SUMMARYIn this paper, a new cryptographic system is constructed using a combination of a hyperelliptic curve of genus g ¼ 2 over the Galois field GF(2 n ) and a Reed-Solomon code (N, K) over the Galois field GF(2 m ) and this system uses a smaller key than the elliptic curves cryptosystem and the Rivest, Shamir, and Adleman cryptosystem. The design criterion for the combination can be expressed as the data compression condition and addressing capability of the code. In addition, the system performance is compared with other systems; extraordinary improvements of 8 and 16.5 dB can be obtained for a BER=10À5 , when compared with binary phase shift keying and differential chaos shift keying, respectively. This system has a polynomial complexity, which depends on data length and the number of operations in GF(2 n ).

Artículo de publicación ISIA system that achieves compression using artificial DNA packaging with the support of two algebraic curves is presented, whereby the Hermitian channel code algorithm introduces gain and safety. Additionally, performance results are presented with a gain of 7 dB against uncoded quadrature phase shift keying and 1 dB against McEliece, for a bit error rate of 10(-3). The results of the security levels compared with the McEliece system are also presented.Project USACH/Dicyt 061413SG Center for Multidisciplinary Research on Signal Processing Conicyt/ACT112

A B S T R A C TA Galois field GFðp n Þ with p ! 2 a prime number and n ! 1 is a mathematical structure widely used in Cryptography and Error Correcting Codes Theory. In this paper, we propose a novel DNA-based model for arithmetic over GFðp n Þ. Our model has three main advantages over other previously described models. First, it has a flexible implementation in the laboratory that allows the realization arithmetic calculations in parallel for p ! 2, while the tile assembly and the sticker models are limited to p ¼ 2. Second, the proposed model is less prone to error, because it is grounded on conventional Polymerase Chain Reaction (PCR) amplification and gel electrophoresis techniques. Hence, the problems associated to models such as tile-assembly and stickers, that arise when using more complex molecular techniques, such as hybridization and denaturation, are avoided. Third, it is simple to implement and requires 50 ng/μL per DNA double fragment used to develop the calculations, since the only feature of interest is the size of the DNA double strand fragments. The efficiency of our model has execution times of order Oð1Þ and OðnÞ, for the addition and multiplication over GFðp n Þ, respectively. Furthermore, this paper provides one of the few experimental evidences of arithmetic calculations for molecular computing and validates the technical applicability of the proposed model to perform arithmetic operations over GFðp n Þ.

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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 G F (2 p ), and coding via an algebraic geometric code built using a Hermitian curve on a Galois field G F 2 2q , where p > 2q. 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 Electronic supplementary material The online version of this article (4 University of Newcastle upon Tyne, Tyne and Wear, UK 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.