On construction of resilient functions

  • Chuan-Kun Wu
  • Ed Dawson
Session 3: Encryption and Cryptographic Functions
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1172)


An (n, m, t) resilient function is a function f: GF(2) n GF(2) m such that every possible output m-tuple is equally likely to occur when the values of t arbitrary inputs are fixed by an opponent and the remaining n−t input bits are chosen independently at random. The existence of resilient functions has been largely studied in terms of lower and upper bounds. The construction of such functions which have strong cryptographic significance, however, needs to be studied further. This paper aims at presenting an efficient method for constructing resilient functions from odd ones based on the theory of error-correcting codes, which has further expanded the construction proposed by X.M.Zhang and Y.Zheng. Infinite classes of resilient functions having variant parameters can be constructed given an old one and a linear error-correcting code. The method applies to both linear and nonlinear resilient functions.


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  1. 1.
    C.H.Bennett, G.Brassard and J.M.Robert, “Privacy amplification by public discussion”, SIAM J. Comput. 17 (1988), 210–229.Google Scholar
  2. 2.
    J.Bierbrauer, K.Gopalakrishnan, and D.R.Stinson, “Bounds on resilient functions and orthogonal arrays”, Advances in Cryptology — CRYPTO'94, Springer-Verlag, (1994) 247–256.Google Scholar
  3. 3.
    B.Chor, O.Goldreich, J.Hastad, J.Friedman, S.Rudich and R.Smolensky, “The bit extraction problem or t-resilient functions”, Proc. of 26th IEEE Symp. on Foundations of Computer Science, (1985) 396–407.Google Scholar
  4. 4.
    P.Camion and A.Canteaut, “Construction of t-resilient functions over a finite alphabet”, Proc. Eurocrypt'96, Verlin: Springer-Verlag, 1996.Google Scholar
  5. 5.
    K.Gopalakrishnan, D.G.Hoffman, and D.R.Stinson, “A note on a conjecture concerning symmetric resilient functions”, Information Processing Letters 47 (1993), 139–143.Google Scholar
  6. 6.
    J.H. van Lint, Introduction to Coding Theory, Springer-Verlag, 1992.Google Scholar
  7. 7.
    T.Siegenthaler, “Correlation-immunity of nonlinear combining functions for cryptographic applications”, IEEE Trans. on Infor. Theory, Vol. IT-30 (1984) 5, 776–780.Google Scholar
  8. 8.
    D.R.Stinson, “Resilient functions and large sets of orthogonal arrays”, Congressus Numerantium 92 (1993), 105–110.Google Scholar
  9. 9.
    D.R.Stinson and J.L.Massey, “An infinite class of counterexamples to a conjecture concerning nonlinear resilient functions”, J. of Cryptology, 8 (1995), 167–173.Google Scholar
  10. 10.
    C.K.Wu, “On the independency of Boolean functions of their variables”, J. of Xidian University, (1988) 73–81. (in Chinese)Google Scholar
  11. 11.
    X.M.Zhang and Y.Zheng, “On nonlinear resilient functions (extended abstract)”, Proc. of Eurocrypt'95, Springer-Verlag (1995) 274–288; See also “Cryptographically resilient functions”, IEEE Trans. on Inform. Theory, (1996/97) to appear.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Chuan-Kun Wu
    • 1
  • Ed Dawson
    • 1
  1. 1.Information Security Research CentreQueensland University of TechnologyBrisbaneAustralia

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