ECC$$^2$$: Error Correcting Code and Elliptic Curve Based Cryptosystem

Abstract

With the fast development of quantum computation, code-based cryptography arises public concern as a candidate for post quantum cryptography. However, the large key-size becomes a drawback such that the code-based schemes seldom become practical. Algebraic geometry codes was considered to be a good solution to reduce the size of keys, but its special structure results in lots of attacks. In this paper, we propose a public key encryption scheme based on elliptic codes which can resist the known attacks. By choosing the rational points carefully, we build elliptic codes that can resist Minder’s attack. We apply the list decoding algorithm to decryption thus more errors beyond half of the minimum distance of the code could be correct, which is the key point to resist other known attacks for AG code based cryptosystems.