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Cryptography and Communications
Published in: Cryptography and Communications 6/2018

09-11-2017

Correlation immune functions with respect to the q-transform

Authors: Ting Gu, Zhixiong Chen, Andrew Klapper

Published in: Cryptography and Communications | Issue 6/2018

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Abstract

Correlation immunity is a measure of resistance to Siegenthaler’s divide and conquer attack on nonlinear combiners. In this work, we study functions with regard to the q-transform, a generalization of the Walsh-Hadamard transform, that measures the proximity of a function to the set of functions obtained from a function q(x) by linear base change. We propose two notions of q-correlation immune functions and study their relationship between them. We also analyze certain properties of these functions and present some techniques to design these functions.
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Footnotes
1
Of course, there maybe several coset leaders for a coset. We only need one of them.
 
2
The minimum distance of a linear code is the minimum Hamming weight of its nonzero code words.
 
Literature
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Golomb, S.: Shift Register Sequences. Aegean Park Press, Laguna Hills (1982)MATH
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Klapper, A.: A new transform related to distance from a boolean function (extended abstract). In: Schmidt, K.-U., Winterhof, A. (eds.) Sequences and Their Applications–SETA 2014, Lecture Notes in Computer Science, vol. 8865, pp 47–59. Springer International Publishing (2014)
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Neyman, J., Pearson, E. S.: On the problem of the most efficient tests of statistical hypotheses. In: Kotz, S., Johnson, N. (eds.) Breakthroughs in Statistics, pp 73–108. Springer, New York (1992)
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Siegenthaler, T.: Decrypting a class of stream ciphers using ciphertext only. IEEE Trans. Comput. 100.1, 81–85 (1985)CrossRef
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Wu, C. -K., Dawson, E.: Construction of correlation immune boolean functions. Aust. J. Commun. 21, 141–166 (2000)MathSciNetMATH
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Xiao, G., Massey, J.: A spectral characterization of correlation-immune combining functions. IEEE Trans. Inf. Theory 34.3, 569–571 (1988)MathSciNetCrossRefMATH
Metadata
Title
Correlation immune functions with respect to the q-transform
Authors
Ting Gu
Zhixiong Chen
Andrew Klapper
Publication date
09-11-2017
Publisher
Springer US
Published in
Cryptography and Communications / Issue 6/2018
Print ISSN: 1936-2447
Electronic ISSN: 1936-2455
DOI
https://doi.org/10.1007/s12095-017-0267-0

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