The Error Linear Complexity Spectrum as a Cryptographic Criterion of Boolean Functions

The error linear complexity spectrum constitutes a well-known cryptographic criterion for sequences, indicating how the linear complexity of the sequence decreases as the number of bits allowed to be modified per period increases. In this paper, via defining an association between <inline-formula...

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Veröffentlicht in:IEEE transactions on information theory Jg. 65; H. 12; S. 8345 - 8356
Hauptverfasser: Limniotis, Konstantinos, Kolokotronis, Nicholas
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York IEEE 01.12.2019
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Algorithms
Approximation algorithms
Approximations
Boolean algebra
Boolean functions
Ciphers
Codes
Communication channels
Complexity
Complexity theory
Correlation
Criteria
Cryptography
error linear complexity spectrum
Input variables
Lauder-Paterson algorithm
Upper bounds
ISSN:0018-9448, 1557-9654
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Zusammenfassung:The error linear complexity spectrum constitutes a well-known cryptographic criterion for sequences, indicating how the linear complexity of the sequence decreases as the number of bits allowed to be modified per period increases. In this paper, via defining an association between <inline-formula> <tex-math notation="LaTeX">2^{n} </tex-math></inline-formula>-periodic binary sequences and Boolean functions on <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula> variables, it is shown that the error linear complexity spectrum also provides useful cryptographic information for the corresponding Boolean function <inline-formula> <tex-math notation="LaTeX">f </tex-math></inline-formula> - namely, it yields an upper bound on the minimum Hamming distance between <inline-formula> <tex-math notation="LaTeX">f </tex-math></inline-formula> and the set of functions depending on fewer number of variables. Therefore, the prominent Lauder-Paterson algorithm for computing the error linear complexity spectrum of a sequence may also be used for efficiently determining approximations of a Boolean function that depend on fewer number of variables. Moreover, it is also shown that, through this approach, low-degree approximations of a Boolean function can be also obtained in an efficient way.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2019.2933533