Optimized interpolation attacks on LowMC

Itai Dinur; Yunwen Liu; Willi Meier; Qingju Wang

doi:https://doi.org/10.1007/978-3-662-48800-3_22

Optimized interpolation attacks on LowMC

Itai Dinur, Yunwen Liu, Willi Meier, Qingju Wang

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

Abstract

LowMC is a collection of block cipher families introduced at Eurocrypt 2015 by Albrecht et al. Its design is optimized for instantiations of multi-party computation, fully homomorphic encryption, and zero-knowledge proofs. A unique feature of LowMC is that its internal affine layers are chosen at random, and thus each block cipher family contains a huge number of instances. The Eurocrypt paper proposed two specific block cipher families of LowMC, having 80-bit and 128-bit keys. In this paper, we mount interpolation attacks (algebraic attacks introduced by Jakobsen and Knudsen) on LowMC, and show that a practically significant fraction of 2⁻³⁸ of its 80-bit key instances could be broken 2²³ times faster than exhaustive search. Moreover, essentially all instances that are claimed to provide 128-bit security could be broken about 1000 times faster. In order to obtain these results we optimize the interpolation attack using several new techniques. In particular, we present an algorithm that combines two main variants of the interpolation attack, and results in an attack which is more efficient than each one.

Original language	American English
Title of host publication	Advances in Cryptology – ASIACRYPT 2015 - 21st International Conference on the Theory and Application of Cryptology and Information Security, Proceedings
Editors	Tetsu Iwata, Jung Hee Cheon
Publisher	Springer Verlag
Pages	535-560
Number of pages	26
ISBN (Print)	9783662487990
DOIs	https://doi.org/10.1007/978-3-662-48800-3_22
State	Published - 1 Jan 2015
Externally published	Yes
Event	21st International Conference on the Theory and Application of Cryptology and Information Security, ASIACRYPT 2015 - Auckland, New Zealand Duration: 29 Nov 2015 → 3 Dec 2015

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9453

Conference

Conference	21st International Conference on the Theory and Application of Cryptology and Information Security, ASIACRYPT 2015
Country/Territory	New Zealand
City	Auckland
Period	29/11/15 → 3/12/15

Keywords

Block cipher
High-order differential cryptanalysis
Interpolation attack
LowMC

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science

Access to Document

https://doi.org/10.1007/978-3-662-48800-3_22

Cite this

Dinur, I., Liu, Y., Meier, W., & Wang, Q. (2015). Optimized interpolation attacks on LowMC. In T. Iwata, & J. H. Cheon (Eds.), Advances in Cryptology – ASIACRYPT 2015 - 21st International Conference on the Theory and Application of Cryptology and Information Security, Proceedings (pp. 535-560). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9453). Springer Verlag. https://doi.org/10.1007/978-3-662-48800-3_22

Dinur, Itai ; Liu, Yunwen ; Meier, Willi 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, Proceedings. editor / Tetsu Iwata ; Jung Hee Cheon. Springer Verlag, 2015. pp. 535-560 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "LowMC is a collection of block cipher families introduced at Eurocrypt 2015 by Albrecht et al. Its design is optimized for instantiations of multi-party computation, fully homomorphic encryption, and zero-knowledge proofs. A unique feature of LowMC is that its internal affine layers are chosen at random, and thus each block cipher family contains a huge number of instances. The Eurocrypt paper proposed two specific block cipher families of LowMC, having 80-bit and 128-bit keys. In this paper, we mount interpolation attacks (algebraic attacks introduced by Jakobsen and Knudsen) on LowMC, and show that a practically significant fraction of 2−38 of its 80-bit key instances could be broken 223 times faster than exhaustive search. Moreover, essentially all instances that are claimed to provide 128-bit security could be broken about 1000 times faster. In order to obtain these results we optimize the interpolation attack using several new techniques. In particular, we present an algorithm that combines two main variants of the interpolation attack, and results in an attack which is more efficient than each one.",

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author = "Itai Dinur and Yunwen Liu and Willi Meier and Qingju Wang",

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Dinur, I, Liu, Y, Meier, W & Wang, Q 2015, Optimized interpolation attacks on LowMC. in T Iwata & JH Cheon (eds), Advances in Cryptology – ASIACRYPT 2015 - 21st International Conference on the Theory and Application of Cryptology and Information Security, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9453, Springer Verlag, pp. 535-560, 21st International Conference on the Theory and Application of Cryptology and Information Security, ASIACRYPT 2015, Auckland, New Zealand, 29/11/15. https://doi.org/10.1007/978-3-662-48800-3_22

Optimized interpolation attacks on LowMC. / Dinur, Itai; Liu, Yunwen; Meier, Willi et al.
Advances in Cryptology – ASIACRYPT 2015 - 21st International Conference on the Theory and Application of Cryptology and Information Security, Proceedings. ed. / Tetsu Iwata; Jung Hee Cheon. Springer Verlag, 2015. p. 535-560 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9453).

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

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T1 - Optimized interpolation attacks on LowMC

AU - Dinur, Itai

AU - Liu, Yunwen

AU - Meier, Willi

AU - Wang, Qingju

N1 - Publisher Copyright: © International Association for Cryptologic Research 2015.

PY - 2015/1/1

Y1 - 2015/1/1

N2 - LowMC is a collection of block cipher families introduced at Eurocrypt 2015 by Albrecht et al. Its design is optimized for instantiations of multi-party computation, fully homomorphic encryption, and zero-knowledge proofs. A unique feature of LowMC is that its internal affine layers are chosen at random, and thus each block cipher family contains a huge number of instances. The Eurocrypt paper proposed two specific block cipher families of LowMC, having 80-bit and 128-bit keys. In this paper, we mount interpolation attacks (algebraic attacks introduced by Jakobsen and Knudsen) on LowMC, and show that a practically significant fraction of 2−38 of its 80-bit key instances could be broken 223 times faster than exhaustive search. Moreover, essentially all instances that are claimed to provide 128-bit security could be broken about 1000 times faster. In order to obtain these results we optimize the interpolation attack using several new techniques. In particular, we present an algorithm that combines two main variants of the interpolation attack, and results in an attack which is more efficient than each one.

AB - LowMC is a collection of block cipher families introduced at Eurocrypt 2015 by Albrecht et al. Its design is optimized for instantiations of multi-party computation, fully homomorphic encryption, and zero-knowledge proofs. A unique feature of LowMC is that its internal affine layers are chosen at random, and thus each block cipher family contains a huge number of instances. The Eurocrypt paper proposed two specific block cipher families of LowMC, having 80-bit and 128-bit keys. In this paper, we mount interpolation attacks (algebraic attacks introduced by Jakobsen and Knudsen) on LowMC, and show that a practically significant fraction of 2−38 of its 80-bit key instances could be broken 223 times faster than exhaustive search. Moreover, essentially all instances that are claimed to provide 128-bit security could be broken about 1000 times faster. In order to obtain these results we optimize the interpolation attack using several new techniques. In particular, we present an algorithm that combines two main variants of the interpolation attack, and results in an attack which is more efficient than each one.

KW - Block cipher

KW - High-order differential cryptanalysis

KW - Interpolation attack

KW - LowMC

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DO - https://doi.org/10.1007/978-3-662-48800-3_22

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T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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Y2 - 29 November 2015 through 3 December 2015

ER -

Dinur I, Liu Y, Meier W, Wang Q. Optimized interpolation attacks on LowMC. In Iwata T, Cheon JH, editors, Advances in Cryptology – ASIACRYPT 2015 - 21st International Conference on the Theory and Application of Cryptology and Information Security, Proceedings. Springer Verlag. 2015. p. 535-560. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: https://doi.org/10.1007/978-3-662-48800-3_22

Optimized interpolation attacks on LowMC

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Keywords

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