diff --git a/src/traits.rs b/src/traits.rs
index 8db963a..630e510 100644
--- a/src/traits.rs
+++ b/src/traits.rs
@@ -224,6 +224,166 @@ pub trait VartimeMultiscalarMul {
     }
 }
 
+/// A trait for constant-time multiscalar multiplication with precomputation.
+///
+/// A general multiscalar multiplication with precomputation can be written as
+/// $$
+/// Q = a_1 A_1 + \cdots + a_n A_n + b_1 B_1 + \cdots + b_m B_m,
+/// $$
+/// where the \\(B_i\\) are *static* points, for which precomputation
+/// is possible, and the \\(A_j\\) are *dynamic* points, for which
+/// precomputation is not possible.
+pub trait PrecomputedMultiscalarMul: Sized {
+    /// The type of point to be multiplied, e.g., `RistrettoPoint`.
+    type Point;
+
+    /// Given the static points \\( B_i \\), perform precomputation
+    /// and return the precomputation data.
+    fn new<I>(static_points: I) -> Self
+    where
+        I: IntoIterator,
+        I::Item: Borrow<Self::Point>;
+
+    /// Given `static_scalars`, an iterator of (possibly secret)
+    /// scalars \\(b_i\\), `dynamic_scalars`, an iterator of (possibly
+    /// secret) scalars \\(a_i\\), and `dynamic_points`, an iterator
+    /// of points \\(A_i\\), compute
+    /// $$
+    /// Q = a_1 A_1 + \cdots + a_n A_n + b_1 B_1 + \cdots + b_m B_m,
+    /// $$
+    /// 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.
+    ///
+    /// The trait bound aims for maximum flexibility: the inputs must be
+    /// convertable to iterators (`I: IntoIter`), and the iterator's items
+    /// must be `Borrow<Scalar>` (or `Borrow<Point>`), to allow
+    /// iterators returning either `Scalar`s or `&Scalar`s.
+    fn mixed_multiscalar_mul<I, J, K>(
+        &self,
+        static_scalars: I,
+        dynamic_scalars: J,
+        dynamic_points: K,
+    ) -> Self::Point
+    where
+        I: IntoIterator,
+        I::Item: Borrow<Scalar>,
+        J: IntoIterator,
+        J::Item: Borrow<Scalar>,
+        K: IntoIterator,
+        K::Item: Borrow<Self::Point>;
+
+    /// Given `static_scalars`, an iterator of (possibly secret)
+    /// scalars \\(b_i\\), compute
+    /// $$
+    /// Q = b_1 B_1 + \cdots + b_m B_m,
+    /// $$
+    /// 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.
+    ///
+    /// The trait bound aims for maximum flexibility: the input must
+    /// be convertable to iterators (`I: IntoIter`), and the
+    /// iterator's items must be `Borrow<Scalar>`, to allow iterators
+    /// returning either `Scalar`s or `&Scalar`s.
+    fn multiscalar_mul<I>(&self, static_scalars: I) -> Self::Point
+    where
+        I: IntoIterator,
+        I::Item: Borrow<Scalar>,
+    {
+        use core::iter;
+
+        Self::mixed_multiscalar_mul(
+            self,
+            static_scalars,
+            iter::empty::<Scalar>(),
+            iter::empty::<Self::Point>(),
+        )
+    }
+}
+
+/// A trait for variable-time multiscalar multiplication with precomputation.
+///
+/// A general multiscalar multiplication with precomputation can be written as
+/// $$
+/// Q = a_1 A_1 + \cdots + a_n A_n + b_1 B_1 + \cdots + b_m B_m,
+/// $$
+/// where the \\(B_i\\) are *static* points, for which precomputation
+/// is possible, and the \\(A_j\\) are *dynamic* points, for which
+/// precomputation is not possible.
+pub trait VartimePrecomputedMultiscalarMul: Sized {
+    /// The type of point to be multiplied, e.g., `RistrettoPoint`.
+    type Point;
+
+    /// Given the static points \\( B_i \\), perform precomputation
+    /// and return the precomputation data.
+    fn new<I>(static_points: I) -> Self
+    where
+        I: IntoIterator,
+        I::Item: Borrow<Self::Point>;
+
+    /// Given `static_scalars`, an iterator of public scalars
+    /// \\(b_i\\), `dynamic_scalars`, an iterator of public scalars
+    /// \\(a_i\\), and `dynamic_points`, an iterator of points
+    /// \\(A_i\\), compute
+    /// $$
+    /// Q = a_1 A_1 + \cdots + a_n A_n + b_1 B_1 + \cdots + b_m B_m,
+    /// $$
+    /// 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.
+    ///
+    /// The trait bound aims for maximum flexibility: the inputs must be
+    /// convertable to iterators (`I: IntoIter`), and the iterator's items
+    /// must be `Borrow<Scalar>` (or `Borrow<Point>`), to allow
+    /// iterators returning either `Scalar`s or `&Scalar`s.
+    fn vartime_mixed_multiscalar_mul<I, J, K>(
+        &self,
+        static_scalars: I,
+        dynamic_scalars: J,
+        dynamic_points: K,
+    ) -> Self::Point
+    where
+        I: IntoIterator,
+        I::Item: Borrow<Scalar>,
+        J: IntoIterator,
+        J::Item: Borrow<Scalar>,
+        K: IntoIterator,
+        K::Item: Borrow<Self::Point>;
+
+    /// Given `static_scalars`, an iterator of public scalars
+    /// \\(b_i\\), compute
+    /// $$
+    /// Q = b_1 B_1 + \cdots + b_m B_m,
+    /// $$
+    /// 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.
+    ///
+    /// The trait bound aims for maximum flexibility: the input must
+    /// be convertable to iterators (`I: IntoIter`), and the
+    /// iterator's items must be `Borrow<Scalar>`, to allow iterators
+    /// returning either `Scalar`s or `&Scalar`s.
+    fn vartime_multiscalar_mul<I>(&self, static_scalars: I) -> Self::Point
+    where
+        I: IntoIterator,
+        I::Item: Borrow<Scalar>,
+    {
+        use core::iter;
+
+        Self::vartime_mixed_multiscalar_mul(
+            self,
+            static_scalars,
+            iter::empty::<Scalar>(),
+            iter::empty::<Self::Point>(),
+        )
+    }
+}
+
 // ------------------------------------------------------------------------
 // Private Traits
 // ------------------------------------------------------------------------