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Higher Order Derivatives and Differential Cryptanalysis

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Communications and Cryptography

Part of the book series: The Springer International Series in Engineering and Computer Science ((SECS,volume 276))

Abstract

High-order derivatives of multi-variable functions are studied in this paper as a natural generalization of the basic concept used in differential cryptanalysis. Possible applications of such derivatives in cryptology are discussed.

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References

  1. X. Lai and J. L. Massey, “A Proposal for a New Block Encryption Standard” Advances in Cryptology - EUROCRYPT’90, Proceedings, LNCS 473 pp. 389–404, Springer-Verlag, Berlin, 1991.

    Google Scholar 

  2. E. Biham and A. Shamir, “Differential Cryptanalysis of DES-like Cryptosystems” Advances in Cryptology - CRYPTO’90 Proceedings LNCS 537, pp. 2–21, Springer-Verlag, Berlin 1991.

    Google Scholar 

  3. E. Biham and A. Shamir, “Differential Cryptanalysis of the full 16-round DES” Abstracts of CRYPTO’92.

    Google Scholar 

  4. E. Biham and A. Shamir, “Differential Cryptanalysis of FEAL and N-Hash” Advances in Cryptology - EUROCRYPT’91 Proceedings LNCS 547, pp. 1–16, Springer-Verlag, Berlin 1991.

    Google Scholar 

  5. E. Biham and A. Shamir, “Differential Cryptanalysis of Snefru, Khafre, REDOC-II, LOKI and Lucifer” Advances in Cryptology - CRYPTO’91 Proceedings LNCS 576, pp. 156–171, Springer-Verlag, Berlin 1992.

    Google Scholar 

  6. X. Lai, J. L. Massey and S. Murphy, “Markov Ciphers and Differential Cryptanalysis” Advances in Cryptology - EUROCRYPT’91 Proceedings LNCS 547, pp. 17–38, Springer-Verlag, Berlin, 1991.

    Google Scholar 

  7. C. Harpes, “Notes on High Order Differential Cryptanalysis of DES,” Internal report, Signal and Information Processing Laboratory, Swiss Federal Institute of Technology, August 12, 1993.

    Google Scholar 

  8. E. Biham, “Higher Order Differential Cryptanalysis,” (Preliminary draft) August 13, 1993.

    Book  Google Scholar 

  9. D. Chaum and J.H. Evertse, “Cryptanalysis of DES with a reduced number of rounds,” Advances in Cryptology - CRYPTO’85 Proceedings pp. 192–211, Springer-Verlag, 1986.

    Google Scholar 

  10. J.H. Evertse, “Linear structures in block ciphers,” Advances in Cryptology - EUROCRYPT’87 Proceedings pp. 249–266, Springer-Verlag, 1988.

    Google Scholar 

  11. W. Meier and O. Staffelbach, “Nonlinearity criteria for cryptographic functions,” Advances in Cryptology - EUROCRYPT’89 Proceedings pp. 549–562, Springer-Verlag, 1990.

    Google Scholar 

  12. K. Nyberg, “On the construction of highly nonlinear permutations,” Advances in Cryptology - EUROCRYPT’92 Proceeding s, pp. 92–98, Springer-Verlag, 1993.

    Google Scholar 

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© 1994 Springer Science+Business Media New York

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Lai, X. (1994). Higher Order Derivatives and Differential Cryptanalysis. In: Blahut, R.E., Costello, D.J., Maurer, U., Mittelholzer, T. (eds) Communications and Cryptography. The Springer International Series in Engineering and Computer Science, vol 276. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2694-0_23

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  • DOI: https://doi.org/10.1007/978-1-4615-2694-0_23

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-6159-6

  • Online ISBN: 978-1-4615-2694-0

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