In recent years, the isogeny-based protocol, namely supersingular isogeny Diffie-Hellman (SIDH) has become highly attractive for its small public key size. In addition, public-key compression makes supersingular isogeny key encapsulation scheme (SIKE) more competitive in the NIST post-quantum cryptography standardization effort. However, compared to other post-quantum protocols, the computational cost of SIDH is relatively high, and so is public-key compression. On the other hand, the storage for pairing computation and discrete logarithms to speed up the current implementation of the key compression is somewhat large.

In this paper, we mainly improve the performance of public-key compression of SIDH, especially the efficiency and the storage of pairing computation involved. Our experimental results show that the memory requirement for pairing computation is reduced by a factor of about 1.31, and meanwhile, the instantiation of key generation of SIDH is 3.99% ~ 5.95% faster than the current state-of-the-art. Besides, in the case of Bob, we present another method to further reduce the storage cost, while the acceleration is not as obvious as the former.

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