Efficient Software Implementation of the SIKE Protocol Using New Data Representation

In the SIKE implementation, the Montgomery representation has been mostly adopted in the finite field arithmetic computing as the corresponding reduction algorithm is considered the fastest method for implementing the modular reduction. In this paper, we propose a new data representation for the supersingular isogeny-based elliptic-curve cryptography (ECC), of which the SIKE is a subclass. The new representation can facilitate faster modular reduction implementation than the Montgomery reduction. Meanwhile, the other finite field arithmetic operations in the ECC can also benefit from the proposed data representation. We have implemented all the arithmetic operations in C language with constant execution time based on our proposed data representation and applied them to the newest SIKE software library. Targeting at the SIKEp751, we run our design and the optimized generic implementation on a 2.6GHz Intel Xeon E5-2690 processor. The experiment results show that for the parameters of SIKEp751, the proposed modular reduction algorithm is about 2.61x faster than the best Montgomery one and our scheme also performs significantly better for the other finite field operations. With these improvements, the overall software implementation for the SIKEp751 achieves about 1.65x speedup compared to the state-of-the-art generic implementatio