Internal state recovery of keystream generator LILI-128 based on a novel weakness of the employed Boolean function

Authors:
Miodrag J. Mihaljević;Sugata Gangopadhyay;Goutam Paul;Hideki Imai
Affiliations:
Mathematical Institute, Serbian Academy of Sciences and Arts, Kneza Mihaila 36, Belgrade, Serbia and Research Institute for Secure Systems, National Institute of Advanced Industrial Science and Te ...;Department of Mathematics, Indian Institute of Technology, Roorkee 247 667, India;Department of Computer Science and Engineering, Jadavpur University, Kolkata 700 032, India;Faculty of Sciences and Engineering, Chuo University 1-13-27 Kasuga, Bunkyo-ku, Tokyo, 112-8551, Japan and National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Japan
Venue:
Information Processing Letters
Year:
2012

Citing 8
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Information Processing Letters
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FSE '01 Revised Papers from the 8th International Workshop on Fast Software Encryption
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FSE '02 Revised Papers from the 9th International Workshop on Fast Software Encryption
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EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
On the security of the LILI family of stream ciphers against algebraic attacks

ACISP'07 Proceedings of the 12th Australasian conference on Information security and privacy
On the degree, nonlinearity, algebraic thickness, and nonnormality of Boolean functions, with developments on symmetric functions

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Abstract

This paper proposes an algorithm for internal state recovery of the keystream generator LILI-128 and introduces a novel approach for cryptanalysis of certain stream ciphers which belong to the class of nonlinear filters. The proposed cryptanalysis is based on a cryptographic feature/weakness of the Boolean function employed as the nonlinear filter. It is shown that the developed algorithm is significantly more efficient than the previously reported ones against LILI-128 and can recover the internal state with time complexities of pre-processing and processing of the order of 2^4^7 and 2^3^5, respectively, the space complexity of 2^4^7, and a sample of dimension approximately equal to 2^4^6. The developed cryptanalysis is also a practical confirmation on the significance of the so-called ''non-normality'' design criterion for Boolean functions.