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CRYPTO 2022: Advances in Cryptology – CRYPTO 2022 pp 64–93Cite as

Superposition Meet-in-the-Middle Attacks: Updates on Fundamental Security of AES-like Hashing

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13507))

Abstract

The Meet-in-the-Middle approach is one of the most powerful cryptanalysis techniques, demonstrated by its applications in preimage attacks on the full MD4, MD5, Tiger, HAVAL, and Haraka-512 v2 hash functions, and key recovery of the full block cipher KTANTAN. The success relies on the separation of a primitive into two independent chunks, where each active cell of the state is used to represent only one chunk or is otherwise considered unusable once mixed. We observe that some of such cells are linearly mixed and can be as useful as the independent ones. This leads to the introduction of superposition states and a whole suite of accompanied techniques, which we incorporate into the MILP-based search framework proposed by Bao et al. at EUROCRYPT 2021 and Dong et al. at CRYPTO 2021, and find applications on a wide range of AES-like hash functions and block ciphers.

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Notes

  1. 1.

    Here, the use of phrases “make a concession” or “give in” is due to a view of the forward computation and backward computation be in a competition for being able to be propagated unaffected. In previous attacks, for forward computation, propagation of Blue-attribute is of high priority. When unaffected propagation of Blue-attribute becomes not straightforward due to the existence of cells of Red-attribute, we may try to cancel the impact by consuming the freedom of backward to ensure the propagation of Blue-attribute. We say such cancellation of impact by consuming freedom “concede”, “make a concession” or “give in”.

  2. 2.

    Since we allow bi-direction attribute propagation in superposition states, it might bring benefit to guess a superposition cell to be simultaneously Blue and Red. Thus, here is a slight generalization of the previous GnD strategy.

  3. 3.

    Kiasu-BC  [18] is a tweakable block cipher, the only difference with AES-128 is XOR-ing a 64-bit tweak value to the first two rows of the state after each AddRoundKey.

  4. 4.

    In MITM key-recovery attack, the degree of matching can be efficiently increased using simultaneous matching with multiple plaintext/ciphertext pairs [12].

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Acknowledgements

We thank anonymous reviewers for their valuable comments. This research is partially supported by the National Natural Science Foundation of China (Grants No. 62172410, 61802400, 61732021, 61802399, 61961146004), the National Key R\( { \& }\)D Program of China (Grants No. 2018YFA0704704, 2018YFA0704701), the Youth Innovation Promotion Association of Chinese Academy of Sciences; Nanyang Technological University in Singapore under Grant 04INS000397C230, Ministry of Education in Singapore under Grants RG91/20 and MOE2019-T2-1-060; the Gopalakrishnan – NTU Presidential Postdoctoral Fellowship 2020; the Major Program of Guangdong Basic and Applied Research (Grant No. 2019B030302008), Shandong Province Key R\( { \& }\)D Project (Nos. 2020ZLYS09 and 2019JZZY010133).

Author information

Authors and Affiliations

  1. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China

    Danping Shi

  2. School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore

    Zhenzhen Bao, Jian Guo & Yi Tu

  3. Institute for Network Sciences and Cyberspace, BNRist, Tsinghua University, Beijing, China

    Zhenzhen Bao

  4. School of Cyber Security, University of Chinese Academy of Sciences, Beijing, China

    Danping Shi

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  1. Zhenzhen Bao
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  2. Jian Guo
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  4. Yi Tu
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Correspondence to Danping Shi .

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Editors and Affiliations

  1. New York University, New York, NY, USA

    Yevgeniy Dodis

  2. University of Florida, Gainesville, FL, USA

    Thomas Shrimpton

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Bao, Z., Guo, J., Shi, D., Tu, Y. (2022). Superposition Meet-in-the-Middle Attacks: Updates on Fundamental Security of AES-like Hashing. In: Dodis, Y., Shrimpton, T. (eds) Advances in Cryptology – CRYPTO 2022. CRYPTO 2022. Lecture Notes in Computer Science, vol 13507. Springer, Cham. https://doi.org/10.1007/978-3-031-15802-5_3

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