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.
Supersingular isogeny Diffie-Hellman (SIDH) is attractive for its relatively small public key size, but it is still unsatisfactory due to its efficiency, compared to other post-quantum proposals. In this paper, we focus on the performance of SIDH when the starting curve is E 6 : y 2 = x 3 + 6x 2 + x, which is fixed in Round-3 SIKE implementation. Inspired by previous works [1], [2], we present several tricks to accelerate key generation of SIDH and each process of SIKE. Our experimental results show that the performance of this work is at least 6.09% faster than that of the SIKE implementation, and we can further improve the performance when large storage is available.
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