curve: Support MSM #static scalars <= #static points (#668)

curve25519-dalek/src/backend/serial/scalar_mul/precomputed_straus.rs

@@ -75,7 +75,7 @@ impl VartimePrecomputedMultiscalarMul for VartimePrecomputedStraus {
 
         let sp = self.static_lookup_tables.len();
         let dp = dynamic_lookup_tables.len();
-        assert_eq!(sp, static_nafs.len());
+        assert!(sp >= static_nafs.len());
         assert_eq!(dp, dynamic_nafs.len());
 
         // We could save some doublings by looking for the highest
@@ -99,7 +99,7 @@ impl VartimePrecomputedMultiscalarMul for VartimePrecomputedStraus {
             }
 
             #[allow(clippy::needless_range_loop)]
-            for i in 0..sp {
+            for i in 0..static_nafs.len() {
                 let t_ij = static_nafs[i][j];
                 match t_ij.cmp(&0) {
                     Ordering::Greater => {

curve25519-dalek/src/backend/vector/scalar_mul/precomputed_straus.rs

@@ -83,7 +83,7 @@ pub mod spec {
 
             let sp = self.static_lookup_tables.len();
             let dp = dynamic_lookup_tables.len();
-            assert_eq!(sp, static_nafs.len());
+            assert!(sp >= static_nafs.len());
             assert_eq!(dp, dynamic_nafs.len());
 
             // We could save some doublings by looking for the highest
@@ -107,7 +107,7 @@ pub mod spec {
                 }
 
                 #[allow(clippy::needless_range_loop)]
-                for i in 0..sp {
+                for i in 0..static_nafs.len() {
                     let t_ij = static_nafs[i][j];
                     match t_ij.cmp(&0) {
                         Ordering::Greater => {

curve25519-dalek/src/ristretto.rs

@@ -1869,4 +1869,148 @@ mod test {
         assert_eq!(P.compress(), R.compress());
         assert_eq!(Q.compress(), R.compress());
     }
+
+    #[test]
+    #[cfg(feature = "alloc")]
+    fn partial_precomputed_mixed_multiscalar_empty() {
+        let mut rng = rand::thread_rng();
+
+        let n_static = 16;
+        let n_dynamic = 8;
+
+        let static_points = (0..n_static)
+            .map(|_| RistrettoPoint::random(&mut rng))
+            .collect::<Vec<_>>();
+
+        // Use zero scalars
+        let static_scalars = Vec::new();
+
+        let dynamic_points = (0..n_dynamic)
+            .map(|_| RistrettoPoint::random(&mut rng))
+            .collect::<Vec<_>>();
+
+        let dynamic_scalars = (0..n_dynamic)
+            .map(|_| Scalar::random(&mut rng))
+            .collect::<Vec<_>>();
+
+        // Compute the linear combination using precomputed multiscalar multiplication
+        let precomputation = VartimeRistrettoPrecomputation::new(static_points.iter());
+        let result_multiscalar = precomputation.vartime_mixed_multiscalar_mul(
+            &static_scalars,
+            &dynamic_scalars,
+            &dynamic_points,
+        );
+
+        // Compute the linear combination manually
+        let mut result_manual = RistrettoPoint::identity();
+        for i in 0..static_scalars.len() {
+            result_manual += static_points[i] * static_scalars[i];
+        }
+        for i in 0..n_dynamic {
+            result_manual += dynamic_points[i] * dynamic_scalars[i];
+        }
+
+        assert_eq!(result_multiscalar, result_manual);
+    }
+
+    #[test]
+    #[cfg(feature = "alloc")]
+    fn partial_precomputed_mixed_multiscalar() {
+        let mut rng = rand::thread_rng();
+
+        let n_static = 16;
+        let n_dynamic = 8;
+
+        let static_points = (0..n_static)
+            .map(|_| RistrettoPoint::random(&mut rng))
+            .collect::<Vec<_>>();
+
+        // Use one fewer scalars
+        let static_scalars = (0..n_static - 1)
+            .map(|_| Scalar::random(&mut rng))
+            .collect::<Vec<_>>();
+
+        let dynamic_points = (0..n_dynamic)
+            .map(|_| RistrettoPoint::random(&mut rng))
+            .collect::<Vec<_>>();
+
+        let dynamic_scalars = (0..n_dynamic)
+            .map(|_| Scalar::random(&mut rng))
+            .collect::<Vec<_>>();
+
+        // Compute the linear combination using precomputed multiscalar multiplication
+        let precomputation = VartimeRistrettoPrecomputation::new(static_points.iter());
+        let result_multiscalar = precomputation.vartime_mixed_multiscalar_mul(
+            &static_scalars,
+            &dynamic_scalars,
+            &dynamic_points,
+        );
+
+        // Compute the linear combination manually
+        let mut result_manual = RistrettoPoint::identity();
+        for i in 0..static_scalars.len() {
+            result_manual += static_points[i] * static_scalars[i];
+        }
+        for i in 0..n_dynamic {
+            result_manual += dynamic_points[i] * dynamic_scalars[i];
+        }
+
+        assert_eq!(result_multiscalar, result_manual);
+    }
+
+    #[test]
+    #[cfg(feature = "alloc")]
+    fn partial_precomputed_multiscalar() {
+        let mut rng = rand::thread_rng();
+
+        let n_static = 16;
+
+        let static_points = (0..n_static)
+            .map(|_| RistrettoPoint::random(&mut rng))
+            .collect::<Vec<_>>();
+
+        // Use one fewer scalars
+        let static_scalars = (0..n_static - 1)
+            .map(|_| Scalar::random(&mut rng))
+            .collect::<Vec<_>>();
+
+        // Compute the linear combination using precomputed multiscalar multiplication
+        let precomputation = VartimeRistrettoPrecomputation::new(static_points.iter());
+        let result_multiscalar = precomputation.vartime_multiscalar_mul(&static_scalars);
+
+        // Compute the linear combination manually
+        let mut result_manual = RistrettoPoint::identity();
+        for i in 0..static_scalars.len() {
+            result_manual += static_points[i] * static_scalars[i];
+        }
+
+        assert_eq!(result_multiscalar, result_manual);
+    }
+
+    #[test]
+    #[cfg(feature = "alloc")]
+    fn partial_precomputed_multiscalar_empty() {
+        let mut rng = rand::thread_rng();
+
+        let n_static = 16;
+
+        let static_points = (0..n_static)
+            .map(|_| RistrettoPoint::random(&mut rng))
+            .collect::<Vec<_>>();
+
+        // Use zero scalars
+        let static_scalars = Vec::new();
+
+        // Compute the linear combination using precomputed multiscalar multiplication
+        let precomputation = VartimeRistrettoPrecomputation::new(static_points.iter());
+        let result_multiscalar = precomputation.vartime_multiscalar_mul(&static_scalars);
+
+        // Compute the linear combination manually
+        let mut result_manual = RistrettoPoint::identity();
+        for i in 0..static_scalars.len() {
+            result_manual += static_points[i] * static_scalars[i];
+        }
+
+        assert_eq!(result_multiscalar, result_manual);
+    }
 }

curve25519-dalek/src/traits.rs

@@ -285,7 +285,7 @@ pub trait VartimeMultiscalarMul {
 ///   to be composed into the input iterators.
 ///
 /// All methods require that the lengths of the input iterators be
-/// known and matching, as if they were `ExactSizeIterator`s.  (It
+/// known, as if they were `ExactSizeIterator`s.  (It
 /// does not require `ExactSizeIterator` only because that trait is
 /// broken).
 pub trait VartimePrecomputedMultiscalarMul: Sized {
@@ -306,8 +306,10 @@ pub trait VartimePrecomputedMultiscalarMul: Sized {
     /// $$
     /// where the \\(B_j\\) are the points that were supplied to `new`.
     ///
-    /// It is an error to call this function with iterators of
-    /// inconsistent lengths.
+    /// It is valid for \\(b_i\\) to have a shorter length than \\(B_j\\).
+    /// In this case, any "unused" points are ignored in the computation.
+    /// It is an error to call this function if \\(b_i\\) has a longer
+    /// length than \\(B_j\\).
     ///
     /// The trait bound aims for maximum flexibility: the input must
     /// be convertable to iterators (`I: IntoIter`), and the
@@ -337,8 +339,11 @@ pub trait VartimePrecomputedMultiscalarMul: Sized {
     /// $$
     /// where the \\(B_j\\) are the points that were supplied to `new`.
     ///
-    /// It is an error to call this function with iterators of
-    /// inconsistent lengths.
+    /// It is valid for \\(b_i\\) to have a shorter length than \\(B_j\\).
+    /// In this case, any "unused" points are ignored in the computation.
+    /// It is an error to call this function if \\(b_i\\) has a longer
+    /// length than \\(B_j\\), or if \\(a_i\\) and \\(A_i\\) do not have
+    /// the same length.
     ///
     /// The trait bound aims for maximum flexibility: the inputs must be
     /// convertable to iterators (`I: IntoIter`), and the iterator's items
@@ -378,8 +383,11 @@ pub trait VartimePrecomputedMultiscalarMul: Sized {
     ///
     /// If any of the dynamic points were `None`, return `None`.
     ///
-    /// It is an error to call this function with iterators of
-    /// inconsistent lengths.
+    /// It is valid for \\(b_i\\) to have a shorter length than \\(B_j\\).
+    /// In this case, any "unused" points are ignored in the computation.
+    /// It is an error to call this function if \\(b_i\\) has a longer
+    /// length than \\(B_j\\), or if \\(a_i\\) and \\(A_i\\) do not have
+    /// the same length.
     ///
     /// This function is particularly useful when verifying statements
     /// involving compressed points.  Accepting `Option<Point>` allows