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A Distinguisher-Based Attack on a Variant of McEliece's Cryptosystem Based on Reed-Solomon Codes [article]

Valérie Gauthier and Ayoub Otmani and Jean-Pierre Tillich
2012 arXiv   pre-print
This work can be viewed as another illustration of how a distinguisher of Reed-Solomon codes can be used to devise an attack on cryptosystems based on them.  ...  Baldi et al. proposed a variant of McEliece's cryptosystem. The main idea is to replace its permutation matrix by adding to it a rank 1 matrix.  ...  In this paper we propose a cryptanalysis against a variant of McEliece's cryptosystem [McE78] proposed in [BBC + 11] which is based on on the aforementioned version of our distinguisher presented in  ... 
arXiv:1204.6459v1 fatcat:jmwb5vixafbd3foverbmohbnqy

Distinguisher-based attacks on public-key cryptosystems using Reed–Solomon codes

Alain Couvreur, Philippe Gaborit, Valérie Gauthier-Umaña, Ayoub Otmani, Jean-Pierre Tillich
2014 Designs, Codes and Cryptography  
The purpose of this paper is to demonstrate that a distinguisher of Reed-Solomon codes based on the square code construction leads to the cryptanalysis of several cryptosystems relying on them.  ...  generator matrix of a secretly chosen generalized Reed-Solomon code.  ...  Acknowledgement: We thank the anonymous reviewer for a careful reading of this submission which helped us to improve its editorial quality.  ... 
doi:10.1007/s10623-014-9967-z fatcat:jqu5i56i7zdxjc76fuwohqsrrm

Key Reduction of McEliece's Cryptosystem Using List Decoding [article]

Morgan Barbier, Barreto S. L. M. Paulo
2011 arXiv   pre-print
Different variants of the code-based McEliece cryptosystem were pro- posed to reduce the size of the public key.  ...  In light of a new study on list decoding algorithms for binary Goppa codes, we explain how to increase the security level for given public keysizes.  ...  Matthieu Finiasz, Jérôme Milan, Rafael Misoczki and Ayoub Otmani for stimulating discussions and improving the editorial quality, and to express his gratitude to Nicolas Sendrier who kindly let us build on  ... 
arXiv:1102.2566v2 fatcat:fytfc5y4ffgrdabqq3ua7e7i64

Reducing Key Length of the McEliece Cryptosystem [chapter]

Thierry P. Berger, Pierre-Louis Cayrel, Philippe Gaborit, Ayoub Otmani
2009 Lecture Notes in Computer Science  
The McEliece cryptosystem is one of the oldest public-key cryptosystem ever designated. It is also the first public-key cryptosystem based on linear error-correcting codes.  ...  Starting from subfield subcodes of quasi-cyclic generalized Reed-Solomon codes, we propose a system with several size of parameters from 6,000 to 11,000 bits with a security ranging from 2 80 to 2 107  ...  Minder and Shokrollahi presented in [19] a structural attack that creates a private key against a cryptosystem based on Reed-Muller codes [25] .  ... 
doi:10.1007/978-3-642-02384-2_6 fatcat:tdu7qveerjhclpbh3l4i4gmilm

Key reduction of McEliece's cryptosystem using list decoding

Morgan Barbier, Paulo S. L. M. Barreto
2011 2011 IEEE International Symposium on Information Theory Proceedings  
Different variants of the code-based McEliece cryptosystem were proposed to reduce the size of the public key.  ...  In light of a new study on list decoding algorithms for binary Goppa codes, we explain how to increase the security level for given public keysizes.  ...  Matthieu Finiasz, Jérôme Milan, Rafael Misoczki and Ayoub Otmani for stimulating discussions and improving the editorial quality, and to express his gratitude to Nicolas Sendrier who kindly let us build on  ... 
doi:10.1109/isit.2011.6034058 dblp:conf/isit/BarbierB11 fatcat:hruobvzk6reixguubzah2thmry

A Smart approach for GPT cryptosystem based on rank codes

Haitham Rashwan, Ernst M. Gabidulin, Bahram Honary
2010 2010 IEEE International Symposium on Information Theory  
The concept of Public- key cryptosystem was innovated by McEliece's cryptosystem. The public key cryptosystem based on rank codes was presented in 1991 by Gabidulin -Paramonov-Trejtakov(GPT).  ...  In this paper, we introduce a new approach, called the Smart approach, which is based on a proper choice of the distortion matrix X.  ...  Neiderreiter [2] has introduced a new PKC based on a family of Generalized Reed-Solomon codes; its public key size is less than the McEliece cryptosystem, but still large for practical application.  ... 
doi:10.1109/isit.2010.5513549 dblp:conf/isit/RashwanGH10 fatcat:z5pgposmzfemtd2kl4y3vsqqni

Variations of the McEliece Cryptosystem [article]

Jessalyn Bolkema, Heide Gluesing-Luerssen, Christine A. Kelley, Kristin Lauter, Beth Malmskog, Joachim Rosenthal
2017 arXiv   pre-print
Two variations of the McEliece cryptosystem are presented. The first one is based on a relaxation of the column permutation in the classical McEliece scrambling process.  ...  The second variation is based on the use of spatially coupled moderate-density parity-check codes as secret codes.  ...  Acknowledgements We would like to thank the organizers of the IPAM workshop on Algebraic Geometry for Coding Theory and Cryptography for inviting us to the event.  ... 
arXiv:1612.05085v2 fatcat:iotsnlu6qzdqjpatxcv2vmvrqe

On the security of subspace subcodes of Reed-Solomon codes for public key encryption [article]

Alain Couvreur, Matthieu Lequesne
2021 arXiv   pre-print
This article discusses the security of McEliece-like encryption schemes using subspace subcodes of Reed-Solomon codes, i.e. subcodes of Reed-Solomon codes over 𝔽_q^m whose entries lie in a fixed collection  ...  These codes appear to be a natural generalisation of Goppa and alternant codes and provide a broader flexibility in designing code based encryption schemes.  ...  The use of subspace subcodes of Reed-Solomon codes is of particular interest in code based cryptography since it includes McEliece's original proposal based on Goppa codes on the one hand and encryption  ... 
arXiv:2009.05826v2 fatcat:nb5hv6ytz5fuxfuu2wg67n3d7m

A distinguisher for high rate McEliece cryptosystems

Jean-Charles Faugere, Valerie Gauthier-Umana, Ayoub Otmani, Ludovic Perret, Jean-Pierre Tillich
2011 2011 IEEE Information Theory Workshop  
Our distinguisher is based on a recent algebraic attack against compact variants of McEliece which reduces the key-recovery to the problem of solving an algebraic system of equations.  ...  To our point of view, disproving/mitigating this hardness assumption is a breakthrough in code-based cryptography and may open a new direction to attack McEliece cryptosystems.  ...  This was the key of the cryptanalysis of McEliece's variant based on generalized Reed-Solomon codes [30] . The general case is still unsolved.  ... 
doi:10.1109/itw.2011.6089437 dblp:conf/itw/FaugereGOPT11 fatcat:bskpih4hczfbrkpf2stish6pfa

A Distinguisher for High-Rate McEliece Cryptosystems

Jean-Charles Faugere, Valerie Gauthier-Umana, Ayoub Otmani, Ludovic Perret, Jean-Pierre Tillich
2013 IEEE Transactions on Information Theory  
Our distinguisher is based on a recent algebraic attack against compact variants of McEliece which reduces the key-recovery to the problem of solving an algebraic system of equations.  ...  To our point of view, disproving/mitigating this hardness assumption is a breakthrough in code-based cryptography and may open a new direction to attack McEliece cryptosystems.  ...  This was the key of the cryptanalysis of McEliece's variant based on generalized Reed-Solomon codes [30] . The general case is still unsolved.  ... 
doi:10.1109/tit.2013.2272036 fatcat:6unjob76nbgvtjyndsiyhcfsk4

Code Based Cryptography and Steganography [chapter]

Pascal Véron
2013 Lecture Notes in Computer Science  
For a long time, coding theory was only concerned by message integrity (how to protect against errors a message sent via some noisely channel).  ...  Nowadays, coding theory plays an important role in the area of cryptography and steganography.  ...  In [82] , steganography is described from a coding theory point of view and numerous bibliographical notes are given about the study of some well known codes in this context (Hamming, Golay, BCH, Reed-Solomon  ... 
doi:10.1007/978-3-642-40663-8_5 fatcat:t4a63pdm2bbtddmfm7uimzlmdu

Modified GPT Cryptosystem for Information Network Security

Ernst Gabidulin, Nina Pilipchuk
2014 International Journal for Information Security Research  
To provide information security in network we use the public key GPT (Gabidulin-Paramonov-Tretiyakov) cryptosystem based on rank codes. This cryptosystem was the subject of several attacks.  ...  To prevent structural attacks, we change some of its secret keys. We called the modified GPT cryptosystem as GPT-M.  ...  In 1986 year Niederreiter [2] introduced a new version of PKC based on a family of Generalized Reed-Solomon codes. It turned out that this cryptosystem is insecure.  ... 
doi:10.20533/ijisr.2042.4639.2014.0050 fatcat:ws7dcmsaoncf3jjgipx6ldtx2i

Code based Cryptography: Classic McEliece [article]

Harshdeep Singh
2020 arXiv   pre-print
This article addresses code-based cryptography and is designed to depict the complete outline of a code based public key cryptosystem.  ...  We discuss the hard problems of coding theory which are used in code based cryptography and some classic attacks on it like information-set decoding (ISD).  ...  One such modification includes a "dual" variant of Generalized Reed Solomon codes, namely, Niederreiter in 1986.  ... 
arXiv:1907.12754v2 fatcat:gt4rleeorba6zjtvol6qmwfyle

polarRLCE: A New Code-Based Cryptosystem Using Polar Codes

Jingang Liu, Yongge Wang, Zongxiang Yi, Zhiqiang Lin
2019 Security and Communication Networks  
Code-based cryptography leverages difficult problems in coding theory and is one of the main techniques enabling cryptographic primitives in the postquantum scenario.  ...  In this work, we propose the first efficient secure scheme based on polar codes (i.e., polarRLCE) which is inspired by the RLCE scheme, a candidate for the NIST postquantum cryptography standardization  ...  Vlad Dragoi for insightful discussions. is work was supported in part by the National Natural Science Foundation of China (Grant no. 61702124), Qatar Foundation (Grant no.  ... 
doi:10.1155/2019/3086975 fatcat:gozlugvfjvfqpajxj4kdggqqgy

Polynomial-Time Key Recovery Attack on the Faure-Loidreau Scheme based on Gabidulin Codes [article]

Philippe Gaborit and Ayoub Otmani and Hervé Talé Kalachi
2017 arXiv   pre-print
We show in this article that this scheme like other schemes based on Gabidulin codes, is also vulnerable to a polynomial-time attack that recovers the private key by applying Overbeck's attack on an appropriate  ...  Encryption schemes based on the rank metric lead to small public key sizes of order of few thousands bytes which represents a very attractive feature compared to Hamming metric-based encryption schemes  ...  For instance the highly structured Reed-Solomon codes are difficult to mask and most of McEliece variants relying on Reed-Solomon codes or variations on Reed-Solomon codes have been broken.  ... 
arXiv:1606.07760v2 fatcat:cdl757yeavb2pebzu5xxeyptna
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