Speeding up Curve25519 using Toeplitz Matrix-vector Multiplication

This paper proposes a new multiplication algorithm over F-2(255)-19 where the de-facto standard Curve25519 [2] algorithm is based on. Our algorithm for the underlying finite field multiplication exploits the Toeplitz matrix-vector multiplication and achieves salient results. We have used a new radix representation that is infeasible when used with schoolbook multiplication techniques but has notable advantages when used with Toeplitz matrix-vector multiplication methods. We present the new algorithm and discuss the comparison and implementation details. In addition, we evaluate the delay complexity of four-core almost embarrassingly parallel implementation of our algorithm when computations are performed using multi-core systems.