.pack()
+    }
+
     /// Get the bits of the scalar, in little-endian order
     pub(crate) fn bits_le(&self) -> impl DoubleEndedIterator<Item = bool> + '_ {
         (0..256).map(|i| {
@@ -1677,6 +1693,23 @@ pub(crate) mod test {
         }
     }
 
+    #[test]
+    fn div_by_2() {
+        // test a range of small scalars
+        for i in 0u64..32 {
+            let scalar = Scalar::from(i);
+            let dividend = scalar.div_by_2();
+            assert_eq!(scalar, dividend + dividend);
+        }
+
+        // test a range of scalars near the modulus
+        for i in 0u64..32 {
+            let scalar = Scalar::ZERO - Scalar::from(i);
+            let dividend = scalar.div_by_2();
+            assert_eq!(scalar, dividend + dividend);
+        }
+    }
+
     #[test]
     fn reduce() {
         let biggest = Scalar::from_bytes_mod_order([0xff; 32]);