Cryptology ePrint Archive: Report 2005/025

Analysis of Affinely Equivalent Boolean Functions

Meng Qing-shu and Yang min and Zhang Huan-guo and Liu Yu-zhen

Abstract: By walsh transform, autocorrelation function, decomposition, derivation and modification of truth table, some new invariants are obtained. Based on invariant theory, we get two results: first a general algorithm which can be used to judge if two boolean functions are affinely equivalent and to obtain the affine equivalence relationship if they are equivalent. For example, all 8-variable homogenous bent functions of degree 3 are classified into 2 classes; second, the classification of the Reed-Muller code $R(4,6)/R(1,6),R(3,7)/R(1,7),$ which can be used to almost enumeration of 8-variable bent functions.

Category / Keywords: foundations / boolean functions,linearly equivalent, affine group

Date: received 30 Jan 2005, last revised 20 Oct 2005

Contact author: mqseagle at sohu com

Available formats: Postscript (PS) | Compressed Postscript (PS.GZ) | PDF | BibTeX Citation

Note: a wrong word in title is corrected

Version: 20051021:001509 (All versions of this report)

Discussion forum: Show discussion | Start new discussion