An improved McEliece cryptosystem based on QC-MDPC code with compact key size

The McEliece cryptosystem based on quasi-cyclic moderate-density parity-check with adaptive chosen-ciphertext attack conversion is secure against information set decoding and message-resend attacks. However, it is vulnerable to reaction based key recovery attacks and cannot be implemented over the noise channel. To overcome this problem, we propose an improved McEliece cryptosystem based on quasi-cyclic quasi moderate-density parity-check (QC-QMDPC). In this cryptosystem, a stamp generation function which is based on the pseudorandom sequence is designed to resist the message-resend attack. The random channel noise is employed to enhance security. Furthermore, the upper bound of the density of QC-QMDPC code is proved for optimal efficiency. The index-based storage technique is proposed so that the key size can be reduced to approximately quadruple code length. The encoding and decoding algorithms are optimized to reduce the computational cost on the hardware platform. We analyze the performance of the proposed cryptosystem and compare it with other McEliece cryptosystems. The results show that the proposed cryptosystem is secure against critical attacks while keeping high error correction ability and efficiency.