首页|New Algebraic Attacks on Grendel with the Strategy of Bypassing SPN Steps

New Algebraic Attacks on Grendel with the Strategy of Bypassing SPN Steps

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The rapid development of modern cryptographic applications such as zero-knowledge,secure multi-party computation,fully homomorphic encryption has motivated the design of new so-called arithmetization-oriented symmetric primitives.As designing ciphers in this domain is relatively new and not well-understood,the security of these new ciphers remains to be completely assessed.In this paper,we revisit the security analysis of arithmetization-oriented cipher Grendel.Grendel uses the Legendre symbol as a component,which is tailored specifically for the use in zero-knowledge and efficiently-varifiable proof systems.At FSE 2022,the first preimage attack on some original full GrendelHash instances was proposed.As a countermeasure,the designer adds this attack into the security analysis and updates the formula to derive the secure number of rounds.In our work,we present new algebraic attacks on GrendelHash.For the preimage attack,we can reduce the complexity or attack one more round than previous attacks for some instances.In addition,we present the first collision attack on some round-reduced instances by solving the constrained input/constrained output problem for the underlying permutations.

GrendelSolving univariate equationBypassing substitution-permutation networks stepsPreim-age attackCollision attack

Wenxiao QIAO、Siwei SUN、Lei HU

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State Key Laboratory of Information Security,Institute of Information Engineering,Chinese Academy of Sciences,Beijing 100085,China

School of Cyber Security,University of Chinese Academy of Sciences,Beijing 100049,China

School of Cryptology,University of Chinese Academy of Sciences,Beijing 100049,China

State Key Laboratory of Cryptology,P.O.Box 5159,Beijing 100878,China

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National Key Research and Development Program of ChinaNational Natural Science Foundation of ChinaFundamental Research Funds for the Central Universities

2022YFB270190062202444

2024

10.23919/cje.2023.00.127

电子学报(英文)

电子学报(英文)

CSTPCDEI
ISSN：1022-4653
年,卷(期)：2024.33(3)