An Alternative Approach for Computing Discrete Logarithms in Compressed SIDH

TL;DR

This paper introduces a new approach to compute fewer discrete logarithms in compressed SIDH, reducing computational steps and offering a flexible trade-off between memory and efficiency, with competitive performance.

Contribution

It presents novel algorithms that compute only 3 discrete logarithms instead of 4 in compressed SIDH, optimizing efficiency and memory usage.

Findings

Algorithms perform close to previous methods

Better performance in specific cases

Trade-off between memory and efficiency achieved

Abstract

Currently, public-key compression of supersingular isogeny Diffie-Hellman (SIDH) and its variant, supersingular isogeny key encapsulation (SIKE) involve pairing computation and discrete logarithm computation. In this paper, we propose novel methods to compute only 3 discrete logarithms instead of 4, in exchange for computing a lookup table efficiently. The algorithms also allow us to make a trade-off between memory and efficiency. Our implementation shows that the efficiency of our algorithms is close to that of the previous work, and our algorithms perform better in some special cases.