Generation of Boolean functions using Genetic Algorithm for cryptographic applications

Boolean functions exhibiting strong cryptographic characteristics are essential crypto primitive to be included in the design of secure cryptosystems. It is not only common to incorporate Boolean functions in the design of symmetric block and stream ciphers but they also have a key place in the design of cryptographic hash functions. Strong Boolean functions make the system secure and resistant against cryptanalytic attacks. A wide range of approaches have been adopted in the discovery of Boolean functions that excel in terms of several cryptographic characteristics. In this paper, we present a new scheme based on Genetic Algorithm to generate Boolean functions which satisfy balancedness, correlation immunity, algebraic degree and nonlinearity characteristics. Proposed scheme generates strong Boolean functions with desired values of these characteristics.

[1]  Willi Meier,et al.  Nonlinearity Criteria for Cryptographic Functions , 1990, EUROCRYPT.

[2]  D. E. Goldberg,et al.  Genetic Algorithms in Search , 1989 .

[3]  Lawrence. Davis,et al.  Handbook Of Genetic Algorithms , 1990 .

[4]  William Millan,et al.  Heuristic Design of Cryptographically Strong Balanced Boolean Functions , 1998, EUROCRYPT.

[5]  William Millan,et al.  Boolean Function Design Using Hill Climbing Methods , 1999, ACISP.

[6]  William Millan,et al.  Smart Hill Climbing Finds Better Boolean Functions , 1997 .

[7]  Susan Stepney,et al.  Evolving Boolean Functions Satisfying Multiple Criteria , 2002, INDOCRYPT.

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

[9]  David Coley,et al.  Introduction to Genetic Algorithms for Scientists and Engineers , 1999 .

[10]  Claude E. Shannon,et al.  Communication theory of secrecy systems , 1949, Bell Syst. Tech. J..

[11]  Chang Wook Ahn,et al.  On the practical genetic algorithms , 2005, GECCO '05.

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

[13]  Ren Kui,et al.  On the construction of cryptographically strong boolean functions with desirable trade-off , 2005 .

[14]  Subhamoy Maitra,et al.  Further constructions of resilient Boolean functions with very high nonlinearity , 2002, IEEE Trans. Inf. Theory.

[15]  Ram Ratan,et al.  Applications of Genetic Algorithms in Cryptology , 2013, SocProS.

[16]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[17]  William Millan,et al.  AUSTRALASIAN JOURNAL OF COMBINATORICS Volume 29 (2004), Pages 231–247 Simpler methods for generating better Boolean functions with good cryptographic properties , 2022 .

[18]  Bimal K. Roy,et al.  A Brief Outline of Research on Correlation Immune Functions , 2002, ACISP.