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Construction of cryptographically important Boolean functions

Maity, S and Johansson, Thomas LU (2002) INDOCRYPT 2002: Third International Conference on Cryptology In Progress in Cryptology / Lecture Notes in Computer Science 2551. p.234-245
Abstract
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... (More)
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. (Less)
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author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
function, stream cipher, combinatorial problems, resiliency, correlation immunity, algebraic degree, Boolean function, balancedness, bent function, nonlinearity, perfectly nonlinear
in
Progress in Cryptology / Lecture Notes in Computer Science
volume
2551
pages
234 - 245
publisher
Springer
conference name
INDOCRYPT 2002: Third International Conference on Cryptology
external identifiers
  • wos:000181957300019
  • scopus:84974722388
ISSN
1611-3349
0302-9743
DOI
10.1007/3-540-36231-2_19
language
English
LU publication?
yes
id
8f6f3472-0d0a-4876-abd7-20a22d2c47ee (old id 313915)
date added to LUP
2007-11-19 13:14:14
date last changed
2017-05-14 03:41:23
@inproceedings{8f6f3472-0d0a-4876-abd7-20a22d2c47ee,
  abstract     = {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.},
  author       = {Maity, S and Johansson, Thomas},
  booktitle    = {Progress in Cryptology / Lecture Notes in Computer Science},
  issn         = {1611-3349},
  keyword      = {function,stream cipher,combinatorial problems,resiliency,correlation immunity,algebraic degree,Boolean function,balancedness,bent function,nonlinearity,perfectly nonlinear},
  language     = {eng},
  pages        = {234--245},
  publisher    = {Springer},
  title        = {Construction of cryptographically important Boolean functions},
  url          = {http://dx.doi.org/10.1007/3-540-36231-2_19},
  volume       = {2551},
  year         = {2002},
}