A new DNA cryptosystem based on AG codes evaluated in gaussian channels

Abstract

This paper proposes a new cryptosystem sys-tem that combines DNA cryptography and algebraic curvesdefined over different Galois fields. The security of the pro-posed cryptosystem is based on the combination of DNAencoding, a compression process using a hyperelliptic curveover a Galois fieldGF(2p), and coding via an algebraic geo-metric code built using a Hermitian curve on a Galois fieldGF(22q), wherep>2q. The proposed cryptosystem resiststhe newest attacks found in the literature because there is nolinear relationship between the original data and the infor-mation encoded with the Hermitian code. Further, the workfactor for such attacks increases proportionally to the numberof possible choices for the generator matrix of the Hermitiancode. Simulations in terms of BER and signal-to-noise ratio(SNR) are included, which evaluate the gain of the trans-mitted data in an AWGN channel. The performance of the DNA/AG cryptosystem scheme is compared with un-codedQPSK, and the McEliece code in terms of BER. Further, theproposed DNA/AG system outperforms the security level ofthe McEliece algorithm.