Abstract
Motivated by applications in advanced cryptographic protocols, research on arithmetization-oriented symmetric primitives has been rising in the field of symmetric cryptography in recent years. In this paper, the authors focus on on the collision attacks for a family of arithmetization-oriented symmetric ciphers GMiMCHash. The authors firstly enhance the algebraically controlled differential attacks proposed by introducing more variables. Then, combining algebraic attacks and differential attacks, the authors propose algebraic-differential attacks on GMiMCHash. This attack method is shown to be effective by experiments on toy versions of GMiMCHash. The authors further introduce some tricks to reduce the complexities of algebraic-differential attacks and improve the success probability of finding collisions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aly A, Ashur T, Ben-Sasson E, et al., Design of symmetric-key primitives for advanced cryptographic protocols, IACR Trans. Symmetric Cryptol., 2020, 2020(3): 1–45.
Albrecht M, Rechberger C, Schneider T, et al., Ciphers for MPC and FHE, Advances in Cryptology - EUROCRYPT 2015-34th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Sofia, 2015.
Albrecht M, Grassi L, Rechberger C, et al., MiMC: Efficient encryption and cryptographic hashing with minimal multiplicative complexity, Advances in Cryptology - ASIACRYPT 2016-22nd International Conference on the Theory and Application of Cryptology and Information Security, Hanoi, 2016.
Ashur T and Dhooghe S, MARVELlous: A STARK-friendly family of cryptographic primitives, 2018, https://eprint.iacr.org/2018/1098.
Albrecht M, Grassi L, Perrin L, et al., Feistel structures for MPC, and more, Computer Security -ESORICS 2019-24th European Symposium on Research in Computer Security, Luxembourg, 2019.
Grassi L, Luftenegger R, Rechberger C, et al., On a generalization of substitution-permutation networks: The HADES design strategy, Advances in Cryptology - EUROCRYPT 2020-39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Zagreb, 2020.
Canteaut A, Beyne T, Dinuret I, et al., Report on the security of stark-friendly hash functions (version 2.0), 2020, https://hal.inria.fr/hal-02883253/document.
Dinur I, Liu Y, Meier W, et al., Optimized interpolation attacks on LowMC, Advances in Cryptology - ASIACRYPT 2015-21st International Conference on the Theory and Application of Cryptology and Information Security, Auckland, 2015.
Dobraunig C, Eichlseder M, and Mendel F, Higher-order cryptanalysis of LowMC, Information Security and Cryptology - ICISC 2015–18th International Conference, Seoul, 2015.
Rechberger C, Soleimany H, and Tiessen T, Cryptanalysis of low-data instances of full LowMCv2, IACR Trans. Symmetric Cryptol., 2018, 2018(3): 163–181.
Banik S, Barooti K, Durak F, et al., Cryptanalysis of LowMC instances using single plaintext/ciphertext pair, IACR Trans. Symmetric Cryptol., 2020, 2020(4): 130–146.
Albrecht M, Cid C, Grassi L, et al., Algebraic cryptanalysis of STARK-friendly designs: Application to MARVELlous and MiMC, Advances in Cryptology - ASIACRYPT 2019–25th International Conference on the Theory and Application of Cryptology and Information Security, Kobe, 2019.
Li C and Preneel B, Improved interpolation attacks on cryptographic primitives of low algebraic degree, Selected Areas in Cryptography-SAC 2019–26th International Conference, Waterloo, 2019.
Roy A, Andreeva E, and Sauer J, Interpolation cryptanalysis of unbalanced feistel networks with low degree round functions, Selected Areas in Cryptography - SAC 2020-27th International Conference, Halifax, 2020.
Beyne T, Canteaut A, Dinur I, et al., Out of oddity-new cryptanalytic techniques against symmetric primitives optimized for integrity proof systems, Advances in Cryptology - CRYPTO 2020–40th Annual International Cryptology Conference, Santa Barbara, 2020.
Eichlseder M, Grassi L, Lüftenegger R, et al., An algebraic attack on ciphers with low-degree round functions: Application to full MiMC, Advances in Cryptology - ASIACRYPT 2020–26th International Conference on the Theory and Application of Cryptology and Information Security, Daejeon, 2020.
Bertoni G, Daemen J, Peeters M, et al., On the indifferentiability of the sponge construction, Advances in Cryptology-EUROCRYPT 2008-27th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Istanbul, 2008.
Sun Y and Wang D, The F5 algorithm in Buchberger’s style, Journal of Systems Science & Complexity, 2011, 24(6): 1218–1231.
Wang M, Wang X, and Hui L, Differential-algebraic cryptanalysis of reduced-round of serpent 256, Sci. China Inf. Sci., 2010, 53: 546–556.
Lu D, Sun Y, and Wang D, A survey on algorithms for computing comprehensive Gröbner systems and comprehensive Gröbner bases, Journal of Systems Science & Complexity, 2019, 32(1): 234–255.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
The authors declare no conflict of interest.
Additional information
This research was supported by the National Natural Science Foundation of China under Grant No. 61972393 and the Climbing Program from Institute of Information Engineering CAS under Grant No. E3Z0221112.
Rights and permissions
About this article
Cite this article
Li, Z., Wu, B. & Lin, D. Algebraic-Differential Attacks on a Family of Arithmetization-Oriented Symmetric Ciphers. J Syst Sci Complex 36, 2681–2702 (2023). https://doi.org/10.1007/s11424-023-1511-7
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11424-023-1511-7