On construction of resilient functions
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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