A new decryption algorithm of the quasi-cyclic low-density parity-check codes based McEliece cryptosystem

The McEliece public-key cryptosystem is believed to resist quantum attacks, but has not been used because of the extremely large public key size. In order to decrease the public key size, quasi-cyclic low-density parity-check (QC-LDPC) codes were used instead of Goppa codes in McEliece cryptosystem. A modified version of QC-LDPC McEliece is quasi-cyclic moderate density parity-check (QC-MDPC) McEliece, which focuses on ensuring fixed security level other than error-correction capability. The QC-MDPC McEliece scheme furtherly reduces the public key size at the cost of higher decryption complexity. However, the decryption algorithm of QC-LDPC McEliece variant has not been optimized. In this paper, we proposed a new decryption algorithm of the QC-LDPC McEliece variant. With the decryption algorithm we proposed, the key size reduces about 20% than the original algorithm, even 8% smaller than QC-MDPC variant.