Transparency Order and Cross-Correlation Analysis of Boolean Functions

Generalized Correlation Analysis of Vectorial Boolean Functions

We investigate the security of n-bit to m-bit vectorial Boolean functions in stream ciphers. Such stream ciphers have higher throughput than those using single-bit output Boolean functions. However, as shown by Zhang and Chan at Crypto 2000, linear approximations based on composing the vector output with any Boolean functions have higher bias than those based on the usual correlation attack. In...

Spectral Domain Analysis of Correlation Immune and Resilient Boolean Functions

Analysis of boolean functions with high second order nonlinearity

Highly nonlinear Boolean functions play a central role in the design and security analysis of high speed stream cyphers and block cyphers. We focus on analyzing the structure of Boolean functions that exhibit high second order nonlinearity. We commence with a theoretical overview of Boolean functions and ReedMuller codes. We then introduce a new equivalence relation, 2-equivalence, for which we...

Construction of correlation immune Boolean functions

It is shown in this paper that every correlation immune Boolean function of n variables can be written as f(x) = g(xG ), where 9 is an algebraic non-degenerate Boolean function of k (k :::; n) variables and G is a generating matrix of an tn, k, d] linear code. In this expression the correlation immunity of f(x) must be at least d 1. In this paper we further prove when the correlation immunity e...

Analysis of Boolean Functions

Scribe notes from the 2012 Barbados Workshop on Computational Complexity. A series of lectures on Analysis of Boolean Functions by Ryan O'Donnell, with a guest lecture by Per Austrin.