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Twisted Gabidulin Codes in the GPT Cryptosystem [article]

Sven Puchinger and Julian Renner and Antonia Wachter-Zeh
2018 arXiv   pre-print
In this paper, we investigate twisted Gabidulin codes in the GPT code-based public-key cryptosystem. We show that Overbeck's attack is not feasible for a subfamily of twisted Gabidulin codes.  ...  The resulting key sizes are significantly lower than in the original McEliece system and also slightly smaller than in Loidreau's unbroken GPT variant.  ...  The GPT Crpytosystem and Its Variants The GPT cryptosystem is an instantiation of the McEliece cryptosystem with Gabidulin codes.  ... 
arXiv:1806.10055v2 fatcat:5l5xdlpu4zchpbbnp6gvaqz43a

Rank-Metric Codes and Their Applications [article]

Hannes Bartz, Lukas Holzbaur, Hedongliang Liu, Sven Puchinger, Julian Renner, Antonia Wachter-Zeh
2022 arXiv   pre-print
In distributed data storage, codes in the rank metric have been used repeatedly to construct codes with locality, and in coded caching, they have been employed for the placement of coded symbols.  ...  In code-based cryptography, the hardness of the corresponding generic decoding problem can lead to systems with reduced public-key size.  ...  Acknowledgements The work of L. Holzbaur and A. Wachter  ... 
arXiv:2203.12384v1 fatcat:brysqya7ynem5i25adxfwf5vl4

Rank-Metric Codes and Their Applications

Hannes Bartz, Lukas Holzbaur, Hedongliang Liu, Sven Puchinger, Julian Renner, Antonia Wachter-Zeh
2022 Foundations and Trends in Communications and Information Theory  
In distributed data storage, codes in the rank metric have been used repeatedly to construct codes with locality, and in coded caching, they have been employed for the placement of coded symbols.  ...  In code-based cryptography, the hardness of the corresponding generic decoding problem can lead to systems with reduced public-key size.  ...  The first McEliece variant in the rank metric was proposed by Gabidulin, Paramonov, and Tretjakov [85] and is therefore known as the GPT cryptosystem.  ... 
doi:10.1561/0100000119 fatcat:4wh62agk5rczpjlfr5bp3km67u

Further Generalisations of Twisted Gabidulin Codes [article]

Sven Puchinger and Johan Rosenkilde né Nielsen and John Sheekey
2017 arXiv   pre-print
The new class contains codes that are neither equivalent to a generalised Gabidulin nor to a twisted Gabidulin code, the only two known general constructions of linear MRD codes.  ...  We present a new family of maximum rank distance (MRD) codes.  ...  Conclusion We introduced a new constructive class of rank-metric codes, twisted Gabidulin codes, that contain codes inequivalent to existing classes, such as Gabidulin or the twisted Gabidulin codes in  ... 
arXiv:1703.08093v2 fatcat:aeri247ewfdwrfvzndcgmkc7c4

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

Julien Lavauzelle, Julian Renner
2019 arXiv   pre-print
We also discuss a potential repair of the scheme and an application of the attack to GPT cryptosystems using twisted Gabidulin codes.  ...  In this paper, an efficient key-recovery attack is given on this variant of the McEliece cryptosystem.  ...  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

Two Public-Key Cryptosystems Based on Expanded Gabidulin Codes [article]

Wenshuo Guo, Fang-Wei Fu
2022 arXiv   pre-print
Based on the distinguisher for Gabidulin codes, we propose a distinguisher for expanded Gabidulin codes by introducing the concept of the so-called twisted Frobenius power.  ...  This paper presents two public key cryptosystems based on the so-called expanded Gabidulin codes, which are constructed by expanding Gabidulin codes over the base field.  ...  In [24] the authors proposed the GPT cryptosystem by using Gabidulin codes in the McEliece setting, which requires a public key size of only a few thousand bits for the security of 100 bits.  ... 
arXiv:2107.01610v3 fatcat:7j5h2bq5nzdr3bjsw3ktmqfhle

Constructions of optimal rank-metric codes from automorphisms of rational function fields [article]

Rakhi Pratihar, Tovohery Hajatiana Randrianarisoa
2021 arXiv   pre-print
The first construction is of generalized Gabidulin codes over rational function fields.  ...  Reducing these codes over finite fields, we obtain maximum rank distance (MRD) codes which are not equivalent to generalized twisted Gabidulin codes.  ...  That is also a reason why twisted Gabidulin codes were not considered to be secure for such GPT cryptosystem. In our case, we have codes where the intersection is trivial.  ... 
arXiv:1907.05508v4 fatcat:3c5nhg7mwvhmrdcpxov5rhbruy

Constructions of optimal rank-metric codes from automorphisms of rational function fields

Rakhi Pratihar, Tovohery Hajatiana Randrianarisoa
2022 Advances in Mathematics of Communications  
The first construction is of generalized Gabidulin codes over rational function fields.  ...  Reducing these codes over finite fields, we obtain maximum rank distance (MRD) codes which are not equivalent to generalized twisted Gabidulin codes.  ...  We would like to thank the anonymous reviewers for their constructive comments which helped to improve the article.  ... 
doi:10.3934/amc.2022034 fatcat:p475vliwpjda3jk74x4t2kbwwi

F_q^n-linear rank distance codes and their distinguishers [article]

Luca Giuzzi, Ferdinando Zullo
2019 arXiv   pre-print
twisted Gabidulin codes as done in GiuZ.  ...  One of the possible applications of MRD-codes is for McEliece--like public key cryptosystems, as proposed by Gabidulin, Paramonov and Tretjakov in GPT.  ...  Gabidulin codes and the twisted Gabidulin codes are both proper subsets of this class.  ... 
arXiv:1904.03104v1 fatcat:igimqitbu5hh7bejoqck57hcem

Equivalence and Characterizations of Linear Rank-Metric Codes Based on Invariants [article]

Alessandro Neri and Sven Puchinger and Anna-Lena Horlemann-Trautmann
2019 arXiv   pre-print
In the end we use the mentioned sequences to characterize Gabidulin codes in various ways.  ...  Furthermore, we give an exact number of equivalence classes Gabidulin codes and derive bounds on the number of equivalence classes for twisted Gabidulin codes.  ...  Overbeck [47] proposed an attack on the Gabidulin-Paramonov-Tretjakov (GPT) cryptosystem [21] , which is based on the fact that (for small enough i) the code C + θ(C) + · · · + θ i (C) has much smaller  ... 
arXiv:1911.13059v1 fatcat:zdueyyybcvf4bamwle2kqq5yzy

A Survey on Code-Based Cryptography [article]

Violetta Weger, Niklas Gassner, Joachim Rosenthal
2022 arXiv   pre-print
We cover the main frameworks introduced in code-based cryptography and analyze their security assumptions.  ...  We provide the mathematical background in a lecture notes style, with the intention of reaching a wider audience.  ...  Acknowledgement The first author is supported by the Swiss National Science Foundation grant number 195290.  ... 
arXiv:2201.07119v3 fatcat:oo53emg22jdxtmsevemlit7hlm

A Public-Key Cryptosystem from Interleaved Goppa Codes [article]

Molka Elleuch, Antonia Wachter-Zeh, Alexander Zeh
2018 arXiv   pre-print
In this paper, a code-based public-key cryptosystem based on interleaved Goppa codes is presented.  ...  The scheme is based on encrypting several ciphertexts with the same Goppa code and adding a burst error to them.  ...  ACKNOWLEDGMENT The authors would like to thank Lukas Holzbaur, Sven Puchinger, and Vladimir Sidorenko for the valuable discussions.  ... 
arXiv:1809.03024v1 fatcat:mqoahhi7inbsfa4vbarxbyhnka

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
As the quantum devices are expected to steadily scale up in the next few years, quantum decoherence and qubit interconnectivity are two of the major challenges to achieve quantum advantage in the NISQ  ...  Indeed, the demonstration of quantum supremacy marks a significant milestone in the Noisy Intermediate Scale Quantum (NISQ) era - the next logical step being the quantum advantage whereby quantum computers  ...  Code-based cryptosystems Author Cryptosystem Error-Correcting Codes (ECC) Major Strengths Jäämeri [182] McEliece, Gabidulin- Paramonov-Tretjakov (GPT) Rank ECC, Gabidulin codes, Twisted Gabidulin  ... 
arXiv:2010.15559v4 fatcat:y6cuttww5fd5jdmvcer352lh4e

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

Tovohery Hajatiana Randrianarisoa
2018
Another class, discovered by Sheekey, are the twisted Gabidulin codes. The second part of this thesis is devoted to the decoding algorithms for the class of twisted Gabidulin codes.  ...  In the first part of this thesis, we show that when we work in large field, most linear rank metric codes are maximum rank distance codes. Furthermore, only a few of them are Gabidulin codes.  ...  I thank the reviewers for their invaluable comments to improve this thesis. I also would like to acknowledge Prof. Rosenthal, Anna-Lena, Alessandro for their work with me in the co-authored papers.  ... 
doi:10.5167/uzh-153545 fatcat:pl3tftsiajcj3peolhwcwgchje

A study of cryptographic systems based on Rank metric codes

Kyle Daniel Marshall
2016
More recently, Gabidulin proposed using codes in the rank metric to design secure cryptosystems because they could be designed with smaller parameters.  ...  In 1978, McEliece proposed a cryptosystem based on the difficulty of decoding random linear codes but the key sizes were too large for practical consideration.  ...  The first such, the GPT cryptosystem, was proposed by Gabidulin et al. in [28] and a generalization given later by Loidreau in [49] called the GGPT cryptosystem is given in Subsection 4.2.1.  ... 
doi:10.5167/uzh-127105 fatcat:s7rbrpfrjnbglhv766pdnqah2i
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