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LIGA: A Cryptosystem Based on the Hardness of Rank-Metric List and Interleaved Decoding [article]

Julian Renner, Sven Puchinger, Antonia Wachter-Zeh
2020 arXiv   pre-print
We propose the new rank-metric code-based cryptosystem LIGA which is based on the hardness of list decoding and interleaved decoding of Gabidulin codes.  ...  It is not based on hiding the structure of a code.  ...  Further, we thank Pierre Loidreau for his valuable comments on a previous version of this  ... 
arXiv:1812.04892v2 fatcat:mz3o2goz3zdnno6dcfgcy2fuye

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 code-based cryptography, the hardness of the corresponding generic decoding problem can lead to systems with reduced public-key size.  ...  Codes designed for the rank metric have attracted considerable attention in recent years, reinforced by network coding and further motivated by a variety of applications.  ...  We introduce subspace codes, with a focus on constructions based on lifting rank-metric codes and provide upper bounds on the size of subspace codes.  ... 
doi:10.1561/0100000119 fatcat:4wh62agk5rczpjlfr5bp3km67u

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
In particular, we apply rank-metric codes to McNie.  ...  In this paper, we suggest a code-based public key encryption scheme, called McNie.  ...  This is the first rank metric based cryptosystem with poor algebraic structure, and is still consid- ered secure. Furthermore, the double circulant variant provides very small key sizes.  ... 
arXiv:1812.05008v2 fatcat:wsagwr4tofd3fdn2cxpp3vogte

Efficient Encryption from Random Quasi-Cyclic Codes [article]

Carlos Aguilar, Olivier Blazy, Jean-Christophe Deneuville, Philippe Gaborit, Gilles Zémor
2016 arXiv   pre-print
Our schemes benefit from a very fast decryption algorithm together with small key sizes of only a few thousand bits.  ...  We propose two new cryptosystems instantiated within our framework: the Hamming Quasi-Cyclic cryptosystem (HQC), based on the Hamming metric, and the Rank Quasi-Cyclic cryptosystem (RQC), based on the  ...  Our analysis allows us to give small parameters for code-based encryption in Hamming and Rank metrics.  ... 
arXiv:1612.05572v1 fatcat:up7iubangna3db2gd77tfi3ywe

Security of the GPT-Type Cryptosystems

Maximilien Gadouleau, Zhiyuan Yan
2006 2006 IEEE International Symposium on Information Theory  
The Gabidulin-Paramonov-Tretjakov (GPT) publickey cryptosystem and the GPT system with column scrambler, both based on Gabidulin codes, seem to have some advantages over McEliece's public-key cryptosystems  ...  using Goppa codes.  ...  Gabidulin, Paramonov, and Tretjakov [4] proposed a new public-key cryptosystem which uses a new class of codes proposed by Gabidulin [2] based on the rank metric.  ... 
doi:10.1109/isit.2006.261627 dblp:conf/isit/GadouleauY06 fatcat:lqy3kqbce5cxdkucxkntplz5sq

A New Rank Metric Codes Based Encryption Scheme [chapter]

Pierre Loidreau
2017 Lecture Notes in Computer Science  
We design a new McEliece-like rank metric based encryption scheme from Gabidulin codes. We explain why it is not affected by the invariant subspace attacks also known as Overbeck's attacks.  ...  For a given security our public-keys are more compact than for the same security in the Hamming metric based settings.  ...  used in the cryptosystem Conclusion We proposed a new code-based public-key cryptosystem based on the derivation of Gabidulin codes.  ... 
doi:10.1007/978-3-319-59879-6_1 fatcat:kqdhhgfszbfinpdfbdu24af6wy

DRANKULA: A McEliece-like Rank Metric based Cryptosystem Implementation

Ameera Salem Al Abdouli, Mohamed Al Ali, Emanuele Bellini, Florian Caullery, Alexandros Hasikos, Marc Manzano, Victor Mateu
2018 Proceedings of the 15th International Joint Conference on e-Business and Telecommunications  
We present and analyze the performance of DRANKULA, a McEliece-like cryptosystem implementation using rank metric instead of Hamming distance.  ...  We provide the pseudo-code of the core algorithms of the cryptosystem. In addition, we also show code optimization when special instructions like Carry-less multiplications are available.  ...  proposed the GPT cryptosystem, a McEliece-like cryptosystem based on Rank metric (Gabidulin et al., 1991) .  ... 
doi:10.5220/0006838102300241 dblp:conf/icete/AbdouliABCHMM18 fatcat:kvohfmb4drfljkh6t3o7y47phq

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
We introduce a new rank-based key encapsulation mechanism (KEM) with public key and ciphertext sizes around 3.5 Kbytes each, for 128 bits of security, without using ideal structures.  ...  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  ...  Rank-based cryptography is similar to code-based cryptography, with the difference that the errorcorrecting codes are embedded in a rank-metric space (often over a prime order field extension).  ... 
arXiv:2206.11961v1 fatcat:5kpaeml5vbdzjlf4hy4ke3ysba

Geo Security using GPT Cryptosystem

Eraj Khan, Abbas Khalid, Arshad Ali, Muhammad Atif, Ahmad Salman
2020 International Journal of Advanced Computer Science and Applications  
This paper describes an implementation of location-based encryption using a public key cryptosystem based on the rank error correcting codes.  ...  In any code based cryptosystem, public and private keys are in the form of matrices based over the finite field.  ...  a GPT public key cryptosystem based on rank error correcting codes.  ... 
doi:10.14569/ijacsa.2020.0110265 fatcat:xm4ooxhbq5danl34ae6hf7y7qi

Location Based Security for Smart Grid Applications

Eraj Khan, Bamidele Adebisi, Bahram Honary
2013 Energy Procedia  
The scheme uses an algebraic code based cryptosystems known as GPT (Gabidulin -Paramonov-Trejtakov), which provides a very strong protection while utilising the smallest key size as compared to other cryptosystems  ...  based on algebraic codes.  ...  This is because the GPT is based on rank error correcting codes and uses the Rank metric instead of Hamming metric. Rank codes are well-structured codes.  ... 
doi:10.1016/j.egypro.2013.11.030 fatcat:7rdngmkoazby3ioh6eu3xgekza

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 code-based cryptography, the hardness of the corresponding generic decoding problem can lead to systems with reduced public-key size.  ...  Codes designed for the rank metric have attracted considerable attention in recent years, reinforced by network coding and further motivated by a variety of applications.  ...  Holzbaur and A. Wachter  ... 
arXiv:2203.12384v1 fatcat:brysqya7ynem5i25adxfwf5vl4

Repairing the Faure-Loidreau Public-Key Cryptosystem [article]

Antonia Wachter-Zeh and Sven Puchinger and Julian Renner
2018 arXiv   pre-print
A repair of the Faure-Loidreau (FL) public-key code-based cryptosystem is proposed. The FL cryptosystem is based on the hardness of list decoding Gabidulin codes which are special rank-metric codes.  ...  Compared to other code-based cryptosystems, we obtain significantly smaller key sizes for the same security level.  ...  m = m − Tr q mu /q m (αx). definition of the public key: 2, Ch. 7, Sec. 2.1] is based on a similar principle as Overbeck uses to attack the McEliece cryptosystem based on rank-metric codes [8].  ... 
arXiv:1801.03688v2 fatcat:hba3jwr35ra7xfpsvg66rdtofm

Optimized implementation of the NIST PQC submission ROLLO on microcontroller [article]

Jérôme Lablanche, Lina Mortajine, Othman Benchaalal, Pierre-Louis Cayrel, Nadia El Mrabet
2019 IACR Cryptology ePrint Archive  
We present in this paper an efficient implementation of the code-based cryptosystem ROLLO, a candidate to the NIST PQC project, on a device available on the market.  ...  Finally, the cryptosystem outperforms the public key exchange protocol ECDH for a security level of 192 bits showing then the possibility of the integration of this new cryptosystem in current chips.  ...  As ROLLO cryptosystem is based on codes embedded with rank metric over F n q m , we will leave aside the Hamming metric for the rest of this paper.  ... 
dblp:journals/iacr/LablancheMBCM19 fatcat:k2xkcpwdhnbkzao7fwrtkr3pdq

A New Algorithm for Solving the Rank Syndrome Decoding Problem

Nicolas Aragon, Philippe Gaborit, Adrien Hauteville, Jean-Pierre Tillich
2018 2018 IEEE International Symposium on Information Theory (ISIT)  
We give examples of broken parameters for recently proposed cryptosystems based on LRPC codes or Gabidulin codes.  ...  In this paper, we propose an improvement of the attack on the Rank Syndrome Decoding (RSD) problem found in [1], usually the best attack considered for evaluating the security of rank based cryptosystems  ...  One of the main drawback of these cryptosystems are the relatively large public key sizes. A solution to decrease their size is to change the metric used for the code.  ... 
doi:10.1109/isit.2018.8437464 dblp:conf/isit/AragonGHT18 fatcat:yefiu2cabjchbmznxn4jwoa3hi

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.  ...  E X A M P L E PA R A M E T E R S In this Section, the security level, the rate and the keysize of the GPT cryptosystem based on twisted Gabidulin codes is compared with McEliece's cryptosystem based on  ... 
arXiv:1806.10055v2 fatcat:5l5xdlpu4zchpbbnp6gvaqz43a
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