Partial Sums Meet FFT: Improved Attack on 6-Round AES

Orr Dunkelman; Shibam Ghosh; Nathan Keller; Gaëtan Leurent; Avichai Marmor; Victor Mollimard

doi:10.1007/978-3-031-58716-0_5

Partial Sums Meet FFT: Improved Attack on 6-Round AES

Orr Dunkelman, Shibam Ghosh, Nathan Keller, Gaëtan Leurent, Avichai Marmor, Victor Mollimard

Department of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

The partial sums cryptanalytic technique was introduced in 2000 by Ferguson et al., who used it to break 6-round AES with time complexity of 2⁵² S-box computations – a record that has not been beaten ever since. In 2014, Todo and Aoki showed that for 6-round AES, partial sums can be replaced by a technique based on the Fast Fourier Transform (FFT), leading to an attack with a comparable complexity. In this paper we show that the partial sums technique can be combined with an FFT-based technique, to get the best of the two worlds. Using our combined technique, we obtain an attack on 6-round AES with complexity of about 2^46.4 additions. We fully implemented the attack experimentally, along with the partial sums attack and the Todo-Aoki attack, and confirmed that our attack improves the best known attack on 6-round AES by a factor of more than 32. We expect that our technique can be used to significantly enhance numerous attacks that exploit the partial sums technique. To demonstrate this, we use our technique to improve the best known attack on 7-round Kuznyechik by a factor of more than 80.

Original language	English
Title of host publication	Advances in Cryptology – EUROCRYPT 2024 - 43rd Annual International Conference on the Theory and Applications of Cryptographic Techniques, 2024, Proceedings
Editors	Marc Joye, Gregor Leander
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	128-157
Number of pages	30
ISBN (Print)	9783031587153
DOIs	https://doi.org/10.1007/978-3-031-58716-0_5
State	Published - 2024
Event	43rd Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2024 - Zurich, Switzerland Duration: 26 May 2024 → 30 May 2024

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	14651 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	43rd Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2024
Country/Territory	Switzerland
City	Zurich
Period	26/05/24 → 30/05/24

Bibliographical note

Publisher Copyright:
© International Association for Cryptologic Research 2024.

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-031-58716-0_5

Cite this

Dunkelman, O., Ghosh, S., Keller, N., Leurent, G., Marmor, A., & Mollimard, V. (2024). Partial Sums Meet FFT: Improved Attack on 6-Round AES. In M. Joye, & G. Leander (Eds.), Advances in Cryptology – EUROCRYPT 2024 - 43rd Annual International Conference on the Theory and Applications of Cryptographic Techniques, 2024, Proceedings (pp. 128-157). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 14651 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-58716-0_5

Dunkelman, Orr ; Ghosh, Shibam ; Keller, Nathan et al. / Partial Sums Meet FFT : Improved Attack on 6-Round AES. Advances in Cryptology – EUROCRYPT 2024 - 43rd Annual International Conference on the Theory and Applications of Cryptographic Techniques, 2024, Proceedings. editor / Marc Joye ; Gregor Leander. Springer Science and Business Media Deutschland GmbH, 2024. pp. 128-157 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Partial Sums Meet FFT: Improved Attack on 6-Round AES",

abstract = "The partial sums cryptanalytic technique was introduced in 2000 by Ferguson et al., who used it to break 6-round AES with time complexity of 252 S-box computations – a record that has not been beaten ever since. In 2014, Todo and Aoki showed that for 6-round AES, partial sums can be replaced by a technique based on the Fast Fourier Transform (FFT), leading to an attack with a comparable complexity. In this paper we show that the partial sums technique can be combined with an FFT-based technique, to get the best of the two worlds. Using our combined technique, we obtain an attack on 6-round AES with complexity of about 246.4 additions. We fully implemented the attack experimentally, along with the partial sums attack and the Todo-Aoki attack, and confirmed that our attack improves the best known attack on 6-round AES by a factor of more than 32. We expect that our technique can be used to significantly enhance numerous attacks that exploit the partial sums technique. To demonstrate this, we use our technique to improve the best known attack on 7-round Kuznyechik by a factor of more than 80.",

author = "Orr Dunkelman and Shibam Ghosh and Nathan Keller and Ga{\"e}tan Leurent and Avichai Marmor and Victor Mollimard",

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Dunkelman, O , Ghosh, S, Keller, N, Leurent, G, Marmor, A & Mollimard, V 2024, Partial Sums Meet FFT: Improved Attack on 6-Round AES. in M Joye & G Leander (eds), Advances in Cryptology – EUROCRYPT 2024 - 43rd Annual International Conference on the Theory and Applications of Cryptographic Techniques, 2024, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 14651 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 128-157, 43rd Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2024, Zurich, Switzerland, 26/05/24. https://doi.org/10.1007/978-3-031-58716-0_5

Partial Sums Meet FFT: Improved Attack on 6-Round AES. / Dunkelman, Orr ; Ghosh, Shibam; Keller, Nathan et al.
Advances in Cryptology – EUROCRYPT 2024 - 43rd Annual International Conference on the Theory and Applications of Cryptographic Techniques, 2024, Proceedings. ed. / Marc Joye; Gregor Leander. Springer Science and Business Media Deutschland GmbH, 2024. p. 128-157 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 14651 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Dunkelman O , Ghosh S, Keller N, Leurent G, Marmor A, Mollimard V. Partial Sums Meet FFT: Improved Attack on 6-Round AES. In Joye M, Leander G, editors, Advances in Cryptology – EUROCRYPT 2024 - 43rd Annual International Conference on the Theory and Applications of Cryptographic Techniques, 2024, Proceedings. Springer Science and Business Media Deutschland GmbH. 2024. p. 128-157. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-031-58716-0_5