Improved Upper Bound on the Nonlinearity of High Order Correlation Immune Functions

It has recently been shown that when m > 1 2 n - 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 2 n - 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. Key Words: Correlation Immune Functions, Nonlinearity, Resilient Functions, Plateaued Functions, Stream Ciphers

• Type: Conference
• Year: 2000
• Where: SACRYPT
• Authors: Yuliang Zheng, Xian-Mo Zhang
• Keywords: Correlation Immune Functions, Cryptology, Nonlinearity Nf, Nonlinearity Satisfies, SACRYPT 2000