Enhancing the McEliece Scheme Based on Concatenation of Polar Codes and Blocked QC-LDPC Codes

This paper proposes an enhanced McEliece cryptosystem, leveraging a concatenation scheme of Polar codes and blocked QC-LDPC codes. During the key generation phase, the generator matrices for both Polar and blocked QC-LDPC codes are employed as private keys. These matrices are subsequently multiplied by reversible and random permutation matrices respectively. The products of these multiplications are then combined to form the public key, effectively concealing the structural properties of the generator matrices. In the encryption phase, the plaintext is encrypted sequentially through the Polar codes and the blocked QC-LDPC codes. This process introduces two layers of random error vectors, culminating in the generation of the encrypted ciphertext. The proposed scheme reduces the public key length by 54% and doubles the security level compared to the original McEliece scheme with similar parameters. It also significantly reduces the total key length compared to improved schemes based on Polar codes and QC-LDPC/MDPC codes at an 80-bit security level, and shortens the private key length compared to schemes based on Polar-LDPC concatenated codes. Notably, the scheme is secure against known structural and decoding attacks while increases resistance to information set decoding (ISD) attacks. Through the randomization and hashing of the plaintext, the proposed scheme can achieve IND-CCA2 security.