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Goldreich-Goldwasser-Halevi (GGH) public key cryptosystem is an instance oflattice-based cryptosystems whose security is based on the hardness of latticeproblems. In fact, GGH cryptosystem is the lattice version of the firstcode-based cryptosystem, proposed by McEliece. However, it has a number ofdrawbacks such as; large public key length and low security level. On the otherhand, Low Density Lattice Codes (LDLCs) are the practical classes of latticecodes which can achieve capacity on the additive white Gaussian noise (AWGN)channel with low complexity decoding algorithm. This paper introduces a publickey cryptosystem based on LDLCs to withdraw the drawbacks of GGH cryptosystem.To reduce the key length, we employ the generator matrix of the used LDLC inHermite normal form (HNF) as the public key. Also, by exploiting the lineardecoding complexity of the used LDLC, the decryption complexity is decreasedcompared with GGH cryptosystem. These increased efficiencies allow us to usethe bigger values of security parameters. Moreover, we exploit the specialGaussian vector whose variance is upper bounded by the Poltyrev limit as theperturbation vector. These techniques can resist the proposed scheme againstthe most efficient attacks to the GGH-like cryptosystems.

Improving GGH Public Key Scheme Using Low Density Lattice Codes