Certificateless Identification Schemes Using Supersingular Isogenies

Certificateless public key cryptography (CL-PKC) is a cryptosystem that lies between traditional public key cryptography (PKC) and identity-based cryptography (IBC). It not only removes the inherited key escrow property in IBC, but also is free from the problem of certificate management in PKC. In this paper, we propose a new certificateless identification (CLI) scheme that is based on isogenies between supersingular elliptic curves. Since supersingular isogeny problems are believed to be quantum-resistant, our scheme is post-quantum secure assuming hardness of some computational problems related to supersingular isogenies. Our scheme combines De Feo-Jao-Plût identification scheme and SQISign. Note that compared to all other post-quantum signatures, SQISign has the smallest signature and public key sizes combined, this feature benefits our scheme as well. To our best knowledge, our scheme is the first certificateless identification scheme that is based on supersingular isogenies problems. Moreover, it achieves trust level 3 of publickey cryptosystem.