x-only point addition formula and faster torsion basis generation in compressed SIKE
The optimization of the main key compression bottlenecks of the supersingular isogeny key encapsulation mechanism (SIKE) has been a target of research in the last few years. Significant improvements were introduced in the recent works of Costello et al. [6] and Zanon et al. [17,18]. The combination of the techniques in [17,18] reduced the running time of binary torsion basis generation in decompression by a factor of 29 compared to previous work [6]. On the other hand, generating such a basis still takes almost a million cycles on an Intel Core i5-6267U. In this paper, we continue the work of [18] and introduce a technique that drops the complexity of binary torsion basis generation by a factor log p in the number of underlying field multiplications. In particular, our experimental results show that a basis can be generated in about 1.3k cycles, attaining an improvement by a factor more than 600. Although this result eliminates one of the key compression bottlenecks, many other bottlenecks remain. In addition, we give further improvements for the ternary torsion generation with significant impact on the related decompression procedure. Moreover, a new trade-off between ciphertext sizes vs decapsulation speed and storage is introduced and achieves a 2 times faster decapsulation.