Abstract
At CRYPTO 2017, Liu presented a general framework of iterative estimation of algebraic degree for NFSR-based cryptosystems, by exploiting a technique, called numeric mapping, and gave distinguishing attacks on Trivium-like ciphers, including Trivium, Kreyvium and TriviA-SC. This paper aims at further investigating algebraic degree estimation of NFSR-based cryptosystems from a new perspective. A new general framework for algebraic degree estimation of NFSR-based cryptosystems is formalized to exploit a new way of constructing distinguishing attacks. This illustrates that our new framework is more accurate than Liu’s when estimating the upper bound on algebraic degree of NFSR-based cryptosystems. As result, the best known attack on the full simplified variant of TriviA-SC v2 is presented.
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Acknowledgements
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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Appendices
Appendix
A The Procedure \({\textbf {CDE}}{{\textbf {G}}_{Tri}}\) for \(\delta = B\) and \(\delta = C\)
The procedure \({\textbf {CDE}}{{\textbf {G}}_{Tri}}\) in the two cases, \(\delta = B\) and \(\delta = C\), are described in Algorithms 4 and 5, respectively.
B The Cubes Used in Our Attacks
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Ding, L., Wu, Z. (2022). New General Framework for Algebraic Degree Evaluation of NFSR-Based Cryptosystems. In: Park, J.H., Seo, SH. (eds) Information Security and Cryptology – ICISC 2021. ICISC 2021. Lecture Notes in Computer Science, vol 13218. Springer, Cham. https://doi.org/10.1007/978-3-031-08896-4_19
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