Automatic Search for Bit-Based Division Property

Shibam Ghosh; Orr Dunkelman

doi:10.1007/978-3-030-88238-9_13

Automatic Search for Bit-Based Division Property

Shibam Ghosh, Orr Dunkelman

Department of Computer Science

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

Abstract

Division properties, introduced by Todo at Eurocrypt 2015, are an extension of square attack (also called saturation attack or integral cryptanalysis). Given their importance, a large number of works tried to offer automatic tools to find division properties, primarily based on MILP or SAT/SMT. This paper studies better modeling techniques for finding division properties using the Constraint Programming and SAT/SMT-based automatic tools. We use the fact that the Quine-McCluskey algorithm produces a concise CNF representation corresponding to the division trail table of an Sbox. As a result, we can offer significantly more compact models, which allow SAT and Constraint Programming tools to outperform previous results. To show the strength of our new approach, we look at the NIST lightweight candidate KNOT and Ascon. We show several new distinguishers with a lower data complexity for 17-round KNOT-256, KNOT-384 and 19-round KNOT-512. In addition, for the 5-round Ascon, we get a lower data distinguisher than the previous division-based results. Finally, we revisit the method to extend the integral distinguisher by composing linear layers at the input and output. We provide a formulation to find the optimal number of linear combinations that need to be considered. As a result of this new formulation, we prove that 18-round KNOT-256 and KNOT-384 have no integral distinguisher using conventional division property and we show this more efficiently than the previous methods.

Original language	English
Title of host publication	Progress in Cryptology – LATINCRYPT 2021 - 7th International Conference on Cryptology and Information Security in Latin America, Proceedings
Editors	Patrick Longa, Carla Ràfols
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	254-274
Number of pages	21
ISBN (Print)	9783030882372
DOIs	https://doi.org/10.1007/978-3-030-88238-9_13
State	Published - 2021
Event	7th International Conference on Cryptology and Information Security in Latin America, LATINCRYPT 2021 - Bogotá, Colombia Duration: 6 Oct 2021 → 8 Oct 2021

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	12912 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	7th International Conference on Cryptology and Information Security in Latin America, LATINCRYPT 2021
Country/Territory	Colombia
City	Bogotá
Period	6/10/21 → 8/10/21

Bibliographical note

Funding Information:
The research described in this paper was supported in part by the Center for Cyber, Law, and Policy in conjunction with the Israel National Cyber Bureau in the Prime Minister?s Office and by the Israeli Science Foundation through grants No. 880/18 and 3380/19. The authors were also supported by the Data Science Research Center (DSRC), University of Haifa.

Funding Information:
Acknowledgements. The research described in this paper was supported in part by the Center for Cyber, Law, and Policy in conjunction with the Israel National Cyber Bureau in the Prime Minister’s Office and by the Israeli Science Foundation through grants No. 880/18 and 3380/19. The authors were also supported by the Data Science Research Center (DSRC), University of Haifa.

Publisher Copyright:
© 2021, Springer Nature Switzerland AG.

Keywords

Ascon
Constraint programming
Division property
Integral cryptanalysis
KNOT

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-030-88238-9_13

https://eprint.iacr.org/2021/965.pdf

Cite this

Ghosh, S., & Dunkelman, O. (2021). Automatic Search for Bit-Based Division Property. In P. Longa, & C. Ràfols (Eds.), Progress in Cryptology – LATINCRYPT 2021 - 7th International Conference on Cryptology and Information Security in Latin America, Proceedings (pp. 254-274). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12912 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-88238-9_13

Ghosh, Shibam ; Dunkelman, Orr. / Automatic Search for Bit-Based Division Property. Progress in Cryptology – LATINCRYPT 2021 - 7th International Conference on Cryptology and Information Security in Latin America, Proceedings. editor / Patrick Longa ; Carla Ràfols. Springer Science and Business Media Deutschland GmbH, 2021. pp. 254-274 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Automatic Search for Bit-Based Division Property",

abstract = "Division properties, introduced by Todo at Eurocrypt 2015, are an extension of square attack (also called saturation attack or integral cryptanalysis). Given their importance, a large number of works tried to offer automatic tools to find division properties, primarily based on MILP or SAT/SMT. This paper studies better modeling techniques for finding division properties using the Constraint Programming and SAT/SMT-based automatic tools. We use the fact that the Quine-McCluskey algorithm produces a concise CNF representation corresponding to the division trail table of an Sbox. As a result, we can offer significantly more compact models, which allow SAT and Constraint Programming tools to outperform previous results. To show the strength of our new approach, we look at the NIST lightweight candidate KNOT and Ascon. We show several new distinguishers with a lower data complexity for 17-round KNOT-256, KNOT-384 and 19-round KNOT-512. In addition, for the 5-round Ascon, we get a lower data distinguisher than the previous division-based results. Finally, we revisit the method to extend the integral distinguisher by composing linear layers at the input and output. We provide a formulation to find the optimal number of linear combinations that need to be considered. As a result of this new formulation, we prove that 18-round KNOT-256 and KNOT-384 have no integral distinguisher using conventional division property and we show this more efficiently than the previous methods.",

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Ghosh, S & Dunkelman, O 2021, Automatic Search for Bit-Based Division Property. in P Longa & C Ràfols (eds), Progress in Cryptology – LATINCRYPT 2021 - 7th International Conference on Cryptology and Information Security in Latin America, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 12912 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 254-274, 7th International Conference on Cryptology and Information Security in Latin America, LATINCRYPT 2021, Bogotá, Colombia, 6/10/21. https://doi.org/10.1007/978-3-030-88238-9_13

Automatic Search for Bit-Based Division Property. / Ghosh, Shibam ; Dunkelman, Orr.
Progress in Cryptology – LATINCRYPT 2021 - 7th International Conference on Cryptology and Information Security in Latin America, Proceedings. ed. / Patrick Longa; Carla Ràfols. Springer Science and Business Media Deutschland GmbH, 2021. p. 254-274 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12912 LNCS).

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

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AU - Dunkelman, Orr

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N2 - Division properties, introduced by Todo at Eurocrypt 2015, are an extension of square attack (also called saturation attack or integral cryptanalysis). Given their importance, a large number of works tried to offer automatic tools to find division properties, primarily based on MILP or SAT/SMT. This paper studies better modeling techniques for finding division properties using the Constraint Programming and SAT/SMT-based automatic tools. We use the fact that the Quine-McCluskey algorithm produces a concise CNF representation corresponding to the division trail table of an Sbox. As a result, we can offer significantly more compact models, which allow SAT and Constraint Programming tools to outperform previous results. To show the strength of our new approach, we look at the NIST lightweight candidate KNOT and Ascon. We show several new distinguishers with a lower data complexity for 17-round KNOT-256, KNOT-384 and 19-round KNOT-512. In addition, for the 5-round Ascon, we get a lower data distinguisher than the previous division-based results. Finally, we revisit the method to extend the integral distinguisher by composing linear layers at the input and output. We provide a formulation to find the optimal number of linear combinations that need to be considered. As a result of this new formulation, we prove that 18-round KNOT-256 and KNOT-384 have no integral distinguisher using conventional division property and we show this more efficiently than the previous methods.

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KW - Integral cryptanalysis

KW - KNOT

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Ghosh S , Dunkelman O. Automatic Search for Bit-Based Division Property. In Longa P, Ràfols C, editors, Progress in Cryptology – LATINCRYPT 2021 - 7th International Conference on Cryptology and Information Security in Latin America, Proceedings. Springer Science and Business Media Deutschland GmbH. 2021. p. 254-274. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-88238-9_13

Automatic Search for Bit-Based Division Property

Abstract

Publication series

Conference

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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Cite this