Document Type : Research Article



This paper proposes an efficient joint secret key encryption-channel coding cryptosystem, based on regular Extended Difference Family Quasi-Cyclic Low-Density Parity-Check codes. The key length of the proposed cryptosystem decreases up to 85 percent using a new efficient compression algorithm. Cryptanalytic methods show that the improved cryptosystem has a significant security advantage over Rao-Nam cryptosystem against chosen plaintext attacks, benefiting from an improvement on the structure of the Rao-Nam cryptosystem and proper choices of code parameters. Moreover, the proposed cryptosystem benefits from the highest code rate and a proper error performance.


[1] C. N. Mathur. A mathematical framework for combining error correction and encryption. PhD thesis, Department of Electrical and Computer Engineering, Stevens Institute of Technology, Castle Point on Hudson, Hoboken, NJ, USA, 2007.
[2] T. R. N. Rao. Joint encryption and error correction schemes. In Proceedings of the 11th annual international symposium on computer architecture, pages 240-241, 1984.
[3] T. R. N. Rao and K. H. Nam. Private-key algebraic-code encryption. IEEE Transactions on Information Theory, IT-35(4):829-833, 1987.
[4] A. A. Sobhi Afshar, T. Eghlidos, and M. R. Aref. Efficient secure channel coding based on quasicyclic low-density parity-check codes. Journal of IET-Communications, 3(2):279-292, 2009.
[5] R. Gallager. Low density parity check codes. PhD thesis, Cambridge, MA: MIT Press, 1963.
[6] T. Xia and B. Xia. Quasi-cyclic codes from extended difference families. In Proceedings of IEEE Wireless Communications and Networking Conference, volume 2, pages 1036-1040, 2005.
[7] D. J. C. Mackay and R.M. Neal. Near Shannon limit performance of low-density parity check codes. Electronics Letters, 32(18):1645-1646, 1996.
[8] M. Tanner. A recursive approach to low complexity codes. IEEE Transactions on Information Theory, IT-27(5):533-547, 1981.
[9] G. A.Malema. Low-density parity-check codes: construction and implementation. PhD thesis, The University of Adelide, Australia, 2007.
[10] Z. Li, L. Chen, L. Zeng, S. Lin, and W. H. Fong. Efficient encoding of quasi-cyclic low-density parity-check codes. IEEE Transactions on Communications, 54(1):71-81, 2006.
[11] S. Lin and D. J. Costello. Error Control Coding: Fundamentals and Applications. Prentice-Hall, NJ, USA, 2nd edition, 2004.
[12] M. Baldi, F. Chiaraluce, R. Garello, and F. Mininni. Quasi-cyclic low-density parity- check codes in the McEliece cryptosystem. IEEE International Conference on Communications (ICC'07), pages 951-956, 2007.
[13] S. J. Johnson and S. R. Weller. A family of irregular ldpc codes with low encoding complexity. IEEE Communications Letters, 7(2):79-81, 2003.
[14] M. Buratti. Constructions of (q, k, 1) difference families with q a prime power and k=4, 5. Discrete Mathematics, 138(1-3):169-175, 1995.
[15] J. V. Tilburg. Security-analysis of a class of cryptosystems based on linear error-correcting codes. PhD thesis, Technische Universiteit Eindhoven, 1994.
[16] R. Struik and J. Tilburg. The Rao-Nam scheme is insecure against a chosen-plaintext attack. In Advances in Cryptology-CRYPTO'87, Lecture Notes in Computer Science, pages 445-457. Springer, 1988.
[17] A. Otmani, J.P. Tillich, and L. Dallot. Cryptanalysis of two McEliece cryptosystems based on quasi-cyclic codes. Mathematics in Computer Science, 3(2):129-140, 2010.
[18] M. Baldi and F. Chiaraluce. Cryptanalysis of a new instance of McEliece cryptosystem based on QC-LDPC codes. In IEEE International Symposium on Information Theory, volume 2, pages 2591-2595, Nice, France, 2007.
[19] A. I. Barbero and O. Ytrehus. Modifications of the Rao-Nam Cryptosystem. In Proceedings of International Conference on Coding Theory, Cryptography and Related Areas (ICCC98), pages 1-13, Guanajuato, Mexico, 1998.
[20] Marco Baldi, Marco Bodrato, and Franco Chiaraluce. A new analysis of the McEliece cryptosys-tem based on QC-LDPC codes. In Proceedings of the 6th International Conference on Security and Cryptography for Networks, Lecture Notes in Computer Science, pages 246-262. Springer, 2008.
[21] D. J. C. Mackay. Good error correcting codes based on very sparse matrices. IEEE Transactions on Information Theory, IT-45(2):399-341, 1999.