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Linear nonequivalence versus nonlinearity

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Advances in Cryptology — AUSCRYPT '92 (AUSCRYPT 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 718))

Abstract

The choice of a collection of cryptographically strong Boolean functions is crucial in designing a strong hashing algorithm. The paper shows that it is possible to obtain five linearly nonequivalent functions with five Boolean variables which are cryptographically strong and easy to implement. They can be readily used to design hashing algorithms (of the MD5 structure).

Support for this project was provided in part by the Australian Research Council under the reference number A49131885

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References

  1. C. Adams. On immunity against Biham and Shamir's differential cryptanalysis. Information Processing Letters, 41:77–80, 1992.

    Google Scholar 

  2. C. Adams and S. Tavares. The structured design of cryptographically good S-boxes. Journal of Cryptology, 3:27–41, 1990.

    Google Scholar 

  3. M. Beale and M.F. Monaghan. Encryption using random boolean functions. Cryptography and Coding (H. Beker and F. Piper Eds), 1989.

    Google Scholar 

  4. E.R. Berlekamp and L.R. Welch. Weight distribution of the cosets of the (32, 6) Reed-Muller code. IEEE Transactions on Information Theory, IT-18(1):203–207, 1972.

    Google Scholar 

  5. E. Biham and A. Shamir. Differential cryptanalysis of DES-like cryptosystems. Journal of Cryptology, 4(1):3–72, 1991.

    Google Scholar 

  6. E. Biham and A. Shamir. Differential cryptanalysis of Snefru, Khafre, REDOC-II, LOKI and Lucifer. Proceedings of CRYPTO'91, Lecture Notes in Computer Science, Advances in Cryptology, 576:156–171, 1992.

    Google Scholar 

  7. L. Brown and J. Seberry. On the design of permutation P in DES type cryptosystems. Proceedings of EUROCRYPT'89, Lecture Notes in Computer Science, Advances in Cryptology, 434, 1989.

    Google Scholar 

  8. L. Brown and J. Seberry. Key scheduling in DES type cryptosystems. Advances in Cryptology — AUSCRYPT'90, Lecture Notes in Computer Science, 453:176–183, 1990.

    Google Scholar 

  9. W. Burnside. Theory of Groups of Finite Order. Dover Publications, second edition, New York, 1955.

    Google Scholar 

  10. D. Chaum and J.H. Evertse. Cryptanalysis of DES with a reduced number of rounds. Proceedings of CRYPTO'85, Lecture Notes in Computer Science, Advances in Cryptology, 218:192–211, 1986.

    Google Scholar 

  11. J. Detombe and S. Tavares. Constructing large cryptographically strong S-boxes. Preprint, Department of Electrical Engineering, Queen's University at Kingston, April 1992.

    Google Scholar 

  12. J. Detombe and S. Tavares. Constructing near-bent boolean functions of five variables. Technical Report, Department of Electrical Engineering, Queen's University at Kingston, April 1992.

    Google Scholar 

  13. H. Feistel. Cryptography and computer privacy. Scientific American, 228(5):15–23, 1973.

    Google Scholar 

  14. R. Forre. The strict avalanche criterion: spectral properties of boolean functions and an extended definition. Proceedings of CRYPTO'88, Lecture Notes in Computer Science, Advances in Cryptology, 403:450–468, 1989.

    Google Scholar 

  15. J. Kam and G. Davida. Structured design of substitution-permutation networks. IEEE Transactions on Computers, C-28:747–753, 1979.

    Google Scholar 

  16. F.J. MacWilliams and N.J.A. Sloane. The theory of error-correcting codes. North-Holland, Amsterdam, 1977.

    Google Scholar 

  17. W. Meier and O. Staffelbach. Nonlinearity criteria for cryptographic functions. Proceedings of EUROCRYPT'89, Lecture Notes in Computer Science, Advances in Cryptology, 434:549–562, 1989.

    Google Scholar 

  18. NBS. Data Encryption Standard DES. FIPS PUB46, US National Bureau of Standards, Washington, DC, January 1977.

    Google Scholar 

  19. K. Nyberg. Constructions of bent functions and difference sets. In Advances in Cryptology — EUROCRYPT'90, Lecture Notes in Computer Science, Vol.473, pages 151–160. Springer Verlag, May 1990.

    Google Scholar 

  20. K. Nyberg. Perfect nonlinear S-boxes. In Advances in Cryptology — EUROCRYPT'91, Lecture Notes in Computer Science, Vol.547, pages 378–386. Springer Verlag, 1991.

    Google Scholar 

  21. K. Nyberg. On the construction of highly nonlinear permutations. In Extended Abstracts — Eurocrypt'92, pages 89–94, May 1992.

    Google Scholar 

  22. L. O'Connor. An analysis of product ciphers based on the properties of boolean functions. PhD thesis, the University of Waterloo, 1992. Waterloo, Ontario, Canada.

    Google Scholar 

  23. J. Pieprzyk and G. Finkelstein. Towards effective nonlinear cryptosystem design. IEE Proceedings-E, Computers and Digital Techniques, 135(6):325–335, November 1988.

    Google Scholar 

  24. J.P. Pieprzyk. On bent permutations. In Proceedings of the International Conference on Finite Fields, Coding Theory, and Advances in Communications and Computing, Las Vegas, August 1991.

    Google Scholar 

  25. B. Preneel, W. Van Leewijck, L. Van Linden, R. Govaerts, and J. Vandewalle. Propagation characteristics of boolean functions. In Advances in Cryptology — EUROCRYPT'90, Lecture Notes in Computer Science, Vol.473, pages 161–173. Springer Verlag, May 1990.

    Google Scholar 

  26. R. Rivest. The MD5 message digest algorithm. Request for Comments, RFC 1321, 1992.

    Google Scholar 

  27. C. Shannon. Communication theory of secrecy systems. Bell Systems Technical Journal, 28:656–715, 1949.

    Google Scholar 

  28. D. Slepian. On the number of symmetry types of boolean functions of n variables. Canadian Journal of Mathematics, 5:185–193, 1953.

    Google Scholar 

  29. A.F. Webster and S.E. Tavares. On the design of S-boxes. In Lecture Notes in Computer Science, Advances in Cryptology, Proceedings of Crypto'85, pages 523–534. Springer-Verlag, 1985.

    Google Scholar 

  30. Y. Zheng, J. Pieprzyk, and J. Seberry. HAVAL — A one-way hashing algorithm with variable length of output. Abstracts of AUSCRYPT'92, Gold Coast, Australia, December 1992.

    Google Scholar 

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Jennifer Seberry Yuliang Zheng

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© 1993 Springer-Verlag Berlin Heidelberg

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Charnes, C., Pieprzyk, J. (1993). Linear nonequivalence versus nonlinearity. In: Seberry, J., Zheng, Y. (eds) Advances in Cryptology — AUSCRYPT '92. AUSCRYPT 1992. Lecture Notes in Computer Science, vol 718. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57220-1_59

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  • DOI: https://doi.org/10.1007/3-540-57220-1_59

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  • Print ISBN: 978-3-540-57220-6

  • Online ISBN: 978-3-540-47976-5

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