A Lattice Based Joint Encryption, Encoding and Modulation Scheme

Abstract: A new nonlinear Rao-Nam like symmetric key encryption scheme is presented in this paper. QC-LDPC lattices that are practically implementable in high dimensions due to their low complexity encoding and decoding algorithms, are used in our design. Then, a joint scheme is proposed which is capable of encrypting, encoding and data modulation simultaneously. The proposed cryptosystem withstands all variants of chosen plaintext attacks applied on Rao-Nam like cryptosystems due to its nonlinearity. The sparseness of the parity-check matrix of QC-LDPC lattices, quasi-cyclic nature of their generator and parity-check matrices, simple hardware structure for generating intentional error vector, permutation and nonlinear functions, result in a small key size for our scheme. The lattice codes related to the lattices used in this paper have high rate which are suitable for bandlimited AWGN channels. Therefore, the joint scheme based on these lattices facilitates secure, reliable and efficient data transmission in bandlimited AWGN channels.