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Mixing Property Tester: A General Framework for Evaluating the Mixing Properties of Initialization of Stream Ciphers

  • Lin DingEmail author
  • Dawu Gu
  • Lei Wang
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 1122)

Abstract

In this paper, a general framework for evaluating the mixing properties of initialization of stream ciphers, called Mixing Property Tester-MPT, is exploited and formalized. Based on this general framework, we propose a concrete and efficient algorithm, which can compute the maximum number of initialization rounds of a given stream cipher such that any internal state bit or generated keystream bit does not achieve full mixing properties. Our algorithm has linear time complexity and needs a negligible amount of memory. As illustrations, we apply our algorithm to ZUC-128, ZUC-256 and Trivium stream ciphers. The results show that though ZUC-256 has a much larger initial input size than ZUC-128, its mixing properties are almost as good as ZUC-128. As for Trivium, the tap positions of keystream output function are not chosen optimally with respect to this tester and we provide some better selections of tap positions. As a general cryptanalytic tool, MPT can help to give the designers more insights to choose the initialization functions and the required number of initialization rounds.

Keywords

Stream cipher Initialization Mixing property ZUC-128 ZUC-256 Trivium 

Notes

Acknowledgments

The authors would like to thank the anonymous reviewers for their valuable comments and suggestions. This work was supported by the National Natural Science Foundation of China under Grant 61602514, 61802437, 61272488, 61202491, 61572516, 61272041, 61772547, National Cryptography Development Fund under Grant MMJJ20170125 and National Postdoctoral Program for Innovative Talents under Grant BX201700153.

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© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of Computer Science and EngineeringShanghai Jiao Tong UniversityShanghaiChina
  2. 2.PLA SSF Information Engneering UniversityZhengzhouChina
  3. 3.Westone Cryptologic Research CenterBeijingChina

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