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References

:ref:`A <ref-A>` :ref:`B <ref-B>` :ref:`C <ref-C>` :ref:`D <ref-D>` :ref:`E <ref-E>` :ref:`F <ref-F>` :ref:`G <ref-G>` :ref:`H <ref-H>` :ref:`I <ref-I>` :ref:`J <ref-J>` :ref:`K <ref-K>` :ref:`L <ref-L>` :ref:`M <ref-M>` :ref:`N <ref-N>` :ref:`O <ref-O>` :ref:`P <ref-P>` :ref:`Q <ref-Q>` :ref:`R <ref-R>` :ref:`S <ref-S>` :ref:`T <ref-T>` :ref:`U <ref-U>` :ref:`V <ref-V>` :ref:`W <ref-W>` :ref:`X <ref-X>` :ref:`Y <ref-Y>` :ref:`Z <ref-Z>`

A

[AGHT18]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

B

[BFP09]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
[BFP12]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
[BCCHK23]Ward Beullens, Fabio Campos, Sofía Celi, Basil Hess, and Matthias J. Kannwischer. MAYO: Specifications https://pqmayo.org/assets/specs/mayo.pdf
[Beu20]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
[BBCPSTV22]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
[BBPS20]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
[BKW19]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
[BFSS11]

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

[BBBGNRT20]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
[BBCGPSTV20]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
[BBBGT23]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
[BCCCNSY10]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
[BLP11]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
[BJMM12]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
[BM18]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
[BLP08]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

C

[CCJ23]Eliana Carozza, Geoffroy Couteau, and Antoine Joux. Short Signatures from Regular Syndrome Decoding in the Head, EUROCRYPT 2023 https://eprint.iacr.org/2023/1035
[CGMT02]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
[CKPS]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
[CS96]Florent Chabaud, Jacques Stern. The cryptographic security of the syndrome decoding problem for rank distance codes https://doi.org/10.1007/BFb0034862

D

[Dua20]João Diogo Duarte. On the Complexity of the Crossbred Algorithm
[Dum91]Ilya Dumer. On minimum distance decoding of linear codes
[Din21a]Itai Dinur. Improved Algorithms for Solving Polynomial Systems over GF(2) by Multiple Parity-Counting https://arxiv.org/pdf/2005.04800.pdf
[Din21b]Itai Dinur. Cryptanalytic Applications of the Polynomial Method for Solving Multivariate Equation Systems over GF(2) https://eprint.iacr.org/2021/578.pdf

E

[ES23]Andre Esser and Paolo Santini. Not Just Regular Decoding: Asymptotics and Improvements of Regular Syndrome Decoding Attacks https://eprint.iacr.org/2023/1568
[EB22]Andre Esser and Emanuele Bellini. Syndrome Decoding Estimator https://eprint.iacr.org/2021/1243.pdf
[EZ23]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

F

[FNT21]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

G

[GRS16]Philippe Gaborit, Olivier Ruatta, and Julien Schrek On the Complexity of the Rank Syndrome Decoding Problem https://doi.org/10.1109/TIT.2015.2511786

H

[Has21]Yasufumi Hashimoto. An improvement of algorithms to solve under-defined systems of multivariate quadratic equations https://eprint.iacr.org/2021/1045.pdf

I

J

[JV18]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

K

[KPG99]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
[KMP19]Eliane Koussa, Gilles Macario{-}Rat and Jacques Patarin. On the complexity of the Permuted Kernel Problem https://eprint.iacr.org/2019/412.pdf

L

[LB88]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
[Leo82]Jeffrey S. Leon. Computing automorphism groups of error-correcting codes https://doi.org/10.1109/TIT.1982.1056498
[LPTWY17]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

M

[MMT11]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
[MO15]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
[MHT13]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

N

O

[OJ02]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

P

[Pra62]Eugene Prange. The Use of Information Sets in Decoding Cyclic Codes https://doi.org/10.1109/TIT.1962.1057777
[Pet11]Christiane Peters. Information-set decoding for linear codes over Fq https://link.springer.com/chapter/10.1007/978-3-642-12929-2_7

Q

R

S

[SBC22]Paolo Santini, Marco Baldi, and Franco Chiaraluce. Computational Hardness of the Permuted Kernel and Subcode Equivalence Problems https://eprint.iacr.org/2022/1749.pdf
[Sen06]Nicolas Sendrier. The Support Splitting Algorithm https://hal.inria.fr/inria-00073037/document
[Ste88]Jacques Stern. A method for finding codewords of small weight https://doi.org/10.1007/BFb0019850

T

[TW12]Enrico Thomae and Christopher Wolf. Solving Underdetermined Systems of Multivariate Quadratic Equations Revisited https://doi.org/10.1007/978-3-642-30057-8_10

U

V

W

X

Y

Z