Nonlinear Vector Resilient Functions

An (n, m, k)-resilient function is a function f : Fn 2 → Fm 2 such that every possible output m-tuple is equally likely to occur when the values of k arbitrary inputs are fixed by an adversary and the remaining n − k input bits are chosen independently at random. In this paper we propose a new method to generate a (n + D + 1, m, d − 1)-resilient function for any non-negative integer D whenever a [n, m, d] linear code exists. This function has algebraic degree D and nonlinearity at least 2n+D − 2n √ 2n+D+1 + 2n−1 . If we apply this method to the simplex code, we can get a (t(2m − 1) + D + 1, m, t2m−1 − 1)-resilient function with algebraic degree D for any positive integers m, t and D. Note that if we increase the input size by D in the proposed construction, we can get a resilient function with the same parameter except algebraic degree increased by D. Key words: Resilient functions, nonlinearity, correlation immunity, linearized polynomials

• Type: Conference
• Year: 2001
• Where: CRYPTO
• Authors: Jung Hee Cheon
• Keywords: 1)-resilient Function, Algebraic Degree, CRYPTO 2001, Cryptology, Possible Output M-tuple