Towards the Links of Cryptanalytic Methods on MPC/FHE/ZK-Friendly Symmetric-Key Primitives

Authors

  • Shiyao Chen Strategic Centre for Research in Privacy-Preserving Technologies and Systems, Nanyang Technological University, Singapore, Singapore; Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore; School of Cyber Science and Technology, Shandong University, Qingdao, China
  • Chun Guo School of Cyber Science and Technology, Shandong University, Qingdao, China; Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education, Shandong University, Qingdao, China; Shandong Research Institute of Industrial Technology, Jinan, China
  • Jian Guo Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore
  • Li Liu School of Cyber Science and Technology, Shandong University, Qingdao, China; Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education, Shandong University, Qingdao, China
  • Meiqin Wang School of Cyber Science and Technology, Shandong University, Qingdao, China; Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education, Shandong University, Qingdao, China; Quan Cheng Laboratory, Jinan, China
  • Puwen Wei School of Cyber Science and Technology, Shandong University, Qingdao, China; Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education, Shandong University, Qingdao, China; Quan Cheng Laboratory, Jinan, China
  • Zeyu Xu School of Cyber Science and Technology, Shandong University, Qingdao, China; Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education, Shandong University, Qingdao, China

DOI:

https://doi.org/10.46586/tosc.v2023.i2.132-175

Keywords:

Symmetric-Key, Cryptanalysis, Proof, MPC/FHE/ZK-Friendly Primitives, Generalized Feistel, GMiMC

Abstract

Symmetric-key primitives designed over the prime field Fp with odd characteristics, rather than the traditional Fn2 , are becoming the most popular choice for MPC/FHE/ZK-protocols for better efficiencies. However, the security of Fp is less understood as there are highly nontrivial gaps when extending the cryptanalysis tools and experiences built on Fn2 in the past few decades to Fp.
At CRYPTO 2015, Sun et al. established the links among impossible differential, zero-correlation linear, and integral cryptanalysis over Fn2 from the perspective of distinguishers. In this paper, following the definition of linear correlations over Fp by Baignères, Stern and Vaudenay at SAC 2007, we successfully establish comprehensive links over Fp, by reproducing the proofs and offering alternatives when necessary. Interesting and important differences between Fp and Fn2 are observed.
- Zero-correlation linear hulls can not lead to integral distinguishers for some cases over Fp, while this is always possible over Fn2
proven by Sun et al..
- When the newly established links are applied to GMiMC, its impossible differential, zero-correlation linear hull and integral distinguishers can be increased by up to 3 rounds for most of the cases, and even to an arbitrary number of rounds for some special and limited cases, which only appeared in Fp. It should be noted that all these distinguishers do not invalidate GMiMC’s security claims.
The development of the theories over Fp behind these links, and properties identified (be it similar or different) will bring clearer and easier understanding of security of primitives in this emerging Fp field, which we believe will provide useful guides for future cryptanalysis and design.

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Published

2023-06-16

How to Cite

Chen, S., Guo, C., Guo, J., Liu, L., Wang, M., Wei, P., & Xu, Z. (2023). Towards the Links of Cryptanalytic Methods on MPC/FHE/ZK-Friendly Symmetric-Key Primitives. IACR Transactions on Symmetric Cryptology, 2023(2), 132–175. https://doi.org/10.46586/tosc.v2023.i2.132-175

Issue

Vol. 2023 No. 2

Section

Articles

License

Copyright (c) 2023 Shiyao Chen, Chun Guo, Jian Guo, Li Liu, Meiqin Wang, Puwen Wei, Zeyu Xu

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.