Fast Discrete Fourier Spectra Attacks on Stream Ciphers

In this paper, some new results are presented on the selective discrete Fourier spectra attack introduced first as the Rønjom-Helleseth attack and the modifications due to Rønjom, Gong, and Helleseth. The first part of this paper fills some gaps in the theory of analysis in terms of the discrete Fou...

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Veröffentlicht in:IEEE transactions on information theory Jg. 57; H. 8; S. 5555 - 5565
Hauptverfasser: Guang Gong, Ronjom, S., Helleseth, T., Honggang Hu
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York, NY IEEE 01.08.2011
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Algebra
Applied sciences
Boolean functions
Complexity theory
Cryptography
Discrete Fourier transform (DFT)
Discrete Fourier transforms
Exact sciences and technology
fast algebraic attack
filter generator
Flexibility
Fourier analysis
Fourier transforms
Generators
Information theory
Information, signal and communications theory
linear feedback shift register (LFSR)
Mathematical model
Polynomials
Signal and communications theory
Spectra
spectral immunity
Streams
Telecommunications and information theory
Discrete Fourier transform (DFT)
spectral immunity
Stream ciphering
Fast Fourier transformation
Spectral properties
Discrete Fourier transformation
filter generator
Boolean function
fast algebraic attack
Flexibility
Shift register
Private key
linear feedback shift register (LFSR)
Security of data
Linear complexity
Cryptanalysis
Cryptography
ISSN:0018-9448, 1557-9654
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Beschreibung
Zusammenfassung:In this paper, some new results are presented on the selective discrete Fourier spectra attack introduced first as the Rønjom-Helleseth attack and the modifications due to Rønjom, Gong, and Helleseth. The first part of this paper fills some gaps in the theory of analysis in terms of the discrete Fourier transform (DFT). The second part introduces the new fast selective DFT attacks, which are closely related to the fast algebraic attacks in the literature. However, in contrast to the classical view that successful algebraic cryptanalysis of LFSR-based stream cipher depends on the degree of certain annihilators, the analysis in terms of the DFT spectral properties of the sequences generated by these functions is far more refined. It is shown that the selective DFT attack is more efficient than known methods for the case when the number of observed consecutive bits of a filter generator is less than the linear complexity of the sequence. Thus, by utilizing the natural representation imposed by the underlying LFSRs, in certain cases, the analysis in terms of DFT spectra is more efficient and has more flexibility than classical and fast algebraic attacks. Consequently, the new attack imposes a new criterion for the design of cryptographic strong Boolean functions, which is defined as the spectral immunity of a sequence or a Boolean function.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2011.2158480