SimS: A Simplification of SiGamal

At Asiacrypt 2020, Moriya et al. introduced two new IND-CPA secure supersingular isogeny based Public Key Encryption (PKE) protocols: SiGamal and C-SiGamal. Unlike the PKEs canonically derived from SIDH CSIDH, protocols provide security without use of hash functions. C-SiGamal are however not IND-CCA secure. suggested a variant that could be secure, but left its study as an open problem. In this paper, we revisit by First, show for is, in fact, Secondly, propose isogeny-based PKE protocol named SimS, obtained simplifying SiGamal. SimS has smaller public keys ciphertexts than (C-)SiGamal it is more efficient. We prove under CSIDH assumptions one Knowledge Exponent-type assumption introduce. Interestingly, also much closer to protocol, facilitating comparison between CSIDH.