References¶
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Nicolas Aragon, Philippe Gaborit, Adrien Hauteville, Jean-Pierre Tillich. A New Algorithm for Solving the Rank Syndrome Decoding Problem http://doi.org/10.1109/ISIT.2018.8437464
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Luk Bettale, Jean-Charles Faugère and Ludovic Perret. Hybrid Approach for Solving Multivariate Systems over Finite Fields https://doi.org/10.1515/JMC.2009.009
Luk Bettale, Jean-Charles Faugère and Ludovic Perret. Solving Polynomial Systems over Finite Fields: Improved Analysis of the Hybrid Approach https://doi.org/10.1145/2442829.2442843
Ward Beullens, Fabio Campos, Sofía Celi, Basil Hess, and Matthias J. Kannwischer. MAYO: Specifications https://pqmayo.org/assets/specs/mayo.pdf
Ward Beullens. Not Enough LESS: An Improved Algorithm for Solving Code Equivalence Problems over Fq https://doi.org/10.1007/978-3-030-81652-0_15
John Baena, Pierre Briaud, Daniel Cabarcas, Ray Perlner, Daniel Smith-Tone, and Javier Verbel. Improving Support-Minors rank attacks: applications to GeMSS and Rainbow https://eprint.iacr.org/2021/1677.pdf
Alessandro Barenghi, Jean-Francois Biasse, Edoardo Persichetti and Paolo Santini. {LESS-FM:} Fine-Tuning Signatures from the Code Equivalence Problem https://doi.org/10.1007/978-3-030-81293-5_2
Andreas Björklund, Petteri Kaski, and Ryan Williams. Solving Systems of Polynomial Equations over GF(2) by a Parity-Counting Self-Reduction https://drops.dagstuhl.de/opus/volltexte/2019/10602/pdf/LIPIcs-ICALP-2019-26.pdf
Magali Bardet, Jean-Charles Faugère, Bruno Salvy, and Pierre-Jean Spaenlehauer. On the Complexity of Solving Quadratic Boolean Systems
https://www.sciencedirect.com/science/article/pii/S0885064X12000611
Magali Bardet, Pierre Briaud, Maxime Bros, Philippe Gaborit, Vincent Neiger, Olivier Ruatta and Jean-Pierre Tillich An algebraic attack on rank metric code-based cryptosystems https://doi.org/10.1007/978-3-030-45727-3_3
Magali Bardet, Maxime Bros, Daniel Cabarcas, Philippe Gaborit, Ray Perlner, Daniel Smith-Tone, Jean-Pierre Tillich and Javier Verbel Improvements of Algebraic Attacks for Solving the Rank Decoding and MinRank Problems https://doi.org/10.1007/978-3-030-64837-4_17
Magali Bardet, Pierre Briaud, Maxime Bros, Philippe Gaborit, and Jean-Pierre Tillich Revisiting algebraic attacks on MinRank and on the rank decoding problem https://doi.org/10.1007/s10623-023-01265-x
Charles Bouillaguet, Hsieh-Chung Chen, Chen-Mou Cheng, Tung Chou, Ruben Niederhagen, Adi Shamir, and Bo-Yin Yang. Fast Exhaustive Search for Polynomial Systems in F_2 https://www.iacr.org/archive/ches2010/62250195/62250195.pdf
Daniel J. Bernstein and Tanja Lange and Christiane Peters Smaller decoding exponents: ball-collision decoding https://link.springer.com/chapter/10.1007/978-3-642-22792-9_42
Anja Becker, Antoine Joux, Alexander May and Alexander Meurer. Decoding random binary linear codes in 2^(n/20): How 1+ 1= 0 improves information set decoding https://eprint.iacr.org/2012/026.pdf
Leif Both and Alexander May. Decoding Linear Codes with High Error Rate and its Impact for LPN Security https://eprint.iacr.org/2017/1139.pdf
Daniel J. Bernstein and Tanja Lange and Christiane Peters Attacking and Defending the McEliece Cryptosystem https://link.springer.com/chapter/10.1007/978-3-540-88403-3_3
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Eliana Carozza, Geoffroy Couteau, and Antoine Joux. Short Signatures from Regular Syndrome Decoding in the Head, EUROCRYPT 2023 https://eprint.iacr.org/2023/1035
Nicolas Courtois, Louis Goubin, Willi Meier, and Jean-Daniel Tacier. Solving Underdefined Systems of Multivariate Quadratic Equations https://link.springer.com/chapter/10.1007/3-540-45664-3_15
Nicolas Courtois, Alexander Klimov, Jacques Patarin, and Adi Shamir. Efficient Algorithms for Solving Overdefined Systems of Multivariate Polynomial Equations https://www.iacr.org/archive/eurocrypt2000/1807/18070398-new.pdf
Florent Chabaud, Jacques Stern. The cryptographic security of the syndrome decoding problem for rank distance codes https://doi.org/10.1007/BFb0034862
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João Diogo Duarte. On the Complexity of the Crossbred Algorithm
Ilya Dumer. On minimum distance decoding of linear codes
Itai Dinur. Improved Algorithms for Solving Polynomial Systems over GF(2) by Multiple Parity-Counting https://arxiv.org/pdf/2005.04800.pdf
Itai Dinur. Cryptanalytic Applications of the Polynomial Method for Solving Multivariate Equation Systems over GF(2) https://eprint.iacr.org/2021/578.pdf
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Andre Esser and Paolo Santini. Not Just Regular Decoding: Asymptotics and Improvements of Regular Syndrome Decoding Attacks https://eprint.iacr.org/2023/1568
Andre Esser and Emanuele Bellini. Syndrome Decoding Estimator https://eprint.iacr.org/2021/1243.pdf
Andre Esser and Floyd Zweydinger. New Time-Memory Trade-Offs for Subset Sum – Improving ISD in Theory and Practice https://eprint.iacr.org/2022/1329.pdf
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Hiroki Furue, Shuhei Nakamura, Tsuyoshi Takagi. Improving Thomae-Wolf Algorithm for Solving Underdetermined Multivariate Quadratic Polynomial Problem https://dl.acm.org/doi/10.1007/978-3-030-81293-5_4
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Philippe Gaborit, Olivier Ruatta, and Julien Schrek On the Complexity of the Rank Syndrome Decoding Problem https://doi.org/10.1109/TIT.2015.2511786
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Yasufumi Hashimoto. An improvement of algorithms to solve under-defined systems of multivariate quadratic equations https://eprint.iacr.org/2021/1045.pdf
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Antoine Joux and Vanessa Vitse. A Crossbred Algorithm for Solving Boolean Polynomial Systems https://link.springer.com/chapter/10.1007/978-3-319-76620-1_1
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Aviad Kipnis, Jacques Patarin, and Louis Goubin. Unbalanced Oil and Vinegar Signature Schemes https://link.springer.com/chapter/10.1007/3-540-48910-X_15
Eliane Koussa, Gilles Macario{-}Rat and Jacques Patarin. On the complexity of the Permuted Kernel Problem https://eprint.iacr.org/2019/412.pdf
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Pil Joong Lee and Ernest Brickell. An Observation on the Security of McEliece’s Public-Key Cryptosystem https://doi.org/10.1007/3-540-45961-8_25
Jeffrey S. Leon. Computing automorphism groups of error-correcting codes https://doi.org/10.1109/TIT.1982.1056498
Daniel Lokshtanov, Ramamohan Paturi, Suguru Tamaki, Ryan Williams, and Huacheng Yu. Beating Brute Force for Systems of Polynomial Equation over Finite Fields https://people.csail.mit.edu/rrw/polyEqSoda2017Submit.pdf
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Alexander May, Alexander Meurer, and Enrico Thomae. Decoding Random Linear Codes in 2^(0.054n) https://link.springer.com/chapter/10.1007/978-3-642-25385-0_6
Alexander May and Ilya Ozerov. On Computing Nearest Neighbors with Applications to Decoding of Binary Linear Codes https://link.springer.com/chapter/10.1007/978-3-662-46800-5_9
Hiroyuki Miura, Yasufumi Hashimoto, and Tsuyoshi Takagi. Extended Algorithm for Solving Underdefined Multivariate Quadratic Equations https://link.springer.com/chapter/10.1007/978-3-642-38616-9_8
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Alexei Ourivski, and Thomas Johansson. New Technique for Decoding Codes in the Rank Metric and Its Cryptography Applications https://doi.org/10.1023/A:1020369320078
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Eugene Prange. The Use of Information Sets in Decoding Cyclic Codes https://doi.org/10.1109/TIT.1962.1057777
Christiane Peters. Information-set decoding for linear codes over Fq https://link.springer.com/chapter/10.1007/978-3-642-12929-2_7
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Paolo Santini, Marco Baldi, and Franco Chiaraluce. Computational Hardness of the Permuted Kernel and Subcode Equivalence Problems https://eprint.iacr.org/2022/1749.pdf
Nicolas Sendrier. The Support Splitting Algorithm https://hal.inria.fr/inria-00073037/document
Jacques Stern. A method for finding codewords of small weight https://doi.org/10.1007/BFb0019850
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Enrico Thomae and Christopher Wolf. Solving Underdetermined Systems of Multivariate Quadratic Equations Revisited https://doi.org/10.1007/978-3-642-30057-8_10
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