@inproceedings{6d9b4611351d414896a99f3fceca0721,
title = "Improved upper bound on the nonlinearity of high order correlation immune functions",
abstract = "It has recently been shown that when m > (Formula Presented)-1, the nonlinearity Nf of an mth-order correlation immune function f with n variables satisfies the condition of Nf ≤ 2n−1 − 2m, and that when m > 1(Formula Presented) − 2 and f is a balanced function, the nonlinearity satisfies Nf ≤ 2n−1 − 2m+1. In this work we prove that the general inequality, namely Nf ≤ 2n−1 − 2m, can be improved to Nf ≤ 2n−1 − 2m+1 for m ≥ 0.6n − 0.4, regardless of the balance of the function. We also show that correlation immune functions achieving the maximum nonlinearity for these functions have close relationships with plateaued functions. The latter have a number of cryptographically desirable properties.",
keywords = "Correlation Immune Functions, Nonlinearity, Plateaued Functions, Resilient Functions, Stream Ciphers",
author = "Yuliang Zheng and Zhang, {Xian Mo}",
year = "2001",
language = "English",
isbn = "354042069X",
volume = "2012",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer, Springer Nature",
pages = "262--274",
booktitle = "Selected Areas in Cryptography - 7th Annual International Workshop, SAC 2000, Proceedings",
address = "United States",
note = "7th Annual International Workshop on Selected Areas in Cryptography, SAC 2000 ; Conference date: 14-08-2000 Through 15-08-2000",
}