Code-based Cryptosystem from Quasi-Cyclic Elliptic Codes
With the fast development of quantum computation, codebased cryptography arises public concern as a candidate of post quantum cryptography. However, the large key-size becomes a main drawback such that the code-based schemes seldom become practical although they performed pretty well on the speed of both encryption and decryption algorithm. Algebraic geometry codes was considered to be a good solution to reduce the size of keys, but because of its special construction, there have lots of attacks against them. In this paper, we propose a public key encryption scheme based on elliptic codes which can resist the known attacks. By using automorphism on the rational points of the elliptic curve, we construct quasi-cyclic elliptic codes, which reduce the key size further. 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 the known attacks for AG codes based cryptosystem.