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Fast Correlation Attacks over Extension Fields, Large-Unit Linear Approximation and Cryptanalysis of SNOW 2.0

  • Bin Zhang
  • Chao Xu
  • Willi Meier
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9215)

Abstract

Several improvements of fast correlation attacks have been proposed during the past two decades, with a regrettable lack of a better generalization and adaptation to the concrete involved primitives, especially to those modern stream ciphers based on word-based LFSRs. In this paper, we develop some necessary cryptanalytic tools to bridge this gap. First, a formal framework for fast correlation attacks over extension fields is constructed, under which the theoretical predictions of the computational complexities for both the offline and online/decoding phase can be reliably derived. Our decoding algorithm makes use of Fast Walsh Transform (FWT) to get a better performance. Second, an efficient algorithm to compute the large-unit distribution of a broad class of functions is proposed, which allows to find better linear approximations than the bitwise ones with low complexity in symmetric-key primitives. Last, we apply our methods to SNOW 2.0, an ISO/IEC 18033-4 standard stream cipher, which results in the significantly reduced complexities all below \(2^{164.15}\). This attack is more than \(2^{49}\) times better than the best published result at Asiacrypt 2008. Our results have been verified by experiments on a small-scale version of SNOW 2.0.

Keywords

Stream ciphers Cryptanalysis Large-unit SNOW 2.0 Finite state machine (FSM) Linear feedback shift register (LFSR) 

Notes

Acknowledgments

This work is supported by the National Grand Fundamental Research 973 Program of China (Grant No. 2013CB338002), and the programs of the National Natural Science Foundation of China (Grant No. 60833008, 60603018, 61173134, 91118006, 61272476). The third author was supported in part by the Research Council KU Leuven: a senior postdoctoral scholarship SF/14/010 linked to the GOA TENSE (GOA/11/007).

Supplementary material

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Copyright information

© International Association for Cryptologic Research 2015

Authors and Affiliations

  1. 1.TCA Laboratory, SKLCS, Institute of Software, Chinese Academy of SciencesBeijingChina
  2. 2.State Key Laboratory of CryptologyBeijingChina
  3. 3.FHNWWindischSwitzerland

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