Logic functions for cryptography - A tutorial

Abstract : Significant research has been done on bent functions, yet researchers in switching theory have paid little attention to this important topic. The goal of this paper to provide a concise exposition. Bent functions are the most nonlinear functions among n-variable switching functions, and are useful in cryptographic applications. This paper discusses three other kinds of cyptographic properties, strict avalanche criterion, propation criterion, and correlation immunity. We discuss known properties, as well as open questions. It assumes the reader is familiar with switching circuit theory. Familiarity with Reed-Muller expansions is helpful, but not essential.

[1]  Timo Neumann,et al.  BENT FUNCTIONS , 2006 .

[2]  Claude Carlet,et al.  Upper bounds on the numbers of resilient functions and of bent functions , 2006 .

[3]  Michael Wiener,et al.  Advances in Cryptology — CRYPTO’ 99 , 1999 .

[4]  I. Wegener.  Branching Programs and Binary Deci-sion Diagrams-Theory and Applications , 1987 .

[5]  Tsutomu Sasao,et al.  Logic Synthesis and Optimization , 1997 .

[6]  Mitsuru Matsui,et al.  Linear Cryptanalysis Method for DES Cipher , 1994, EUROCRYPT.

[7]  S. Agaian.  Hadamard Matrices and Their Applications , 1985 .

[8]  Thomas Siegenthaler,et al.  Correlation-immunity of nonlinear combining functions for cryptographic applications , 1984, IEEE Trans. Inf. Theory.

[9]  Mitsuru Matsui,et al.  The First Experimental Cryptanalysis of the Data Encryption Standard , 1994, CRYPTO.

[10]  Martin Rötteler,et al.  On Homogeneous Bent Functions , 2001, AAECC.

[11]  Réjane Forré,et al.  The Strict Avalanche Criterion: Spectral Properties of Boolean Functions and an Extended Definition , 1988, CRYPTO.

[12]  Xiaolin Wang,et al.  A note on homogeneous bent functions , 2007, Eighth ACIS International Conference on Software Engineering, Artificial Intelligence, Networking, and Parallel/Distributed Computing (SNPD 2007).

[13]  Donald E. Knuth.  Introduction to combinatorial algorithms and boolean functions , 2008 .

[14]  Pantelimon Stanica,et al.  Cryptographic Boolean Functions and Applications , 2009 .

[15]  Tsutomu Sasao,et al.  Switching Theory for Logic Synthesis , 1999, Springer US.

[16]  Hans Dobbertin,et al.  Cryptographer's Toolkit for Construction of 8-Bit Bent Functions , 2005, IACR Cryptol. ePrint Arch..

[17]  Tianbing Xia,et al.  Homogeneous bent functions of degree n in 2n variables do not exist for nge3 , 2004, Discret. Appl. Math..

[18]  G. Leander,et al.  Classification of Boolean Quartic Forms in eight variables , 2008 .

[19]  Subhamoy Maitra,et al.  Balanced Boolean Function on 13-variables having Nonlinearity strictly greater than the Bent Concatenation Bound , 2007, IACR Cryptol. ePrint Arch..

[20]  Donald Ervin Knuth,et al.  The Art of Computer Programming , 1968 .

[21]  Pieter Retief Kasselman,et al.  Analysis and design of cryptographic hash functions , 1999 .

[22]  Stafford E. Tavares,et al.  On the Design of S-Boxes , 1985, CRYPTO.