Algebraic Cryptanalysis of STARK-Friendly Designs: Application to MARVELlous and MiMC

Martin R. Albrecht, Carlos Cid, Lorenzo Grassi, Dmitry Khovratovich, Reinhard Lüftenegger, Christian Rechberger, Markus Schofnegger

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

Abstract

The block cipher Jarvis and the hash function Friday, both members of the MARVELlous family of cryptographic primitives, were recently proposed as custom designs aimed at addressing bottlenecks involving practical applications of STARKs. In the proposal several types of algebraic attacks were ruled out, and security arguments from Rijndael/AES were used to inform the choice for the number of rounds, with extra security margin added. In this work we describe new algebraic attacks on Jarvis and Friday using Gröbner bases, showing that the proposed number of rounds is not sufficient to provide security. In Jarvis, the round function is obtained by combining a finite field inversion S-box with a full-degree linearised permutation polynomial. However, we show that even though the high degree of this polynomial should prevent some algebraic attacks (as claimed by the designers), their particular algebraic properties make the designs vulnerable to Gröbner basis attacks. Our analysis illustrates that block cipher designs for algebraic platforms such as STARKs, FHE or MPC may be particularly vulnerable to algebraic attacks. Finally, we argue that MiMC -- a cipher similar in structure to Jarvis -- is resistant against our proposed attack strategy.
Original languageEnglish
Title of host publicationASIACRYPT 2019
Publication statusAccepted/In press - 15 Aug 2019
EventASIACRYPT 2019 - Kobe, Japan
Duration: 8 Dec 201912 Dec 2019

Conference

ConferenceASIACRYPT 2019
CountryJapan
CityKobe
Period8/12/1912/12/19

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Polynomials
Hash functions

Keywords

  • Gröbner Basis
  • MARVELlous
  • Jarvis
  • Friday
  • MiMC
  • STARKs
  • Algebraic Cryptanalysis
  • Arithmetic Circuits

Cite this

Algebraic Cryptanalysis of STARK-Friendly Designs: Application to MARVELlous and MiMC. / Albrecht, Martin R.; Cid, Carlos; Grassi, Lorenzo; Khovratovich, Dmitry; Lüftenegger, Reinhard; Rechberger, Christian; Schofnegger, Markus.

ASIACRYPT 2019. 2019.

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

Albrecht, MR, Cid, C, Grassi, L, Khovratovich, D, Lüftenegger, R, Rechberger, C & Schofnegger, M 2019, Algebraic Cryptanalysis of STARK-Friendly Designs: Application to MARVELlous and MiMC. in ASIACRYPT 2019. ASIACRYPT 2019, Kobe, Japan, 8/12/19.
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AB - The block cipher Jarvis and the hash function Friday, both members of the MARVELlous family of cryptographic primitives, were recently proposed as custom designs aimed at addressing bottlenecks involving practical applications of STARKs. In the proposal several types of algebraic attacks were ruled out, and security arguments from Rijndael/AES were used to inform the choice for the number of rounds, with extra security margin added. In this work we describe new algebraic attacks on Jarvis and Friday using Gröbner bases, showing that the proposed number of rounds is not sufficient to provide security. In Jarvis, the round function is obtained by combining a finite field inversion S-box with a full-degree linearised permutation polynomial. However, we show that even though the high degree of this polynomial should prevent some algebraic attacks (as claimed by the designers), their particular algebraic properties make the designs vulnerable to Gröbner basis attacks. Our analysis illustrates that block cipher designs for algebraic platforms such as STARKs, FHE or MPC may be particularly vulnerable to algebraic attacks. Finally, we argue that MiMC -- a cipher similar in structure to Jarvis -- is resistant against our proposed attack strategy.

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