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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| Published in: | IEEE transactions on information theory Vol. 57; no. 8; pp. 5555 - 5565 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
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New York, NY
IEEE
01.08.2011
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 0018-9448, 1557-9654 |
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| Abstract | 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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| AbstractList | In this paper, some new results are presented on the selective discrete Fourier spectra attack introduced first as the Roenjom-Helleseth attack and the modifications due to Roenjom, 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. 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. In this paper, some new results are presented on the selective discrete Fourier spectra attack introduced first as the Ronjom-Helleseth attack and the modifications due to Ronjom, 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. [PUBLICATION ABSTRACT] |
| Author | Ronjom, S. Guang Gong Honggang Hu Helleseth, T. |
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| Keywords | 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 |
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| References_xml | – volume: 1109 start-page: 358 year: 1996 ident: ref19 article-title: Linear complexity of periodic sequences: A general theory publication-title: Advances in Cryptology Proc Crypto 96 – year: 1983 ident: ref6 publication-title: Theory and Practice of Error Control Codes – volume: 2729 start-page: 162 year: 2003 ident: ref1 article-title: Algebraic attacks on stream combiners with memory publication-title: Advances in Cryptology - CRYPTO 2003 doi: 10.1007/978-3-540-45146-4_10 – volume: 3027 start-page: 474 year: 2004 ident: ref20 article-title: Algebraic attacks and decomposition of Boolean functions publication-title: Advances in CryptologyProc EUROCRYPT 2004 doi: 10.1007/978-3-540-24676-3_28 – volume: 2656 start-page: 345 year: 2003 ident: ref10 article-title: Algebraic attacks on stream ciphers with linear feedback publication-title: Proc Advances in Cryptology-Eurocrypt'2003 doi: 10.1007/3-540-39200-9_21 – ident: ref8 doi: 10.1016/S0747-7171(08)80013-2 – volume: 2729 start-page: 176 year: 2003 ident: ref9 article-title: Fast algebraic attacks on stream ciphers with linear feedback publication-title: Advances in Cryptology - CRYPTO 2003 doi: 10.1007/978-3-540-45146-4_11 – ident: ref18 doi: 10.1109/TIT.1969.1054260 – ident: ref27 doi: 10.1109/TIT.1987.1057268 – ident: ref3 doi: 10.1007/11554868_3 – year: 1977 ident: ref17 publication-title: The Theory of Error-Correcting Codes – year: 1968 ident: ref4 publication-title: Algebraic Coding Theory – year: 0 ident: ref11 publication-title: ESTREAM ECRYPT Stream Cipher Project – start-page: 390 year: 2004 ident: ref12 article-title: Rewriting variables: The complexity of fast algebraic attacks on stream ciphers publication-title: Advances in Cryptology CRYPTO 2004 doi: 10.1007/978-3-540-28628-8_24 – volume: 4547 start-page: 264 year: 2007 ident: ref23 article-title: Attacking the filter generator over <formula formulatype="inline"><tex Notation="TeX">$GF(2^m)$</tex></formula> publication-title: Proc Arithmetic of Finite Fields First International Workshop WAIFA doi: 10.1007/978-3-540-73074-3_20 – start-page: 93 year: 1984 ident: ref13 article-title: Pseudo random properties of cascade connections of clock controlled shift registers publication-title: Proc Advances in Cryptology-Eurocrypt'1984 – year: 1982 ident: ref14 publication-title: Shift Register Sequences – start-page: 88 year: 1984 ident: ref5 article-title: The stop-and-go generator publication-title: Proc Advances in Cryptology-Eurocrypt'1984 – ident: ref21 doi: 10.1023/A:1008256920596 – ident: ref24 doi: 10.1007/978-3-540-77404-4_20 – ident: ref22 doi: 10.1109/TIT.2007.894690 – year: 2001 ident: ref7 publication-title: Specification of the Bluetooth System Version 1 1 – ident: ref15 doi: 10.1017/CBO9780511546907 – ident: ref25 doi: 10.1007/978-3-540-77224-8_2 – volume: 5203 start-page: 197 year: 2008 ident: ref16 publication-title: Sequences and Their Applications – volume: 3017 start-page: 65 year: 2004 ident: ref2 article-title: Improving fast algebraic attacks publication-title: Proc Fast Software Encryption FSE 2004 – ident: ref26 doi: 10.1007/978-3-642-82865-2 |
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| SubjectTerms | 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 |
| Title | Fast Discrete Fourier Spectra Attacks on Stream Ciphers |
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