Accession Number : AD1046882

Title :   Correlation Immunity, Avalanche Features, and Other Cryptographic Properties of Generalized Boolean Functions

Descriptive Note : Technical Report

Corporate Author : Naval Postgraduate School Monterey United States

Personal Author(s) : Martinsen,Thor

Full Text :

Report Date : 01 Sep 2017

Pagination or Media Count : 161

Abstract : This dissertation investigates correlation immunity, avalanche features, and the bent cryptographic properties for generalized Boolean functions defined on V sub n with values in Z sub q. We extend the concept of correlation immunity from the Boolean case to the generalized setting, and provide multiple construction methods for order 1 and higher correlation immune generalized Boolean functions. We establish necessary and sufficient conditions for generalized Boolean functions. Additionally, we discuss correlation immune and rotation symmetric generalized Boolean functions, introducing a construction method along the way. Using a graph-theoretic and probabilistic frame of reference, we subsequently establish several, increasingly stringent, strict avalanche criteria along with a construction method for generalized Boolean functions. We introduce the notion of a uniform avalanche criterion and demonstrate that generalized Boolean functions that satisfy this criterion are also order 1 correlation immune and always have Boolean function components that are both order 1 correlation immune and satisfy the strict avalanche criterion. We subsequently investigate linear structures, directional derivatives and define a unit vector gradient for generalized Boolean function. We introduce the Walsh-Hadamard transform of a generalized Boolean function along with the notion of generalized bent Boolean functions. We provide a construction of generalized bent Boolean functions with outputs in Z sub 8 and establish necessary conditions for generalized bent Boolean functions.

Descriptors :   cryptography , coding , BOOLEAN FUNCTIONS , INFORMATION WARFARE , information security

Subject Categories : Cybernetics
      Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE