Abstract
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.
Preview
Unable to display preview. Download preview PDF.
References
C.H.Bennett, G.Brassard and J.M.Robert, “Privacy amplification by public discussion”, SIAM J. Comput. 17 (1988), 210–229.
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.
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.
P.Camion and A.Canteaut, “Construction of t-resilient functions over a finite alphabet”, Proc. Eurocrypt'96, Verlin: Springer-Verlag, 1996.
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.
J.H. van Lint, Introduction to Coding Theory, Springer-Verlag, 1992.
T.Siegenthaler, “Correlation-immunity of nonlinear combining functions for cryptographic applications”, IEEE Trans. on Infor. Theory, Vol. IT-30 (1984) 5, 776–780.
D.R.Stinson, “Resilient functions and large sets of orthogonal arrays”, Congressus Numerantium 92 (1993), 105–110.
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.
C.K.Wu, “On the independency of Boolean functions of their variables”, J. of Xidian University, (1988) 73–81. (in Chinese)
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.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wu, CK., Dawson, E. (1996). On construction of resilient functions. In: Pieprzyk, J., Seberry, J. (eds) Information Security and Privacy. ACISP 1996. Lecture Notes in Computer Science, vol 1172. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023289
Download citation
DOI: https://doi.org/10.1007/BFb0023289
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61991-8
Online ISBN: 978-3-540-49583-3
eBook Packages: Springer Book Archive