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Post-Quantum and Code-Based Cryptography—Some Prospective Research Directions

Chithralekha Balamurugan, Kalpana Singh, Ganeshvani Ganesan, Muttukrishnan Rajarajan
2021 Cryptography  
This paper provides an overview of the various research directions that have been explored in post-quantum cryptography and, specifically, the various code-based cryptography research dimensions that have  ...  This threat triggered post-quantum cryptography research to design and develop post-quantum algorithms that can withstand quantum computing attacks.  ...  Acknowledgments: This research work has been carried out under the leadership of the Institute for Technological Research SystemX, and therefore granted within the scope of the program "Recherche Exploratoire  ... 
doi:10.3390/cryptography5040038 fatcat:wkb43zunwjagbnljc6brfou4ty

A New Rank Metric Codes Based Encryption Scheme [chapter]

Pierre Loidreau
2017 Lecture Notes in Computer Science  
For a given security our public-keys are more compact than for the same security in the Hamming metric based settings.  ...  The idea of the design mixes two existing approaches designing rank metric based encryption schemes.  ...  Introduction The security of the main post-quantum (PQ) primitives relies on the difficulty of solving decoding problems in some metrics (Hamming metric for codes, Euclidean metric for lattices).  ... 
doi:10.1007/978-3-319-59879-6_1 fatcat:kqdhhgfszbfinpdfbdu24af6wy

Identity-Based Encryption from Codes with Rank Metric [chapter]

Philippe Gaborit, Adrien Hauteville, Duong Hieu Phan, Jean-Pierre Tillich
2017 Lecture Notes in Computer Science  
Among all candidates for post-quantum cryptography, there only exist thus lattice-based IBE.  ...  Beside systems based on the Hamming metric, cryptosystems relying on a different metric, the rank metric, were introduced in 1991 by Gabidulin et al.[21].  ...  This work has been supported in part by the French ANR projects ALAMBIC (ANR-16-CE39-0006) and ID-FIX (ANR-16-CE39-0004).  ... 
doi:10.1007/978-3-319-63697-9_7 fatcat:wscwpb53mnbq3gvupqhivibf6e

Improvements of Algebraic Attacks for solving the Rank Decoding and MinRank problems [article]

Magali Bardet, Maxime Bros, Daniel Cabarcas, Philippe Gaborit, Ray Perlner, Daniel Smith-Tone, Jean-Pierre Tillich, Javier Verbel
2020 arXiv   pre-print
Rank Decoding (RD) is the main underlying problem in rank-based cryptography.  ...  Post-Quantum competition.  ...  Acknowledgements This work has been supported by the French ANR projects CBCRYPT (ANR-17-CE39-0007) and the MOUSTIC project with the support from the European Regional Development Fund (ERDF) and the Regional  ... 
arXiv:2002.08322v3 fatcat:qt3zmk5imjc6neytawezi7j6vq

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  ...  Fig. 2 . 2 The RankSign + signature algorithm Micciancio, Oded Regev, Lattice-based Cryptography Book chapter in Post-quantum Cryptography, D. J. Bernstein and J.  ... 
arXiv:1606.00629v2 fatcat:4r3pcnwlqfczdpx3y7bad7oiue

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.  ...  In preparation for the quantum era the National Institute of Standards and Technology (NIST) has initiated a standardization process for public-key encryption (PKE) schemes, key-encapsulation mechanisms  ...  The second and third author are supported by armasuisse Science and Technology (Project Nr.: CYD C-2020010).  ... 
arXiv:2201.07119v3 fatcat:oo53emg22jdxtmsevemlit7hlm

Attack on the Edon-K Key Encapsulation Mechanism [article]

Matthieu Lequesne, Jean-Pierre Tillich
2018 arXiv   pre-print
The key encapsulation mechanism Edon-K was proposed in response to the call for post-quantum cryptography standardization issued by the National Institute of Standards and Technologies (NIST).  ...  This scheme is inspired by the McEliece scheme but uses another family of codes defined over F_2^128 instead of F_2 and is not based on the Hamming metric.  ...  THE EDON-K KEM EDON-K [GG17] is a key encapsulation mechanism proposed by Gligoroski and Gjøsteen for the NIST post-quantum cryptography call.  ... 
arXiv:1802.06157v1 fatcat:hfczllpoovdanpb45gzx6mhccu

Attack on the Edon-kKey Encapsulation Mechanism

Matthieu Lequesne, Jean-Pierre Tillich
2018 2018 IEEE International Symposium on Information Theory (ISIT)  
The key encapsulation mechanism EDON-K was proposed in response to the call for post-quantum cryptography standardization issued by the National Institute of Standards and Technologies (NIST).  ...  This scheme is inspired by the McEliece scheme but uses another family of codes defined over F 2 128 instead of F2 and is not based on the Hamming metric.  ...  THE EDON-K KEM EDON-K [GG17] is a key encapsulation mechanism proposed by Gligoroski and Gjøsteen for the NIST post-quantum cryptography call.  ... 
doi:10.1109/isit.2018.8437498 dblp:conf/isit/LequesneT18 fatcat:hldie2d3nrhelcdssgkdre3jme

LRPC codes with multiple syndromes: near ideal-size KEMs without ideals [article]

Carlos Aguilar-Melchor, Nicolas Aragon, Victor Dyseryn, Philippe Gaborit, Gilles Zémor
2022 arXiv   pre-print
To the best of our knowledge, our scheme improves in size all the existing unstructured post-quantum lattice or code-based algorithms such as FrodoKEM or Classic McEliece.  ...  Our technique, whose efficiency relies on properties of rank metric, is to build upon existing Low Rank Parity Check (LRPC) code-based KEMs and to send multiple syndromes in one ciphertext, allowing to  ...  The most common algorithms in post-quantum cryptography are latticebased or code-based.  ... 
arXiv:2206.11961v1 fatcat:5kpaeml5vbdzjlf4hy4ke3ysba

Algebraic Coding Theory for Networks, Storage, and Security (Dagstuhl Seminar 18511)

Eimear Byrne, Martin Bossert, Antonia Wachter-Zeh, Michael Wagner
2019 Dagstuhl Reports  
The ever increasing traffic in networks and the growth of distributed storage systems require advanced techniques based on algebraic coding to meet user demand.  ...  Private access to such services is a major concern for consumers and is still a new field in the context of distributed storage.  ...  Fundamentally, the application of lattices, MDPC codes, or LRPC codes in cryptography represent the same framework under three different metrics: Euclidean, Hamming, and rank metric.  ... 
doi:10.4230/dagrep.8.12.49 dblp:journals/dagstuhl-reports/ByrneBW18 fatcat:qmcdjxigx5ahxe3jpnmns4v6ka

RankSign: An Efficient Signature Algorithm Based on the Rank Metric [chapter]

Philippe Gaborit, Olivier Ruatta, Julien Schrek, Gilles Zémor
2014 Lecture Notes in Computer Science  
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  ...  Introduction In the last few years there has been a burst of activity in post-quantum cryptography.  ... 
doi:10.1007/978-3-319-11659-4_6 fatcat:db2gbgb37nhafgbdkelp2xpuqm

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.  ...  The rank metric measures the distance between two matrices by the rank of their difference.  ...  Acknowledgements The work of L. Holzbaur and A. Wachter  ... 
arXiv:2203.12384v1 fatcat:brysqya7ynem5i25adxfwf5vl4

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

Julien Lavauzelle and Pierre Loidreau and Ba-Duc Pham
2019 arXiv   pre-print
The security only relies on rank metric decoding problems, and does not require to hide the structure of a code.  ...  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 recent NIST Post-Quantum Cryptography Standardization process motivates proposals in this sense.  ... 
arXiv:1911.13119v1 fatcat:63cp4l7kyfcxtawkyxgwbawxi4

Generalizing Syndrome Decoding problem to the totally Non-negative Grassmannian [article]

Kelechi Chuwkunonyerem Emerole
2021 arXiv   pre-print
Finally, experimental results on decoding failure probability and complexity based on row operations are presented and compared to Low Density parity check codes in the Hamming metric.  ...  In this paper, we study and generalize the solution to codes associated with the totally non-negative Grassmannian in the Grassmann metric.  ...  INTRODUCTION The hardness of decoding the syndrome of a linear code [1] has been useful in designing quantum safe encryption in the Hamming metric using Goppa codes [2] and in the rank metric using  ... 
arXiv:2106.15526v1 fatcat:l7ll45ypebgtbl6adjlss2l6ki

Information set decoding of Lee-metric codes over finite rings [article]

Violetta Weger, Massimo Battaglioni, Paolo Santini, Franco Chiaraluce, Marco Baldi, Edoardo Persichetti
2021 arXiv   pre-print
In this paper we switch from the Hamming metric to the Lee metric, and study ISD algorithms and their complexity for codes measured with the Lee metric over finite rings.  ...  Classically, ISD algorithms have been studied for codes in the Hamming metric.  ...  This well-assessed security makes code-based cryptosystems among the most promising solutions for the post-quantum world [30] . All the above examples, however, rely on codes in the Hamming metric.  ... 
arXiv:2001.08425v2 fatcat:fevcgoge6vaujhafzjnqswtklm
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