Code-based cryptography has aroused wide public concern as one of the main candidates for post quantum cryptography to resist attacks against cryptosystems from quantum computation. However, the large key size becomes a drawback that prevents it from wide practical applications although it performs pretty well on the speed of both encryption and decryption. The use of algebraic geometry codes is considered to be a good solution to reduce the key size, but the special structures of algebraic geometry codes results in lots of attacks including Minder’s attack. To cope with the barriers of large key size as well as attacks from the special structures of algebraic codes, we propose a code-based encryption system using elliptic codes. The special structure of elliptic codes helps us to effectively reduce the size of secret key. By choosing the rational points carefully, we build elliptic codes whose minimum weight codeword is hard to sample. Such codes are used in constructing encryption systems such that Minder’s attacks can be resisted. More importantly, we apply the list decoding algorithm in the decryption process thus more errors beyond half of the minimum distance of the code could be corrected, which is the key point to resist other known attacks for algebraic geometry codes based cryptosystems. Our implementation shows that the proposed encryption system performs well on the key size and ciphertext expansion rate.

基于代码的密码学作为后量子密码学的主要候选人之一，已经引起了公众的广泛关注，以抵御来自量子计算的对密码系统的攻击。但是，大的密钥大小成为一个缺点，尽管它在加密和解密的速度上都表现出色，但却阻止了它在广泛的实际应用中使用。代数几何代码的使用被认为是减小密钥大小的好方法，但是代数几何代码的特殊结构导致很多攻击，包括Minder的攻击。为了解决密钥较大的障碍以及代数代码特殊结构的攻击，我们提出了一种使用椭圆代码的基于代码的加密系统。椭圆代码的特殊结构有助于我们有效地减少密钥的大小。通过仔细选择有理点，我们构建了最小权重码字难以采样的椭圆码。此类代码用于构建加密系统，从而可以抵御Minder的攻击。更重要的是，我们在解密过程中应用了列表解码算法，因此可以纠正超出代码最小距离一半的错误，这是抵抗基于代数几何代码的其他已知攻击的关键点。我们的实施表明，所提出的加密系统在密钥大小和密文扩展率上表现良好。我们在解密过程中应用了列表解码算法，因此可以纠正超出代码最小距离一半的错误，这是抵抗基于代数几何代码的其他已知攻击的关键点。我们的实施表明，所提出的加密系统在密钥大小和密文扩展率方面表现良好。我们在解密过程中应用了列表解码算法，因此可以纠正超出代码最小距离一半的错误，这是抵抗基于代数几何代码的其他已知攻击的关键点。我们的实施表明，所提出的加密系统在密钥大小和密文扩展率方面表现良好。