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

This paper proposes a new cryptosystem system that combines DNA cryptography and algebraic curves defined over different Galois fields. The security of the proposed cryptosystem is based on the combination of DNA encoding, a compression process using a hyperelliptic curve over a Galois field $$GF\left( 2^{p}\right) $$ G F 2 p , and coding via an algebraic geometric code built using a Hermitian curve on a Galois field $$GF\left( 2^{2q}\right) $$ G F 2 2 q , where $$p> 2q$$ p > 2 q . The proposed cryptosystem resists the newest attacks found in the literature because there is no linear relationship between the original data and the information encoded with the Hermitian code. Further, the work factor for such attacks increases proportionally to the number of possible choices for the generator matrix of the Hermitian code. Simulations in terms of BER and signal-to-noise ratio (SNR) are included, which evaluate the gain of the transmitted data in an AWGN channel. The performance of the DNA/AG cryptosystem scheme is compared with un-coded QPSK, and the McEliece code in terms of BER. Further, the proposed DNA/AG system outperforms the security level of the McEliece algorithm.