Montgomery multiplication is a critical operation in multi-scalar multiplication (MSM) that significantly impacts performance. The current implementation lacks an optimized Montgomery multiplication tailored for Metal, leading to slower field arithmetic operations on iOS devices.
Details
Implement an optimized version of Montgomery multiplication specifically designed for Metal to enhance the efficiency of field operations within the MSM process. This optimization should leverage Metal's capabilities to perform modular arithmetic more efficiently, thereby reducing the overall MSM runtime.
Acceptance criteria
Develop a Metal shader that performs Montgomery multiplication optimized for Metal’s uint data types.
Benchmark various limb sizes (e.g., 12 to 16 bits) to identify the optimal configuration for Metal on iOS devices.
Adapt Gregor Mitscha-Baude's approach for limb sizes suitable for Metal.
Integrate the optimized Montgomery multiplication into the existing MSM pipeline.
Compare performance against the baseline implementation to demonstrate improvement.
Create unit tests to verify the correctness of the optimized Montgomery multiplication.
Problem
Montgomery multiplication is a critical operation in multi-scalar multiplication (MSM) that significantly impacts performance. The current implementation lacks an optimized Montgomery multiplication tailored for Metal, leading to slower field arithmetic operations on iOS devices.
Details
Implement an optimized version of Montgomery multiplication specifically designed for Metal to enhance the efficiency of field operations within the MSM process. This optimization should leverage Metal's capabilities to perform modular arithmetic more efficiently, thereby reducing the overall MSM runtime.
Acceptance criteria
uintdata types.Reference (optional)