An Algebraic Attack on Rank Metric Code-Based Cryptosystems

Bardet, Magali; Briaud, Pierre; Bros, Maxime; Gaborit, Philippe; Neiger, Vincent; Ruatta, Olivier; Tillich, Jean–Pierre

doi:10.1007/978-3-030-45727-3_3

Cited by 50 publications

(70 citation statements)

References 39 publications

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“…This family of attacks consists in modeling the decoding problem into a system of multivariate polynomial equations and then solve this system. In [11], the constructed system was solved by using Gröbner basis techniques. Similar approaches exist for solving the MinRank problem, such as the Kipnis-Shamir modeling [28] and the minors modeling (described for example in [19]); the complexity of solving MinRank using these modelings has been investigated in [18,19].…”

Section: Problem 2 (Minrank Problem)mentioning

confidence: 99%

“…Our contribution. In this paper, we follow on from the approach in [11] and propose a slightly different modeling to solve the RD problem. This system can be solved "directly" by linearization, avoiding the use of Gröbner basis algorithms such as Faugère's F4 algorithm, see [17].…”

Section: Problem 2 (Minrank Problem)mentioning

confidence: 99%

“…It is equivalent to the Rank Syndrome Decoding problem, written RSD, for which one uses the parity check matrix of the code instead of the generator matrix. There are two approaches to solve RD instances: the combinatorial ones such as those in [23] and [10] and the algebraic ones, such as in [11]; the latter are one of the purposes of this article.…”

Section: Introductionmentioning

confidence: 99%

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Improvements of Algebraic Attacks for Solving the Rank Decoding and MinRank Problems

Bardet

Bros

Cabarcas

et al. 2020

Advances in Cryptology – ASIACRYPT 2020

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113

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Section: Problem 2 (Minrank Problem)mentioning

confidence: 99%

Section: Problem 2 (Minrank Problem)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Improvements of Algebraic Attacks for Solving the Rank Decoding and MinRank Problems

Bardet

Bros

Cabarcas

et al. 2020

Advances in Cryptology – ASIACRYPT 2020

Self Cite

113

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“…Since then, new algebraic attacks have surfaced (see [40,41]) that model the decoding problem as a system of multivariate equations using equations from the extension field structure to solve. The most recent algebraic attack is more efficient than combinatorial approaches against the parameter sets given in ROLLO, resulting in a near-complete break of all three KEMS.…”

Section: Rollomentioning

confidence: 99%

“…The first-round report noted that the strength of algebraic attacks against RSD was not well understood and should be explored. Since then, new algebraic attacks have surfaced which model the decoding problem as a system of multivariate equations using equations from the extension field structure to solve [40,41]. The most recent algebraic attack is more efficient than combinatorial approaches against the parameter sets given in the round 2 specification of RQC, resulting in a near-complete break.…”

Section: Rqcmentioning

confidence: 99%

Status report on the second round of the NIST post-quantum cryptography standardization process

Moody¹,

Alagic²,

Apon³

et al. 2020

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Certain commercial entities, equipment, or materials may be identified in this document in order to describe an experimental procedure or concept adequately. Such identification is not intended to imply recommendation or endorsement by NIST, nor is it intended to imply that the entities, materials, or equipment are necessarily the best available for the purpose. There may be references in this publication to other publications currently under development by NIST in accordance with its assigned statutory responsibilities. The information in this publication, including concepts and methodologies, may be used by federal agencies even before the completion of such companion publications. Thus, until each publication is completed, current requirements, guidelines, and procedures, where they exist, remain operative. For planning and transition purposes, federal agencies may wish to closely follow the development of these new publications by NIST. Organizations are encouraged to review all draft publications during public comment periods and provide feedback to NIST. Many NIST cybersecurity publications, other than the ones noted above, are available at https://csrc.nist.gov/publications.

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Quantum computing: A taxonomy, systematic review and future directions

et al. 2021

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Quantum computing (QC) is an emerging paradigm with the potential to offer significant computational advantage over conventional classical computing by exploiting quantum‐mechanical principles such as entanglement and superposition. It is anticipated that this computational advantage of QC will help to solve many complex and computationally intractable problems in several application domains such as drug design, data science, clean energy, finance, industrial chemical development, secure communications, and quantum chemistry. In recent years, tremendous progress in both quantum hardware development and quantum software/algorithm has brought QC much closer to reality. Indeed, the demonstration of quantum supremacy marks a significant milestone in the Noisy Intermediate Scale Quantum (NISQ) era—the next logical step being the quantum advantage whereby quantum computers solve a real‐world problem much more efficiently than classical computing. As the quantum devices are expected to steadily scale up in the next few years, quantum decoherence and qubit interconnectivity are two of the major challenges to achieve quantum advantage in the NISQ era. QC is a highly topical and fast‐moving field of research with significant ongoing progress in all facets. A systematic review of the existing literature on QC will be invaluable to understand the state‐of‐the‐art of this emerging field and identify open challenges for the QC community to address in the coming years. This article presents a comprehensive review of QC literature and proposes taxonomy of QC. The proposed taxonomy is used to map various related studies to identify the research gaps. A detailed overview of quantum software tools and technologies, post‐quantum cryptography, and quantum computer hardware development captures the current state‐of‐the‐art in the respective areas. The article identifies and highlights various open challenges and promising future directions for research and innovation in QC.

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An Algebraic Attack on Rank Metric Code-Based Cryptosystems

Cited by 50 publications

References 39 publications

Improvements of Algebraic Attacks for Solving the Rank Decoding and MinRank Problems

Improvements of Algebraic Attacks for Solving the Rank Decoding and MinRank Problems

Status report on the second round of the NIST post-quantum cryptography standardization process

Quantum computing: A taxonomy, systematic review and future directions

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