Skip to main content

On the Design of Error-Correcting Ciphers

Abstract

Securing transmission over a wireless network is especially challenging, not only because of the inherently insecure nature of the medium, but also because of the highly error-prone nature of the wireless environment. In this paper, we take a joint encryption-error correction approach to ensure secure and robust communication over the wireless link. In particular, we design an error-correcting cipher (called the high diffusion cipher) and prove bounds on its error-correcting capacity as well as its security. Towards this end, we propose a new class of error-correcting codes (HD-codes) with built-in security features that we use in the diffusion layer of the proposed cipher. We construct an example, 128-bit cipher using the HD-codes, and compare it experimentally with two traditional concatenated systems: (a) AES (Rijndael) followed by Reed-Solomon codes, (b) Rijndael followed by convolutional codes. We show that the HD-cipher is as resistant to linear and differential cryptanalysis as the Rijndael. We also show that any chosen plaintext attack that can be performed on the HD cipher can be transformed into a chosen plaintext attack on the Rijndael cipher. In terms of error correction capacity, the traditional systems using Reed-Solomon codes are comparable to the proposed joint error-correcting cipher and those that use convolutional codes require more data expansion in order to achieve similar error correction as the HD-cipher. The original contributions of this work are (1) design of a new joint error-correction-encryption system, (2) design of a new class of algebraic codes with built-in security criteria, called the high diffusion codes (HD-codes) for use in the HD-cipher, (3) mathematical properties of these codes, (4) methods for construction of the codes, (5) bounds on the error-correcting capacity of the HD-cipher, (6) mathematical derivation of the bound on resistance of HD cipher to linear and differential cryptanalysis, (7) experimental comparison of the HD-cipher with the traditional systems.

[1234567891011121314151617181920212223242526]

References

  1. 1.

    Stallings W: Cryptography and Network Security: Principles and Practice. 2nd edition. Prentice-Hall, Upper Saddle River, NJ, USA; 1999.

    Google Scholar 

  2. 2.

    Nanjunda C, Haleem MA, Chandramouli R: Robust encryption for secure image transmission over wireless channels. Proceedings of IEEE International Conference on Communications (ICC '05), May 2005, Seoul, Korea 2: 1287-1291.

    Google Scholar 

  3. 3.

    van Tilborg HCA: Coding theory at work in cryptology and vice versa. In Handbook of Coding Theory. Edited by: Pless VS, Huffman WC. North-Holland, Amsterdam, The Netherlands; 1998:1195-1227.

    Google Scholar 

  4. 4.

    Berlekamp ER, McEliece RJ, van Tilborg HCA: On the inherent intractability of certain coding problems. IEEE Transactions on Information Theory 1978,24(3):384-386. 10.1109/TIT.1978.1055873

    MATH  MathSciNet  Article  Google Scholar 

  5. 5.

    Menezes AJ, van Oorschot PC, Vanstone SA: Handbook of Applied Cryptography. CRC Press, Boca Raton, Fla, USA; 1996.

    Google Scholar 

  6. 6.

    McEliece RJ: A public-key cryptosystem based on algebraic coding theory. In DNS Progress Reports 42-44. NASA Jet Propulsion Laboratory, Pasadena, Calif, USA; 1978.

    Google Scholar 

  7. 7.

    Hwang T, Rao TRN: Secret error-correcting codes (SECC). Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology (CRYPTO '88), August 1988, Santa Barbara, Calif, USA 540-563.

    Google Scholar 

  8. 8.

    Godoy W Jr., Pereira D Jr.: A proposal of a cryptography algorithm with techniques of error correction. Computer Communications 1997,20(15):1374-1380. 10.1016/S0140-3664(97)00129-1

    Article  Google Scholar 

  9. 9.

    Berson TA: Failure of the McEliece public-key cryptosystem under message-resend and related-message attack. Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology (CRYPTO '97), August 1997, Santa Barbara, Calif, USA, Lecture Notes in Computer Science 213-220.

    Google Scholar 

  10. 10.

    Stinson D: Cryptography: Theory and Practice. 2nd edition. CRC/C&H, London, UK; 2002.

    Google Scholar 

  11. 11.

    FIPS : Specification for the advanced encryption standard (AES). Federal Information Processing Standards Publication 197, 2001

    Google Scholar 

  12. 12.

    Daemen J, Rijmen V: The Design of Rijndael. Springer, New York, NY, USA; 2002.

    Google Scholar 

  13. 13.

    Wicker SB: Error Control Systems for Digital Communication and Storage. Prentice-Hall, Upper Saddle River, NJ, USA; 1995.

    Google Scholar 

  14. 14.

    Daemen J, Rijmen V: The wide trail design strategy. Proceedings of the 8th IMA International Conference on Cryptography and Coding (IMA '01), December 2001, Cirencester, UK 222-238.

    Google Scholar 

  15. 15.

    MacWilliams FJ, Sloane NJA: The Theory of Error-Correcting Codes. I and II, North-Holland Mathematical Library. Volume 16. North-Holland, Amsterdam, The Netherlands; 1977.

    Google Scholar 

  16. 16.

    Chen X: Error-Control Coding for Data Networks. Kluwer Academic, Norwell, Mass, USA; 1999.

    Google Scholar 

  17. 17.

    Daemen J, Knudsen LR, Rijmen V: The block cipher square. Proceedings of 4th International Workshop on Fast Software Encryption (FSE '97), January 1997, Haifa, Israel 149-165.

    Google Scholar 

  18. 18.

    Matsui M: Linear cryptoanalysis method for DES cipher. Proceedings of Advances in Cryptology Workshop on the Theory and Application of of Cryptographic Techniques (EUROCRYPT '93), May 1993, Lofthus, Norway, Lecture Notes in Computer Science 765: 386-397.

    Google Scholar 

  19. 19.

    Biham E, Shamir A: Differential cryptanalysis of Snefru, Khafre, REDOC-II, LOKI and Lucifer. Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology (CRYPTO '91), August 1991, Santa Barbara, Calif, USA, Lecture Notes In Computer Science 576: 156-171.

    Google Scholar 

  20. 20.

    Biham E, Shamir A: Differential cryptanalysis of the full 16-round DES. Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology (CRYPTO '92), August 1992, Santa Barbara, Calif, USA 487-496.

    Google Scholar 

  21. 21.

    Nyberg K: Differentially uniform mappings for cryptography. Proceedings of Advances in Cryptology Workshop on the Theory and Application of of Cryptographic Techniques (EUROCRYPT '93), May 1993, Lofthus, Norway 55-64.

    Google Scholar 

  22. 22.

    Knudsen LR, Wagner D: Integral cryptanalysis. Proceedings of the 9th International Workshop on Fast Software Encryption (FSE '02), February 2002, Leuven, Belgium, Lecture Notes in Computer Science 2365: 112-127.

    Article  Google Scholar 

  23. 23.

    Lucks S: The saturation attack - a bait for twofish. Proceedings of the 8th International Workshop on Fast Software Encryption (FSE '01), April 2001, Yokohama, Japan, Lecture Notes in Computer Science 2355: 1-15.

    Google Scholar 

  24. 24.

    Lucks S: Attacking seven rounds of rijndael under 192-bit and 256-bit keys. Proceedings of the 3rd Advanced Encryption Standard Candidate Conference, April 2000, New York, NY, USA 215-229.

    Google Scholar 

  25. 25.

    Gilbert H, Minier M: A collision attack on 7 rounds of rijndael. Proceedings of the 3rd Advanced Encryption Standard Candidate Conference, April 2000, New York, NY, USA 230-241.

    Google Scholar 

  26. 26.

    Alajaji F, Fuja T: A communication channel modeled on contagion. IEEE Transactions on Information Theory 1994,40(6):2035-2041. 10.1109/18.340476

    MATH  Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Chetan Nanjunda Mathur.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Mathur, C.N., Narayan, K. & Subbalakshmi, K.P. On the Design of Error-Correcting Ciphers. J Wireless Com Network 2006, 042871 (2007). https://doi.org/10.1155/WCN/2006/42871

Download citation

Keywords

  • Error Correction
  • High Diffusion
  • Traditional System
  • Convolutional Code
  • Security Feature