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Plateaued Functions

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Information and Communication Security (ICICS 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1726))

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Abstract

The focus of this paper is on nonlinear characteristics of cryptographic Boolean functions. First, we introduce the notion of plateaued functions that have many cryptographically desirable properties. Second, we establish a sequence of strengthened inequalities on some of the most important nonlinearity criteria, including nonlinearity, propagation and correlation immunity, and prove that critical cases of the inequalities coincide with characterizations of plateaued functions. We then proceed to prove that plateaued functions include as a proper subset all partially-bent functions that were introduced earlier by Carlet. This settles an open question that arises from previously known results on partially-bent functions. In addition, we construct plateaued, but not partially-bent, functions that have many properties useful in cryptography.

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References

  1. Camion, P., Carlet, C., Charpin, P., Sendrier, N.: On correlation-immune functions. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 87–100. Springer, Heidelberg (1992)

    Google Scholar 

  2. Carlet, C.: Partially-bent functions. Designs, Codes and Cryptography 3, 135–145 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  3. Erwe, F.: Differential And Integral Calculus. Oliver And Boyd Ltd., Edinburgh And London (1967)

    MATH  Google Scholar 

  4. Guo-Zhen, X., Massey, J.L.: A spectral characterization of correlationimmune combining functions. IEEE Transactions on Information Theory 34(3), 569–571 (1988)

    Article  MATH  Google Scholar 

  5. MacWilliams, F.J., Sloane, N.J.A.: The Theory of Error-Correcting Codes. North-Holland, Amsterdam (1978)

    Google Scholar 

  6. Meier, W., Staffelbach, O.: Nonlinearity criteria for cryptographic functions. In: Quisquater, J.-J., Vandewalle, J. (eds.) EUROCRYPT 1989. LNCS, vol. 434, pp. 549–562. Springer, Heidelberg (1990)

    Google Scholar 

  7. Preneel, B., Leekwijck, W.V., Linden, L.V., Govaerts, R., Vandewalle, J.: Propagation characteristics of boolean functions. In: Kumar, D. (ed.) SNePS 1989. LNCS, vol. 437, pp. 155–165. Springer, Heidelberg (1991)

    Google Scholar 

  8. Rothaus, O.S.: On “bent” functions. Journal of Combinatorial Theory 20, 300–305 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  9. Seberry, J., Zhang, X.M., Zheng, Y.: Improving the strict avalanche characteristics of cryptographic functions. Information Processing Letters 50, 37–41 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  10. Wang, J.: The linear kernel of boolean functions and partially-bent functions. System Science and Mathematical Science 10, 6–11 (1997)

    MATH  Google Scholar 

  11. Webster, A.F., Tavares, S.E.: On the design of S-boxes. In: Williams, H.C. (ed.) CRYPTO 1985. LNCS, vol. 218, pp. 523–534. Springer, Heidelberg (1986)

    Google Scholar 

  12. Zheng, Y., Zhang, X.M., Imai, H.: Duality of boolean functions and its cryptographic significance. In: Han, Y., Quing, S. (eds.) ICICS 1997. LNCS, vol. 1334, pp. 159–169. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  13. Yarlagadda, R., Hershey, J.E.: Analysis and synthesis of bent sequences. IEEE Proceedings (Part E) 136, 112–123 (1989)

    Google Scholar 

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© 1999 Springer-Verlag Berlin Heidelberg

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Zheng, Y., Zhang, XM. (1999). Plateaued Functions. In: Varadharajan, V., Mu, Y. (eds) Information and Communication Security. ICICS 1999. Lecture Notes in Computer Science, vol 1726. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-47942-0_24

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  • DOI: https://doi.org/10.1007/978-3-540-47942-0_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66682-0

  • Online ISBN: 978-3-540-47942-0

  • eBook Packages: Springer Book Archive

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