Efficient secure channel coding scheme based on low‐density Lattice codes

Abstract

In this study, the authors introduce an efficient secure channel coding (joint cryptography-channel coding) scheme based on Latin square low-density lattice codes (Latin square LDLCs) over unconstrained power additive white Gaussian noise channel. They benefit the properties of Latin square LDLCs to dramatically reduce the key size of the proposed scheme while having an acceptable level of security compared with previous similar schemes. To reduce the key size, they consider two approaches: (i) saving the generating sequence of parity-check matrix of used Latin square LDLC as the part of secret key set; (ii) employing the Hermite normal form of the generator matrix of used Latin square LDLC as the encryption matrix. To provide an acceptable level of security, they consider three other strategies: (i) applying two hard problems related to lattices, i.e. shortest basis problem and closest vector problem; (ii) using a random rational vector as the perturbation (error) vector; (iii) exploiting the special joint encryption/LDLC encoding and joint decryption/LDLC decoding algorithms. Besides, the study discusses other efficiency analysis results consisting error performance and computational complexity of the proposed scheme.