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Improved Cryptanalysis of Rank Metric Schemes Based on Gabidulin Codes [article]

Ayoub Otmani and Hervé Talé Kalachi and Sélestin Ndjeya
2017 arXiv   pre-print
We show that by applying the Frobenius operator appropriately on the public key, it is possible to build a Gabidulin code having the same dimension as the original secret Gabidulin code but with a lower  ...  Consequently, our results show that all the existing techniques aiming to hide the inherent algebraic structure of Gabidulin codes have failed.  ...  This scheme can be seen as an analogue of the McEliece scheme public key cryptosystem based on the class of Gabidulin codes.  ... 
arXiv:1602.08549v2 fatcat:5hrhtrjgpzbefimhoelg77eega

On the Failure of the Smart Approach of the GPT Cryptosystem [article]

Herve Tale Kalachi
2020 arXiv   pre-print
We show that by puncturing the public code several times on specific positions, we get a public code on which applying the Frobenius operator appropriately allows to build an alternative secret key.  ...  This paper describes a new algorithm for breaking the smart approach of the GPT cryptosystem.  ...  In order to solve this problem, several modifications of the scheme have been proposed among which the use of rank metric codes (Gabidulin et al., 1991) instead of the Hamming metric.  ... 
arXiv:2010.15678v1 fatcat:j33bvx5gdneqdkhc4qdoirukkq

A New Rank Metric Codes Based Encryption Scheme [chapter]

Pierre Loidreau
2017 Lecture Notes in Computer Science  
The idea of the design mixes two existing approaches designing rank metric based encryption schemes.  ...  We design a new McEliece-like rank metric based encryption scheme from Gabidulin codes. We explain why it is not affected by the invariant subspace attacks also known as Overbeck's attacks.  ...  Since our interest concerns rank metric, we present how Gabidulin codes and LRPC are used in the design of code-based encryption schemes.  ... 
doi:10.1007/978-3-319-59879-6_1 fatcat:kqdhhgfszbfinpdfbdu24af6wy

RQC revisited and more cryptanalysis for Rank-based Cryptography [article]

Loïc Bidoux, Pierre Briaud, Maxime Bros, Philippe Gaborit
2022 arXiv   pre-print
We propose two main contributions: first, we revisit the encryption scheme Rank Quasi-Cyclic (RQC) by introducing new efficient variations, in particular, a new class of codes, the Augmented Gabidulin  ...  Overall, when all of these new improvements for the RQC scheme are put together, and their security evaluated with our different attacks, they enable one to gain 50% in parameter sizes compared to the  ...  The original scheme based on rank metric was the GPT cryptosystem [18] , an adaptation of the McEliece scheme in a rank metric context where Gabidulin codes [17] , a rank metric analogue of Reed-Solomon  ... 
arXiv:2207.01410v1 fatcat:y33u3qv53bfmliyxuwas7wqfgu

McNie: A code-based public-key cryptosystem [article]

Jon-Lark Kim, Young-Sik Kim, Lucky Galvez, Myeong Jae Kim, Nari Lee
2019 arXiv   pre-print
In particular, we apply rank-metric codes to McNie.  ...  In this paper, we suggest a code-based public key encryption scheme, called McNie.  ...  In 1991, Gabidulin, Paramonov and Tretjakov (GPT) [18] proposed a vari- ant of McEliece based on Gabidulin codes, which are a family of the so-called rank-metric codes with an efficient algebraic polynomial  ... 
arXiv:1812.05008v2 fatcat:wsagwr4tofd3fdn2cxpp3vogte

On the Complexity of the Rank Syndrome Decoding Problem

Philippe Gaborit, Olivier Ruatta, Julien Schrek
2016 IEEE Transactions on Information Theory  
attack based on the error support in a rank metric context.  ...  Very recently a new cryptosystem based on Low Rank Parity Check code (LRPC), a rank equivalent of LDPC codes, was proposed in [26] .  ...  The rank metric for coding theory was introduced by Gabidulin in 1985 in [22] and he proposed a family of codes, the Gabidulin codes, analogous to Reed-Solomon codes in Hamming metric, which can be decoded  ... 
doi:10.1109/tit.2015.2511786 fatcat:quynxesm5vfsvpwkfgdw73bfyi

RAMESSES, a Rank Metric Encryption Scheme with Short Keys [article]

Julien Lavauzelle and Pierre Loidreau and Ba-Duc Pham
2019 arXiv   pre-print
We present a rank metric code-based encryption scheme with key and ciphertext sizes comparable to that of isogeny-based cryptography for an equivalent security level.  ...  The security only relies on rank metric decoding problems, and does not require to hide the structure of a code.  ...  Code-based submissions generically rely on the hardness of decoding problems, either in the Hamming metric or in the rank metric.  ... 
arXiv:1911.13119v1 fatcat:63cp4l7kyfcxtawkyxgwbawxi4

On the complexity of the Rank Syndrome Decoding problem [article]

Philippe Gaborit and Olivier Ruatta and Julien Schrek
2013 arXiv   pre-print
This attack dramatically improves on previous attack by introducing the length n of the code in the exponent of the complexity, which was not the case in previous generic attacks. which can be considered  ...  In this paper we propose two new generic attacks on the Rank Syndrome Decoding (RSD) problem Let C be a random [n,k] rank code over GF(q^m) and let y=x+e be a received word such that x ∈ C and the Rank  ...  The rank metric for coding theory was introduced by Gabidulin in 1985 in [15] and he proposed a family of codes, the Gabidulin codes, analogous to Reed-Solomon codes in Hamming metric, which can be decoded  ... 
arXiv:1301.1026v1 fatcat:gw4zl7fytragplpv5gmmyzcbmm

Security of the GPT-Type Cryptosystems

Maximilien Gadouleau, Zhiyuan Yan
2006 2006 IEEE International Symposium on Information Theory  
The Gabidulin-Paramonov-Tretjakov (GPT) publickey cryptosystem and the GPT system with column scrambler, both based on Gabidulin codes, seem to have some advantages over McEliece's public-key cryptosystems  ...  using Goppa codes.  ...  Gabidulin, Paramonov, and Tretjakov [4] proposed a new public-key cryptosystem which uses a new class of codes proposed by Gabidulin [2] based on the rank metric.  ... 
doi:10.1109/isit.2006.261627 dblp:conf/isit/GadouleauY06 fatcat:lqy3kqbce5cxdkucxkntplz5sq

A Survey on Code-Based Cryptography [article]

Violetta Weger, Niklas Gassner, Joachim Rosenthal
2022 arXiv   pre-print
With this chapter we aim at providing a survey on code-based cryptography, focusing on PKEs and signature schemes.  ...  We cover the main frameworks introduced in code-based cryptography and analyze their security assumptions.  ...  Code-based Signature Schemes We give two approaches of building a code-based signature, one is following the hash-andsign approach of the CFS scheme [76] , which can also be adapted to the rank metric  ... 
arXiv:2201.07119v3 fatcat:oo53emg22jdxtmsevemlit7hlm

LIGA: A Cryptosystem Based on the Hardness of Rank-Metric List and Interleaved Decoding [article]

Julian Renner, Sven Puchinger, Antonia Wachter-Zeh
2020 arXiv   pre-print
We propose the new rank-metric code-based cryptosystem LIGA which is based on the hardness of list decoding and interleaved decoding of Gabidulin codes.  ...  It is not based on hiding the structure of a code.  ...  Further, we thank Pierre Loidreau for his valuable comments on a previous version of this  ... 
arXiv:1812.04892v2 fatcat:mz3o2goz3zdnno6dcfgcy2fuye

LIGA: a cryptosystem based on the hardness of rank-metric list and interleaved decoding

Julian Renner, Sven Puchinger, Antonia Wachter-Zeh
2021 Designs, Codes and Cryptography  
AbstractWe propose the new rank-metric code-based cryptosystem which is based on the hardness of list decoding and interleaved decoding of Gabidulin codes. is an improved variant of the Faure–Loidreau  ...  It is not based on hiding the structure of a code.  ...  Acknowledgements The work of J. Renner and A. Wachter-Zeh was supported by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant Agree-  ... 
doi:10.1007/s10623-021-00861-z fatcat:ugo3dwngfrb7rpnqwiuckzpe5i

Recent Progress in Code-Based Cryptography [chapter]

Pierre-Louis Cayrel, Sidi Mohamed El Yousfi Alaoui, Gerhard Hoffmann, Mohammed Meziani, Robert Niebuhr
2011 Communications in Computer and Information Science  
Section 3 deals with the new improvements of code-based signature schemes and Section 4 presents the new results in code-based secret-key cryptography.  ...  The last three years have witnessed tremendous progress in the understanding of code-based cryptography.  ...  Examples include the Sidelnikov-Shestakov attack against the Niederreiter PKC using GRS (Generalized Reed-Solomon) codes [74] , Overbeck's attack against rank-metric codes [69] , and cryptanalysis of  ... 
doi:10.1007/978-3-642-23141-4_3 fatcat:tydg6d5zunhbplpchcnozoaanm

RankSign: an efficient signature algorithm based on the rank metric [article]

Philippe Gaborit, Olivier Ruatta, Julien Schrek, Gilles Zémor
2017 arXiv   pre-print
In this paper we propose a new approach to code-based signatures that makes use in particular of rank metric codes.  ...  The paper describes RankSign: a new signature algorithm for the rank metric based on a new mixed algorithm for decoding erasures and errors for the recently introduced Low Rank Parity Check (LRPC) codes  ...  Classical code-based cryptography relies on the Hamming distance but it is also possible to use another metric: the rank metric.  ... 
arXiv:1606.00629v2 fatcat:4r3pcnwlqfczdpx3y7bad7oiue

Quantum Cryptanalysis (Dagstuhl Seminar 19421)

Michele Mosca, Maria Naya-Plasencia, Rainer Steinwandt, Michael Wagner
2020 Dagstuhl Reports  
Identifying new cryptanalytic improvements that make use of quantum algorithms and expanding the applicability of the best known cryptanalytic attacks by means of quantum technology.  ...  Dagstuhl seminar on Quantum Cryptanalysis was heavily informed by NIST's ongoing standardization effort in post-quantum cryptography.  ...  on rank-based cryptography, in particular recent submissions to NIST, based on problems with no masking.  ... 
doi:10.4230/dagrep.9.10.47 dblp:journals/dagstuhl-reports/MoscaNS19 fatcat:b4fbhk267zhsdch2lotalrzwoa
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