Fixed-based Montgomery scalar multiplication (#503)

* Fixed-based Montgomery scalar multiplication

Adds `MontgomeryPoint::mul_base` as an API for fixed-base scalar
multiplication which allows for potential future optimizations.

As a baseline implementation, it uses the variable base scalar
multiplication implementation.

This follows the existing `EdwardsPoint::mul_base` and
`RistrettoPoint::mul_base` APIs.

* Added Montgomery mul_base bench

* Switched MontgomeryPoint::mul_base to use EdwardsPoint::mul_base

---------

Co-authored-by: Michael Rosenberg <michael@mrosenberg.pub>

benches/dalek_benchmarks.rs

@@ -1,12 +1,10 @@
 #![allow(non_snake_case)]
 
-use rand::rngs::OsRng;
-use rand::thread_rng;
+use rand::{rngs::OsRng, thread_rng};
 
-use criterion::measurement::Measurement;
-use criterion::BatchSize;
-use criterion::Criterion;
-use criterion::{criterion_group, criterion_main, BenchmarkGroup, BenchmarkId};
+use criterion::{
+    criterion_main, measurement::Measurement, BatchSize, BenchmarkGroup, BenchmarkId, Criterion,
+};
 
 use curve25519_dalek::constants;
 use curve25519_dalek::scalar::Scalar;
@@ -19,26 +17,26 @@ mod edwards_benches {
 
     use curve25519_dalek::edwards::EdwardsPoint;
 
-    fn compress(c: &mut Criterion) {
+    fn compress<M: Measurement>(c: &mut BenchmarkGroup<M>) {
         let B = &constants::ED25519_BASEPOINT_POINT;
         c.bench_function("EdwardsPoint compression", move |b| b.iter(|| B.compress()));
     }
 
-    fn decompress(c: &mut Criterion) {
+    fn decompress<M: Measurement>(c: &mut BenchmarkGroup<M>) {
         let B_comp = &constants::ED25519_BASEPOINT_COMPRESSED;
         c.bench_function("EdwardsPoint decompression", move |b| {
             b.iter(|| B_comp.decompress().unwrap())
         });
     }
 
-    fn consttime_fixed_base_scalar_mul(c: &mut Criterion) {
+    fn consttime_fixed_base_scalar_mul<M: Measurement>(c: &mut BenchmarkGroup<M>) {
         let s = Scalar::from(897987897u64).invert();
         c.bench_function("Constant-time fixed-base scalar mul", move |b| {
             b.iter(|| EdwardsPoint::mul_base(&s))
         });
     }
 
-    fn consttime_variable_base_scalar_mul(c: &mut Criterion) {
+    fn consttime_variable_base_scalar_mul<M: Measurement>(c: &mut BenchmarkGroup<M>) {
         let B = &constants::ED25519_BASEPOINT_POINT;
         let s = Scalar::from(897987897u64).invert();
         c.bench_function("Constant-time variable-base scalar mul", move |b| {
@@ -46,7 +44,7 @@ mod edwards_benches {
         });
     }
 
-    fn vartime_double_base_scalar_mul(c: &mut Criterion) {
+    fn vartime_double_base_scalar_mul<M: Measurement>(c: &mut BenchmarkGroup<M>) {
         c.bench_function("Variable-time aA+bB, A variable, B fixed", |bench| {
             let mut rng = thread_rng();
             let A = EdwardsPoint::mul_base(&Scalar::random(&mut rng));
@@ -58,15 +56,15 @@ mod edwards_benches {
         });
     }
 
-    criterion_group! {
-        name = edwards_benches;
-        config = Criterion::default();
-        targets =
-        compress,
-        decompress,
-        consttime_fixed_base_scalar_mul,
-        consttime_variable_base_scalar_mul,
-        vartime_double_base_scalar_mul,
+    pub(crate) fn edwards_benches() {
+        let mut c = Criterion::default();
+        let mut g = c.benchmark_group("edwards benches");
+
+        compress(&mut g);
+        decompress(&mut g);
+        consttime_fixed_base_scalar_mul(&mut g);
+        consttime_variable_base_scalar_mul(&mut g);
+        vartime_double_base_scalar_mul(&mut g);
     }
 }
 
@@ -211,28 +209,19 @@ mod multiscalar_benches {
         }
     }
 
-    fn multiscalar_multiplications(c: &mut Criterion) {
-        let mut group: BenchmarkGroup<_> = c.benchmark_group("Multiscalar multiplications");
+    pub(crate) fn multiscalar_benches() {
+        let mut c = Criterion::default();
+        let mut g = c.benchmark_group("multiscalar benches");
 
-        consttime_multiscalar_mul(&mut group);
-        vartime_multiscalar_mul(&mut group);
-        vartime_precomputed_pure_static(&mut group);
+        consttime_multiscalar_mul(&mut g);
+        vartime_multiscalar_mul(&mut g);
+        vartime_precomputed_pure_static(&mut g);
 
         let dynamic_fracs = [0.0, 0.2, 0.5];
 
         for frac in dynamic_fracs.iter() {
-            vartime_precomputed_helper(&mut group, *frac);
+            vartime_precomputed_helper(&mut g, *frac);
         }
-
-        group.finish();
-    }
-
-    criterion_group! {
-        name = multiscalar_benches;
-        // Lower the sample size to run the benchmarks faster
-        config = Criterion::default().sample_size(15);
-        targets =
-        multiscalar_multiplications,
     }
 }
 
@@ -240,14 +229,14 @@ mod ristretto_benches {
     use super::*;
     use curve25519_dalek::ristretto::RistrettoPoint;
 
-    fn compress(c: &mut Criterion) {
+    fn compress<M: Measurement>(c: &mut BenchmarkGroup<M>) {
         c.bench_function("RistrettoPoint compression", |b| {
             let B = &constants::RISTRETTO_BASEPOINT_POINT;
             b.iter(|| B.compress())
         });
     }
 
-    fn decompress(c: &mut Criterion) {
+    fn decompress<M: Measurement>(c: &mut BenchmarkGroup<M>) {
         c.bench_function("RistrettoPoint decompression", |b| {
             let B_comp = &constants::RISTRETTO_BASEPOINT_COMPRESSED;
             b.iter(|| B_comp.decompress().unwrap())
@@ -270,26 +259,21 @@ mod ristretto_benches {
         }
     }
 
-    fn double_and_compress_group(c: &mut Criterion) {
-        let mut group: BenchmarkGroup<_> = c.benchmark_group("double & compress batched");
-        double_and_compress_batch(&mut group);
-        group.finish();
-    }
+    pub(crate) fn ristretto_benches() {
+        let mut c = Criterion::default();
+        let mut g = c.benchmark_group("ristretto benches");
 
-    criterion_group! {
-        name = ristretto_benches;
-        config = Criterion::default();
-        targets =
-        compress,
-        decompress,
-        double_and_compress_group,
+        compress(&mut g);
+        decompress(&mut g);
+        double_and_compress_batch(&mut g);
     }
 }
 
 mod montgomery_benches {
     use super::*;
+    use curve25519_dalek::montgomery::MontgomeryPoint;
 
-    fn montgomery_ladder(c: &mut Criterion) {
+    fn montgomery_ladder<M: Measurement>(c: &mut BenchmarkGroup<M>) {
         c.bench_function("Montgomery pseudomultiplication", |b| {
             let B = constants::X25519_BASEPOINT;
             let s = Scalar::from(897987897u64).invert();
@@ -297,17 +281,26 @@ mod montgomery_benches {
         });
     }
 
-    criterion_group! {
-        name = montgomery_benches;
-        config = Criterion::default();
-        targets = montgomery_ladder,
+    fn consttime_fixed_base_scalar_mul<M: Measurement>(c: &mut BenchmarkGroup<M>) {
+        let s = Scalar::from(897987897u64).invert();
+        c.bench_function("Constant-time fixed-base scalar mul", move |b| {
+            b.iter(|| MontgomeryPoint::mul_base(&s))
+        });
+    }
+
+    pub(crate) fn montgomery_benches() {
+        let mut c = Criterion::default();
+        let mut g = c.benchmark_group("montgomery benches");
+
+        montgomery_ladder(&mut g);
+        consttime_fixed_base_scalar_mul(&mut g);
     }
 }
 
 mod scalar_benches {
     use super::*;
 
-    fn scalar_inversion(c: &mut Criterion) {
+    fn scalar_inversion<M: Measurement>(c: &mut BenchmarkGroup<M>) {
         c.bench_function("Scalar inversion", |b| {
             let s = Scalar::from(897987897u64).invert();
             b.iter(|| s.invert());
@@ -332,18 +325,12 @@ mod scalar_benches {
         }
     }
 
-    fn batch_scalar_inversion_group(c: &mut Criterion) {
-        let mut group: BenchmarkGroup<_> = c.benchmark_group("batch scalar inversion");
-        batch_scalar_inversion(&mut group);
-        group.finish();
-    }
+    pub(crate) fn scalar_benches() {
+        let mut c = Criterion::default();
+        let mut g = c.benchmark_group("scalar benches");
 
-    criterion_group! {
-        name = scalar_benches;
-        config = Criterion::default();
-        targets =
-        scalar_inversion,
-        batch_scalar_inversion_group,
+        scalar_inversion(&mut g);
+        batch_scalar_inversion(&mut g);
     }
 }
 

src/montgomery.rs

@@ -118,6 +118,11 @@ impl Zeroize for MontgomeryPoint {
 }
 
 impl MontgomeryPoint {
+    /// Fixed-base scalar multiplication (i.e. multiplication by the base point).
+    pub fn mul_base(scalar: &Scalar) -> Self {
+        EdwardsPoint::mul_base(scalar).to_montgomery()
+    }
+
     /// View this `MontgomeryPoint` as an array of bytes.
     pub const fn as_bytes(&self) -> &[u8; 32] {
         &self.0