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New Approaches for Estimating the Bias of Differential-Linear Distinguishers

Authors:
Ting Peng , Key Laboratory of Cyberspace Security Defense, Institute of Information Engineering, CAS
Wentao Zhang , Key Laboratory of Cyberspace Security Defense, Institute of Information Engineering, CAS
Jingsui Weng , Key Laboratory of Cyberspace Security Defense, Institute of Information Engineering, CAS
Tianyou Ding , Key Laboratory of Cyberspace Security Defense, Institute of Information Engineering, CAS
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DOI: 10.1007/978-3-031-68385-5_6 (login may be required)
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Presentation: Slides
Conference: CRYPTO 2024
Abstract: Differential-linear cryptanalysis was introduced by Langford and Hellman in 1994 and has been extensively studied since then. In 2019, Bar-On et al. presented the Differential-Linear Connectivity Table (DLCT), which connects the differential part and the linear part, thus an attacked cipher is divided to 3 subciphers: the differential part, the DLCT part, and the linear part. In this paper, we firstly present an accurate mathematical formula which establishes a relation between differential-linear and truncated differential cryptanalysis. Using the formula, the bias estimate of a differential-linear distinguisher can be converted to the probability calculations of a series of truncated differentials. Then, we propose a novel and natural concept, the TDT, which can be used to accelerate the calculation of the probabilities of truncated differentials. Based on the formula and the TDT, we propose two novel approaches for estimating the bias of a differential-linear distinguisher. We demonstrate the accuracy and efficiency of our new approaches by applying them to 5 symmetric-key primitives: Ascon, Serpent, AES, CLEFIA, and KNOT. For Ascon and Serpent, we update the best known differential-linear distinguishers. For AES, CLEFIA, and KNOT, for the first time we give the theoretical differential-linear biases for different rounds.
BibTeX
@inproceedings{crypto-2024-34306,
  title={New Approaches for Estimating the Bias of Differential-Linear Distinguishers},
  publisher={Springer-Verlag},
  doi={10.1007/978-3-031-68385-5_6},
  author={Ting Peng and Wentao Zhang and Jingsui Weng and Tianyou Ding},
  year=2024
}