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Algebraic Cryptanalysis of McEliece Variants with Compact Keys [chapter]

Jean-Charles Faugère, Ayoub Otmani, Ludovic Perret, Jean-Pierre Tillich
2010 Lecture Notes in Computer Science  
These two compact variants of McEliece managed to propose keys with less than 20,000 bits. To do so, they proposed to use quasi-cyclic or dyadic structures.  ...  We have used these highly structured algebraic equations to mount an efficient key-recovery attack against two recent variants of the McEliece cryptosystems that aim at reducing public key sizes.  ...  Algebraic Cryptanalysis of the Dyadic Variant The cryptosystem presented in [27] considers particular alternant codes called quasidyadic Goppa codes.  ... 
doi:10.1007/978-3-642-13190-5_14 fatcat:ji7gr6vfojfllaj7deubxau2hm

Quantum resistant random linear code based public key encryption scheme RLCE

Yongge Wang
2016 2016 IEEE International Symposium on Information Theory (ISIT)  
Motivated by Faugere et al's [15] algebraic attacks against quasi-cyclic and quasi-dyadic structure based compact variants of McEliece encryption schemes, Faugere et al [14] designed an efficient algorithm  ...  Berger et al [4] and Misoczki-Barreto [25] proposed quasi-cyclic and quasi-dyadic structure based compact variants of McEliece encryption schemes.  ...  Acknowledgments I would like to thank several colleagues for very detailed comments and suggestionsto improve the presentation of this paper.  ... 
doi:10.1109/isit.2016.7541753 dblp:conf/isit/Wang16a fatcat:4bvyuaciw5bylglb6trpcrtxlu

Post-Quantum Network Security:McEliece and Niederreiter Cryptosystems Analysis and Education Issues

2020 WSEAS transactions on systems and control  
The paper is aimed at analyzing of the classical McEliece and Niederreiter cryptosystems as well as theQuasi-Cyclic MDPC McEliece cipher in a context of the post-quantum network security.  ...  The binary Goppa codes are describedin the context of their role for the cryptanalytic resistance of the classic McEliece and Niederreiter schemes.  ...  CriCTechS seminar for discussion of the presented results.  ... 
doi:10.37394/23203.2020.15.62 fatcat:ycx2ry6l2bdvbeqr5qudu5uhb4

Quantum Resistant Random Linear Code Based Public Key Encryption Scheme RLCE [article]

Yongge Wang
2015 arXiv   pre-print
Though LLL reduction algorithm has been one of the major cryptanalysis techniques for lattice based cryptographic systems, key recovery cryptanalysis techniques for linear code based cryptographic systems  ...  Though most of these cryptanalysis techniques are relatively new, they prove to be very powerful and many systems have been broken using them.  ...  Acknowledgments I would like to thank several colleagues for very detailed comments and suggestionsto improve the presentation of this paper.  ... 
arXiv:1512.08454v1 fatcat:qnuoj7lxbjg2hbwclghex7hdzq

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
McNie is a hybrid version of the McEliece and Niederreiter cryptosystems and its security is reduced to the hard problem of syndrome decoding.  ...  The public key involves a random generator matrix which is also used to mask the code used in the secret key. This makes the system safer against known structural attacks.  ...  .: Structural cryptanalysis of McEliece schemes with compact keys. Designs, Codes and Cryptography 79(1), pp. 87–112 (2016) 14. Faure, C. and Minder, L., 2008, June.  ... 
arXiv:1812.05008v2 fatcat:wsagwr4tofd3fdn2cxpp3vogte

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.  ...  One of its most promising applications is the design of cryptographic schemes with exceptionally strong security guarantees and other desirable properties.  ...  Reducing the key size of the McEliece cryptosystem Since [10] , the idea of using compact representations of the public matrix used in the McEliece encryption scheme has been investigated.  ... 
doi:10.1007/978-3-642-23141-4_3 fatcat:tydg6d5zunhbplpchcnozoaanm

Structural cryptanalysis of McEliece schemes with compact keys

Jean-Charles Faugère, Ayoub Otmani, Ludovic Perret, Frédéric de Portzamparc, Jean-Pierre Tillich
2015 Designs, Codes and Cryptography  
variants of McEliece [8, 35] .  ...  Algebraic cryptanalysis is a general framework that permits to assess the security of a large variety of cryptographic schemes.  ...  Acknowledgements We would like to thank (some) of the referees of EC'14 for helpful comments on a preliminary version of this paper.  ... 
doi:10.1007/s10623-015-0036-z fatcat:5ism76sx35fm5ngemmqpqpse44

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.  ...  Using the state-of-the-art list decoding algorithm instead of unique decoding, we exhibit a keysize gain of about 4% for the standard McEliece cryptosystem and up to 21% for the adjusted dyadic variant  ...  It was specifically designed to break the compact key McEliece variants proposed in [4, 20] , which use the structure of alternant codes.  ... 
arXiv:1102.2566v2 fatcat:fytfc5y4ffgrdabqq3ua7e7i64

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.  ...  Using the state-of-the-art list decoding algorithm instead of unique decoding, we exhibit a keysize gain of about 4% for the standard McEliece cryptosystem and up to 21% for the adjusted dyadic variant  ...  It was specifically designed to break the compact key McEliece variants proposed in [4, 20] , which use the structure of alternant codes.  ... 
doi:10.1109/isit.2011.6034058 dblp:conf/isit/BarbierB11 fatcat:hruobvzk6reixguubzah2thmry

Algebraic Attack against Variants of McEliece with Goppa Polynomial of a Special Form [chapter]

Jean-Charles Faugère, Ludovic Perret, Frédéric de Portzamparc
2014 Lecture Notes in Computer Science  
Finally, the last step of the cryptanalysis of those schemes corresponds to attacking a McEliece scheme instantiated with particular GRS codes (with a polynomial relation between the support and the multipliers  ...  In this paper, we present a new algebraic attack against some special cases of Wild McEliece Incognito, a generalization of the original McEliece cryptosystem.  ...  The authors would also like to thank (some of) the referees as well as PC chairs for their usefull comments on a preliminary version of this paper.  ... 
doi:10.1007/978-3-662-45611-8_2 fatcat:ljgaxzolmjdi3iag4ewy6x7kym

Overview of the Mceliece Cryptosystem and its Security

Marek Repka, Pavol Zajac
2014 Tatra Mountains Mathematical Publications  
McEliece cryptosystem (MECS) is one of the oldest public key cryptosystems, and the oldest PKC that is conjectured to be post-quantum secure.  ...  In this paper we survey the current state of the implementation issues and security of MECS, and its variants.  ...  The solution of the system yields the unknown secret key. Algebraic methods can be used to break proposed McEliece variants with compact public keys [23] .  ... 
doi:10.2478/tmmp-2014-0025 fatcat:jfxogohji5g7nduip5dhrgn62m

polarRLCE: A New Code-Based Cryptosystem Using Polar Codes

Jingang Liu, Yongge Wang, Zongxiang Yi, Zhiqiang Lin
2019 Security and Communication Networks  
In addition to avoiding some weaknesses of the RLCE scheme, we show that, with the proper choice of parameters, using polar codes, it is possible to design an encryption scheme to achieve the intended  ...  security level while retaining a reasonably small public key size.  ...  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

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.  ...  We have verified these formulas with practical experiments, and a theoretical explanation for such defect of rank is also provided.  ...  The key ingredient is a new algebraic technique introduced in [17] to attack two variants [1, 24] of McEliece.  ... 
doi:10.1109/tit.2013.2272036 fatcat:6unjob76nbgvtjyndsiyhcfsk4

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.  ...  We have verified these formulas with practical experiments, and a theoretical explanation for such defect of rank is also provided.  ...  The key ingredient is a new algebraic technique introduced in [17] to attack two variants [1, 24] of McEliece.  ... 
doi:10.1109/itw.2011.6089437 dblp:conf/itw/FaugereGOPT11 fatcat:bskpih4hczfbrkpf2stish6pfa

Enhanced Public Key Security for the McEliece Cryptosystem

Marco Baldi, Marco Bianchi, Franco Chiaraluce, Joachim Rosenthal, Davide Schipani
2014 Journal of Cryptology  
This paper studies a variant of the McEliece cryptosystem able to ensure that the code used as the public key is no longer permutationequivalent to the secret code.  ...  McEliece cryptosystem for security reasons.  ...  Comparison with other variants of the McEliece cryptosystem The main difference between the proposed cryptosystem and many other variants of the McEliece cryptosystem consists in the way the secret generator  ... 
doi:10.1007/s00145-014-9187-8 fatcat:pmm5kpz5jfeelo7uah74ualdlu
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