Authors: Mihaljević, Miodrag J. 
Gangopadhyay, Sugata
Paul, Goutam
Imai, Hideki
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Generic cryptographic weakness of k-normal Boolean functions in certain stream ciphers and cryptanalysis of grain-128
Journal: Periodica Mathematica Hungarica
Volume: 65
Issue: 2
First page: 205
Last page: 227
Issue Date: 1-Oct-2012
Rank: M23
ISSN: 0031-5303
DOI: 10.1007/s10998-012-4631-8
This paper considers security implications of k-normal Boolean functions when they are employed in certain stream ciphers. A generic algorithm is proposed for cryptanalysis of the considered class of stream ciphers based on a security weakness of k-normal Boolean functions. The proposed algorithm yields a framework for mounting cryptanalysis against particular stream ciphers within the considered class. Also, the proposed algorithm for cryptanalysis implies certain design guidelines for avoiding certain weak stream cipher constructions. A particular objective of this paper is security evaluation of stream cipher Grain-128 employing the developed generic algorithm. Contrary to the best known attacks against Grain-128 which provide complexity of a secret key recovery lower than exhaustive search only over a subset of secret keys which is just a fraction (up to 5%) of all possible secret keys, the cryptanalysis proposed in this paper provides significantly lower complexity than exhaustive search for any secret key. The proposed approach for cryptanalysis primarily depends on the order of normality of the employed Boolean function in Grain-128. Accordingly, in addition to the security evaluation insights of Grain-128, the results of this paper are also an evidence of the cryptographic significance of the normality criteria of Boolean functions.
Keywords: cryptanalysis | Grain-128 | k-normal Boolean functions | stream cipher | timememory-data trade-off
Publisher: Springer Link
Project: Advanced Techniques of Cryptology, Image Processing and Computational Topology for Information Security 

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