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Construction of cryptographically important Boolean functions

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Author

Summary, in English

Boolean functions are used as nonlinear combining functions in certain stream ciphers. A Boolean function is said to be correlation immune if its output leaks no information about its input values. Balanced correlation immune functions are called resilient functions. Finding methods for easy construction of resilient functions with additional properties is an active research area. Maitra and Pasalic [3] have constructed 8-variable 1-resilient Boolean functions with nonlinearity 116. Their technique interlinks mathematical results with classical computer search. In this paper we describe a new technique to construct 8-variable 1-resilient Boolean functions with the same nonlinearity. Using a similar technique, we directly construct 10-variable (resp. 12-variable), 1-resilient functions with nonlinearity 488 (resp. 1996). Finally, we describe some results on the construction of n-variable t-resilient functions with maximum nonlinearity.

Publishing year

2002

Language

English

Pages

234-245

Publication/Series

Progress in Cryptology / Lecture Notes in Computer Science

Volume

2551

Document type

Conference paper

Publisher

Springer

Topic

  • Electrical Engineering, Electronic Engineering, Information Engineering

Keywords

  • function
  • stream cipher
  • combinatorial problems
  • resiliency
  • correlation immunity
  • algebraic degree
  • Boolean function
  • balancedness
  • bent function
  • nonlinearity
  • perfectly nonlinear

Conference name

INDOCRYPT 2002: Third International Conference on Cryptology

Conference date

2002-12-16 - 2002-12-18

Conference place

India Hyderabad, India

Status

Published

ISBN/ISSN/Other

  • ISSN: 0302-9743
  • ISSN: 1611-3349