Abstract
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 \(GF\left( 2^{p}\right) \), and coding via an algebraic geometric code built using a Hermitian curve on a Galois field \(GF\left( 2^{2q}\right) \), 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 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.
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References
Adleman, L. M. (1994). Molecular computation of solutions to combinatorial problems. Science-AAAS, 266(5187), 1021–1023.
Aich, A., & Sen, A., et al. (2015). Deoxyribonucleic Acid (DNA) for a Shared Secret Key Cryptosystem with Diffie Hellman Key sharing technique. In: Third International Conference on Computer, Communication, Control and Information Technology (C3IT), 2015, pp. 1 – 6.
Baldi, M. (2014). QC-LDPC code-based cryptography. New York: SpringerBriefs in Electrical and Computer Engineering. ISBN 978-3-319-02556-8.
Berlekamp, E. R. R., McEliece, J., & van Tilborg, H. C. (1978). On the inherent intractability of certain coding problems. IEEE Transactions on Information Theory, IT–24, 384–386.
Carrasco, R., & Johnston, M. (2008). Non-binary error control coding for wireless communication and data storage. New York: Wiley.
Chang, W. L. (2012). Fast Parallel DNA-Based Algorithms for Molecular Computation: Quadratic Congruence and Factoring Integers. IEEE Transactions on Nano Bioscience, 11(1), 62–69.
Chang, W. L., Guo, Ho M., & Guo, M. (2005). Fast Parallel Molecular Algorithms for DNA-Based Computation: Factoring Integers. IEEE Transactions on Nano Bioscience, 4(2), 149–163.
Chen, L., Carrasco, R., & Johnston, M. (2008) Reduced complexity interpolation for list decoding hermitian codes. IEEE Transactions on Wireless Communications, 7, (11) , art. no. 4684611 , pp. 4353–4361.
Chen, L., Carrasco, R., & Johnston, M. (2009). Soft-decision list decoding of hermitian codes. IEEE Transactions on Communications, 57(8), 2169–2176.
Cheng, Q., & Wan, D. (2004). On the list and bounded distance decodibility of ReedSolomon codes. In Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science, 2004, pp. 335-341.
Couvreur, A., Marquez-Corbella, I., & Pellikaan, R. (Jul 2014). ’A polynomial time attack against algebraic geometry code based public key cryptosystems’. IEEE International Symposium on Information Theory (ISIT), Honolulu HI, USA, pp.1446–1450.
Fulton, W. (1969). Algebraic Curves. An introduction to Algebraic Geometry. N.Y.: W.A. Benjamin, Inc.
Garcia, A. (2005). On Curves over Finite Fields. Seminaires & Congres Societe Mathematique de France, 11, 75–110.
Gupta, S., Jain, A. (Mar 2015)’Efficient Image Encryption Algorithm Using DNA Approach’. 2nd International Conference on Computing for Sustainable Global Development (INDIACom), New Delhi, India, pp. 726–731.
Ho, M., Shih, Y. (2008). Fast Parallel Bio-Molecular Logic Computing Algorithms of Discrete Logarithm. In 8th IEEE International Conference on BioInformatics and BioEngineering, 2008, pp. 1 - 6.
Hoholdt, T., & Pellikaan, R. (1995). On the decoding of algebraic-geometric codes. IEEE Transactions on Information Theory, IT–41(6), 1589–1614.
Hungerford, T. W. (2012) Abstract Algebra, an Introduction. 3 edn. Brooks Cole, 1986, (2012)
Hurt, N. E. (2003). Many rational points. Coding theory and algebraic geometry. Dordrecht: Springer Science+BusinessMedia Dordrecht. ISBN 978-90-481-6496-7.
Jiron, I., Soto, I., Carrasco, R., & Becerra, N. (2006). Hyperelliptic curves encryption combined with block codes for Gaussian channel. Int. J. Commun. Syst, 19, 809–830.
Justesen, J., Arsen, J. L., et al. (1989). Construction and Decoding of a Class of Algebraic Geometry Codes. IEEE Transactions on Information Theory, 35(4), 811–821.
Justesen, J., Larsen, K. J., et al. (1992). Fast Decoding of Codes from Algebraic Plane Curves. IEEE Transactions on Information Theory, 38(1), 111–119.
Kari, L., Seki, S., & Sosk, P. (2012). DNA Computing - Foundations and Implications, Handbook of Natural Computing. Berlin: Springer, Berlin Heidelberg.
Koblitz, N. (1998). Algebraic aspect of cryptography, algorithms and computation in mathematics (Vol. 3). Berlin: Springer. ISBN 3-540-63446-0.
Kumar, M., Iqbal, A., & Kumar, P. (2016). A new RGB image encryption algorithm based on DNA encoding and elliptic curve DiffiHellman cryptography. Signal Processing, 125, 187–202.
Kumar Kaundal, A., & Verma, A. K. (2015). Extending Feistel structure to DNA Cryptography. Journal of Discrete Mathematical Sciences and Cryptography, 18(4), 349–362.
Lin, S., & Costello,D. (2004). Error control coding. Fundamentals and applications (2nd ed.). Englewood Cliffs, NJ: Prentice-Hall. ISBN-10:0130426725.
Ontiveros, B., Soto, I., & Carrasco, R. (2006). Construction of an elliptic curve over finite fields to combine with convolutional code for cryptography. IEE Proceedings: Circuits Devices and Systems, 153(4), 299–306.
Paar, Ch., & Pelzl, J. (2010). Understanding Cryptography. A Textbook for Students and Practioners. Berlin: Springer-Verlag, Berlin Heidelberg.
Proakis, J. G., & Masoud, S. (2008). Digital communications (5th ed.). New York: McGraw-Hill. ISBN 9780072957167.
Saranya M. R., Arun, K., Mohan, K., Anusudha, K. (Feb 2015) ’Algorithm for Enhanced Image Security Using DNA and Genetic Algorithm’. IEEE International Conference on Signal Processing, Informatics, Communication and Energy Systems (SPICES), Kerala, India, pp. 1–5.
Schneier, B. (1996). Applied cryptography: Protocols, algorithms, and source codes in C (2nd ed.). New York: Wiley. ISBN-10:0471117099.
Singh, A., Singh, R. (Mar 2015) ’Information Hiding Techniques Based on DNA Inconsistency: An Overview’. 2nd International Conference on Computing for Sustainable Global Development (INDIACom), New Delhi, India, pp. 2068–2072.
Soto, I., Jiron, I., Valencia, A., & Carrasco, R. (2015). Secure DNA data compression using algebraic curves. Electronics Letters, 51(18), 1466–1468.
Stichtenoth, H. (1988). A Note on Hermitian Codes Over \(GF(q^2)\). IEEE Transactions on Information Theory, 34(5), 1345–1348.
Valencia, C., Soto, I., & Carrasco, R. (2007). Secure data compression with sphere packing. Electronics Letters, 43(23), 1298–1300.
Vardy, A. (1997). The Intractability of Computing the Minimum Distance of a Code. IEEE Transactions on Information Theory, 43(6), 1757–1766.
Acknowledgments
The authors acknowledge the financial support of the ’Center for multidisciplinary research on signal processing’ (Project Conicyt/ACT1120), Project USACH/Dicyt No 061413SG, and V.R.I.D.T./U.C.N. Antofagasta.
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Jiron, I., Soto, I., Azurdia-Meza, C.A. et al. A new DNA cryptosystem based on AG codes evaluated in gaussian channels. Telecommun Syst 64, 279–291 (2017). https://doi.org/10.1007/s11235-016-0175-1
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DOI: https://doi.org/10.1007/s11235-016-0175-1