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A New Framework for Finding Nonlinear Superpolies in Cube Attacks Against Trivium-Like Ciphers

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Information Security and Privacy (ACISP 2018)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 10946))

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Abstract

In this paper, we focus on traditional cube attacks against Trivium-like ciphers in which linear and nonlinear superpolies are experimentally tested. We provide a new framework on nonlinear superpoly recoveries by exploiting a kind of linearization technique. It worth noting that, in this new framework, the complexities of testing and recovering nonlinear superpolies are almost the same as those of testing and recovering linear superpolies. Moreover, extensive experiments show that by making use of the new framework, the probability to find a quadratic superpoly is almost twice as large as that to find a linear superpoly for Kreyvium and they are almost the same for Trivium. Hopefully, this new framework would provide some new insights on cube attacks against NFSR-based ciphers, and in particular make nonlinear superpolies potentially useful in the future cube attacks.

Supported by National Natural Science Foundation of China 61672533.

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Author information

Authors and Affiliations

  1. National Digital Switching System Engineering and Technological Research Center, P.O. Box 407, 62 Kexue Road, Zhengzhou, 450001, China

    Chendong Ye & Tian Tian

Authors
  1. Chendong Ye
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  2. Tian Tian
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Corresponding author

Correspondence to Tian Tian .

Editor information

Editors and Affiliations

  1. University of Wollongong, Wollongong, NSW, Australia

    Willy Susilo

  2. University of Wollongong, Wollongong, NSW, Australia

    Guomin Yang

Appendix

Appendix

In this paper, all our programs are implemented with CUDA and we perform experiments on a PC with an Intel(R) Core i7-4790k @4.00 GHZ CPU, 32 G memory and a GTX-1080 GPU. In the following, we list all the experimental results in details.

Table 5. New superpolies of round-reduced Trivium variants
Full size table
Table 6. Superpolies of the 776-round Kreyvium
Full size table
Table 7. Superpolies of round-reduce TriviA-SC-v2 variants
Full size table

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Ye, C., Tian, T. (2018). A New Framework for Finding Nonlinear Superpolies in Cube Attacks Against Trivium-Like Ciphers. In: Susilo, W., Yang, G. (eds) Information Security and Privacy. ACISP 2018. Lecture Notes in Computer Science(), vol 10946. Springer, Cham. https://doi.org/10.1007/978-3-319-93638-3_11

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  • DOI: https://doi.org/10.1007/978-3-319-93638-3_11

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