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A new nonlinear Rao-Nam like symmetric key encryption scheme is presented inthis paper. QC-LDPC lattices that are practically implementable in highdimensions due to their low complexity encoding and decoding algorithms, areused in our design. Then, a joint scheme is proposed which is capable ofencrypting, encoding and data modulation simultaneously. The proposedcryptosystem withstands all variants of chosen plaintext attacks applied onRao-Nam like cryptosystems due to its nonlinearity. The sparseness of theparity-check matrix of QC-LDPC lattices, quasi-cyclic nature of their generatorand parity-check matrices, simple hardware structure for generating intentionalerror vector, permutation and nonlinear functions, result in a small key sizefor our scheme. The lattice codes related to the lattices used in this paperhave high rate which are suitable for bandlimited AWGN channels. Therefore, thejoint scheme based on these lattices facilitates secure, reliable and efficientdata transmission in bandlimited AWGN channels.

A Lattice Based Joint Encryption, Encoding and Modulation Scheme