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Three characterizations of non-binary correlation-immune and resilient functions

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Abstract

A functionf(X 1,X 2, ...,X n ) is said to betth-order correlation-immune if the random variableZ=f(X 1,X 2,...,X n ) is independent of every set oft random variables chosen from the independent equiprobable random variablesX 1,X 2,...,X n . Additionally, if all possible outputs are equally likely, thenf is called at-resilient function. In this paper, we provide three different characterizations oft th-order correlation immune functions and resilient functions where the random variable is overGF (q). The first is in terms of the structure of a certain associated matrix. The second characterization involves Fourier transforms. The third characterization establishes the equivalence of resilient functions and large sets of orthogonal arrays.

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References

  1. Alfred V. Aho, John E. Hopcroft, and Jeffrey D. Ullman,The Design and Analysis of Computer Algorithms, Computer Science and Information Processing, Addison-Wesley Publishing Company (1975).

  2. C. H. Bennett, G. Brassard, and J. M. Robert, Privacy amplification by public discussion,SIAM J. Computing, Vol. 17 (1988) pp. 210–229.

    Google Scholar 

  3. P. Camion, C. Carlet, P. Charpin, and N. Sendrier, On correlation-immune functions, Lecture Notes in Computer Science, Vol. 576 (1992) pp. 86–100.

    Google Scholar 

  4. Benny Chor, Oded Goldreich, Johan Håstad, Joel Friedman, Steven Rudich, and Roman Smolensky, The bit extraction problem ort-resilient functions,26th IEEE Symposium on Foundations of Computcr Science (1985) pp. 396–407.

  5. P. Delsarte, An algebraic approach to the association schemes of coding theory,Philips Research Reports Supplements, Vol. 10 (1973). Thesis, Universite Catholique de Louvain.

  6. Xiao Guo-Zhen and James L. Massey, A spectral characterization of correlation-immune combining functions.IEEE Trans. Inform. Theory, Vol. 34 (1988) pp. 569–571.

    Google Scholar 

  7. Rainer A. Rueppel,Analysis and Design of Stream Ciphers, Springer-Verlag (1986).

  8. T. Siegenthaler, Correlation immunity of nonlinear combining functions for cryptographic applications,IEEE Trans. Inform. Theory, Vol. 30 (1984) pp. 776–780.

    Google Scholar 

  9. D. R. Stinson, Resilient functions and large sets of orthogonal arrays,Congressus Numer., Vol. 92 (1993) pp. 105–110.

    Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science and Engineering, University of Nebraska-Lincoln, 68588, Lincoln, NE

    K. Gopalakrishnan

  2. Department of Computer Science and Engineering and Center for Communication and Information Science, University of Nebraska-Lincoln, 68588, Lincoln, NE

    D. R. Stinson

Authors
  1. K. Gopalakrishnan
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  2. D. R. Stinson
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Gopalakrishnan, K., Stinson, D.R. Three characterizations of non-binary correlation-immune and resilient functions. Des Codes Crypt 5, 241–251 (1995). https://doi.org/10.1007/BF01388386

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  • DOI: https://doi.org/10.1007/BF01388386

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