一种基于量子准循环LDPC码的McEliece公钥密码算法

Quantum McEliece Public-Key Cryptosystem Based on Quantum QC-LDPC Codes

量子公钥体制包括无条件安全的量子公钥和计算安全的量子公钥密码。以经典公钥算法为基础,结合量子密码特性,研究一种基于量子计算安全的公钥密码;在GF(4)域,量子低密度奇偶校码是一线性码,存在BP快速译码算法。由此提出基于量子准循环LDPC码的量子McEliece公钥体制,给出该公钥体制的加密和解密过程。并通过数值仿真方法,分析该体制的安全性。研究结果表明,与经典方法相比,基于准循环量子LDPC码的McEliece公钥体制极大地扩展了密钥空间,有效地提高了系统的安全性,相对于经典McEliece的工作因子(274),量子McE-liece的工作因子达到2270,传输效率为0.60,且可有效地抵抗量子Grover算法攻击。

Quantum public-key cryptosystem includes unconditionally secure one and computationally secure one. In this paper, we presents a quantum public-key cryptosystem of computationally secure by using classical public key algorithm. Quantum LDPC codes is a linear codes over GF （4）, and there exists a quick decoding algorithm, such as BP algorithm. We propose using quantum QC-LDPC codes. We give the encryption a quantum McEliece public-key cryptosystem and decryption of this cryptosystem. By numerical simulation, we analyze the performance of this cryptosystem over quantum McEliece channel. Compared with classical McEliece algorithm, quantum one expands the keyspace greatly, and improves the security of cryptosystem. It is shown that the work factors have been improved from 2TM （ classical McEliece algorithm） to 2^570（ quantum MeElieee algorithm） when transmission rate is 0.60, and quantum one can effectively resist quantum Grover algorithm attack.