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Cryptanalysis of a System Based on Twisted Reed-Solomon Codes [article]

Julien Lavauzelle, Julian Renner
2019 arXiv   pre-print
The algorithm is based on the recovery of the structure of subfield subcodes of twisted Reed--Solomon codes, and it always succeeds.  ...  It was recently proved that twisted Reed--Solomon codes represent a family of codes which contain a large amount of MDS codes, non-equivalent to Reed--Solomon codes.  ...  We would further like to thank the authors of the proposed cryptosystem [4] for validating our attack and pointing out a possible repair of the system with respect to our attack.  ... 
arXiv:1904.11785v1 fatcat:p7svrf6jvbeklofshvqnr4hjyy

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.  ...  based on generalised Reed-Solomon codes on the other hand as the two extremities of a same spectrum.  ... 
arXiv:2009.05826v2 fatcat:nb5hv6ytz5fuxfuu2wg67n3d7m

Implementation of Two Level QR Code (2LQR)

Pallavi Tekade, Anub Vamadevan, Sumit Sawant, Tushar Tamhane, Ganesh Khedkar
2014 IJARCCE  
In this paper, we have proposed a technique known as 2-level QR code which consists of two layers of security provided to the QR code.  ...  We must lay our emphasis on the security and privacy of the QR code as there are chances of it getting into wrong hands.  ...  Above calculation certainly utilizes Reed-Solomon codes for encoding mystery messages earlier than inserting the end result message into QR code. there are numerous elements of Reed-Solomon codes, the  ... 
doi:10.17148/ijarcce.2017.64168 fatcat:fxzriinrfrhbnkbnarphyqrbee

Polynomial Time Attack on Wild McEliece Over Quadratic Extensions [article]

Alain Couvreur, Ayoub Otmani, Jean-Pierre Tillich
2015 arXiv   pre-print
We present a polynomial time structural attack against the McEliece system based on Wild Goppa codes from a quadratic finite field extension.  ...  This attack uses the fact that such codes can be distinguished from random codes to compute some filtration, that is to say a family of nested subcodes which will reveal their secret algebraic description  ...  Subsequently to our attack, this uncertainty on the security of code based cryptosystems using wild Goppa codes has been strengthened by another cryptanalysis based on the resolution of a system of multivariate  ... 
arXiv:1402.3264v2 fatcat:bcqf7vgkzvekdpurbyawx23vjy

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.  ...  For this section, we focus on two of the most preferred codes, one being Reed-Solomon codes and the other being their rank metric analog, Gabidulin codes.  ... 
arXiv:2201.07119v3 fatcat:oo53emg22jdxtmsevemlit7hlm

Smaller Keys for Code-Based Cryptography: McEliece Cryptosystems with Convolutional Encoders [article]

Paulo Almeida, Miguel Beltrá, Diego Napp, Cláudia Sebastião
2021 arXiv   pre-print
The secret key is constituted by a Generalized Reed-Solomon encoder and two Laurent polynomial matrices that contain large parts that are generated completely at random.  ...  In this paper we present a novel class of convolutional codes and investigate its use in a variant of the McEliece cryptosystem that possesses several interesting properties, including a reduction of the  ...  Acknowledgement The authors would like to thank Jorge Brandão, Karan Khathuria and Jean-Pierre Tillich for useful comments on this work.  ... 
arXiv:2104.06809v1 fatcat:kyetetuclnaaran37zie2lo2oy

Post Quantum Cryptography: Techniques, Challenges, Standardization, and Directions for Future Research [article]

Ritik Bavdekar, Eashan Jayant Chopde, Ashutosh Bhatia, Kamlesh Tiwari, Sandeep Joshua Daniel, Atul
2022 arXiv   pre-print
The security of asymmetric algorithms like RSA, Diffie Hellman, and ECC is based on the mathematical hardness of prime factorization and discrete logarithm.  ...  cryptography standardization process, and finally provides a couple of future research directions in this field.  ...  The HQC submitters presented a new decoder that uses Reed-Muller and Reed-Solomon codes. This helped in reducing the key size by a lot.  ... 
arXiv:2202.02826v1 fatcat:ghq4lqiu4rf5vpuv6gbk7ws4jm

Data-Hiding Codes

P. Moulin, R. Koetter
2005 Proceedings of the IEEE  
Such codes have also been called watermarking codes; they can be used in a variety of applications, including copyright protection for digital media, content authentication, media forensics, data binding  ...  Our focus is on the mathematical models, fundamental principles, and code design techniques that are applicable to data hiding.  ...  ACKNOWLEDGMENT The authors would like to thank their current and former students, A. Briassouli, A. K. Goteti, M. Kesal, T. Liu, M. K. Mıhçak, and Y. Wang, for their contributions to this paper.  ... 
doi:10.1109/jproc.2005.859599 fatcat:fshag72wujgntaoom7pd65uf24

Quantum Computing: A Taxonomy, Systematic Review and Future Directions [article]

Sukhpal Singh Gill, Adarsh Kumar, Harvinder Singh, Manmeet Singh, Kamalpreet Kaur, Muhammad Usman, Rajkumar Buyya
2021 arXiv   pre-print
This article presents a comprehensive review of quantum computing literature, and taxonomy of quantum computing.  ...  Quantum computing is a highly topical and fast-moving field of research with significant ongoing progress in all facets.  ...  In literature [182] - [186] , various variants of the McEliece scheme are proposed using different errorcorrecting codes such as Rank ECC, Gabidulin codes, Twisted Gabidulin codes, Twisted Reed-Solomon  ... 
arXiv:2010.15559v4 fatcat:y6cuttww5fd5jdmvcer352lh4e

Survey of Promising Technologies for Quantum Drones and Networks

Adarsh Kumar, Surbhi Bhatia, Keshav Kaushik, Manjula Gandhi, Gayathri Devi, Diego Pacheco, Arwa Mashat
2021 IEEE Access  
These schemes presently suffer from various attacks (like Overbeck attack, attacks over twisted Reed-Solomon codes, and attacks over twisted Gabidulin codes).  ...  A few of these schemes are discussed as follows. i. Code-based Signature Schemes This section discusses various code-based signature schemes in PQC [2] .  ... 
doi:10.1109/access.2021.3109816 fatcat:gkyevfoqrfertef7j7gjzcstii

Proof of All: Verifiable Computation in a Nutshell [article]

Mario Alessandro Barbara
2019 arXiv   pre-print
Such research has often overlapped with the need for private and scalable solutions of Blockchain-based communities, resulting in the first practical implementations of such systems.  ...  Furthermore, I expand on the future of Verifiable Computation, Universal proof compilers and "Proofs of All", by approaching the state-of-the-art zk-STARK construction from a more accessible and informal  ...  Interpolation and evaluation was combined into a single process using a state-of-the-art quasilinear time algorithm for Reed-Solomon codes based on additive-FFT techniques, described in [58] .  ... 
arXiv:1908.02327v2 fatcat:fdhmpzpnqfhprhijoy3zdradze

McEliece-type Cryptosystems over Quasi-cyclic Codes [article]

Upendra Kapshikar
2018 arXiv   pre-print
In this thesis, we study algebraic coding theory based McEliece-type cryptosystems over quasi-cyclic codes.  ...  Apart from this cryptosystem, we also present a class of 1/m quasi-cyclic codes, with small size and large minimal degree of the automorphism group.  ...  However, from the bound on the size of m, it is obviously true that 4p 8 e −δp ≤ (mp log (mp)) −ω(1) for large enough p.  ... 
arXiv:1805.09972v1 fatcat:4ugriofz4fat5fmz72sxx32dqu

Rank metric codes, codes using linear complexity and applications to public key cryptosystems

Tovohery Hajatiana Randrianarisoa
2018
Having this new theory, finally, we consider the codes based on the linear complexity and we design a new cryptosystem using these codes.  ...  We confirm this result by a construction using derivation on polynomial rings. Another class, discovered by Sheekey, are the twisted Gabidulin codes.  ...  Acknowledgments First of all, I would like to give my gratitude to Prof. Joachim Rosenthal for giving me the opportunity to do a PhD under his supervision.  ... 
doi:10.5167/uzh-153545 fatcat:pl3tftsiajcj3peolhwcwgchje

Fundamentals of Cryptology [chapter]

2006 Security in Fixed and Wireless Networks  
Method 8.3.3 The Pollard-U Method 8.3.4 The Index-Calculus Method General Discussion À p , i.e. the Multiplicative Group of GF+ p/ GF(2 n ) 8.4 Problems 9 RSA Based Systems 9.1 The RSA System 9.1.1 Some  ...  How to Take Discrete Logarithms 8.3.1 The Pohlig-Hellman Algorithm Special Case: q 1 2 n General Case: q 1 has only small prime factors An Example of the Pohlig-Hellman Algorithm 8.3.2 The Baby-Step Giant-Step  ...  We owe to him the notations f(x) (1734), e for the base of natural logs (1727), i for the square root of -1 (1777), p for pi, ⁄for summation (1755) etc.  ... 
doi:10.1002/0470863722.ch2 fatcat:3qnksbbsara6vl5fdzynloehcy

Privacy on the line: the politics of wiretapping and encryption

1998 ChoiceReviews  
If we could develop an algorithm based on a mathematical theory of the cryptanalysis of block ciphers, we could have proofs that the algorithm would resist certain types of attacks.  ...  a discussion of the process of cryptanalysis.  ...  , 148, 149 Church Committee on, 137, 170, 170, [200] [201] [202] 11 dimensions of, [141] [142] 128-131, 194 legalization of, 192-195 limits on, 193-195 minimization of, 372 in nineteenth century,  ... 
doi:10.5860/choice.35-6456 fatcat:zlca7qql2ffevobnzs5qckmyqq
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