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Polynomial-Time Key Recovery Attack on the Faure-Loidreau Scheme based on Gabidulin Codes [article]

Philippe Gaborit and Ayoub Otmani and Hervé Talé Kalachi
2017 arXiv   pre-print
We show in this article that this scheme like other schemes based on Gabidulin codes, is also vulnerable to a polynomial-time attack that recovers the private key by applying Overbeck's attack on an appropriate  ...  In 2005 Faure and Loidreau designed a rank-metric encryption scheme which was not in the McEliece setting.  ...  ACKNOWLEDGEMENTS The authors would like to thank Pierre Loidreau for helpful discussions and for bringing reference [LO06] to our attention.  ... 
arXiv:1606.07760v2 fatcat:cdl757yeavb2pebzu5xxeyptna

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.  ...  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.  ...  Acknowledgements The work of L. Holzbaur and A. Wachter  ... 
arXiv:2203.12384v1 fatcat:brysqya7ynem5i25adxfwf5vl4

Decoding supercodes of Gabidulin codes and applications to cryptanalysis [article]

Maxime Bombar, Alain Couvreur
2021 arXiv   pre-print
Using this decoder, we provide polynomial time attacks on the rank-metric encryption schemes RAMESSES and LIGA.  ...  This article discusses the decoding of Gabidulin codes and shows how to extend the usual decoder to any supercode of a Gabidulin code at the cost of a significant decrease of the decoding radius.  ...  With this decoder in hand we perform a polynomial time message recovery attack on Ramesses and Liga.  ... 
arXiv:2103.02700v3 fatcat:gdyep3ndubhgpczwr3edeqakry

LIGA: a cryptosystem based on the hardness of rank-metric list and interleaved decoding

Julian Renner, Sven Puchinger, Antonia Wachter-Zeh
2021 Designs, Codes and Cryptography  
AbstractWe propose the new rank-metric code-based cryptosystem which is based on the hardness of list decoding and interleaved decoding of Gabidulin codes. is an improved variant of the FaureLoidreau  ...  The new key generation algorithm constructs public keys for which all polynomial-time interleaved decoders fail—hence resists the GOT attack.  ...  Acknowledgements The work of J. Renner and A. Wachter-Zeh was supported by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant Agree-  ... 
doi:10.1007/s10623-021-00861-z fatcat:ugo3dwngfrb7rpnqwiuckzpe5i

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.  ...  The new key generation algorithm constructs public keys for which all polynomial-time interleaved decoders fail---hence LIGA resists the GOT attack.  ...  Further, we thank Pierre Loidreau for his valuable comments on a previous version of this  ... 
arXiv:1812.04892v2 fatcat:mz3o2goz3zdnno6dcfgcy2fuye

Extending Coggia-Couvreur Attack on Loidreau's Rank-metric Cryptosystem [article]

Anirban Ghatak
2020 arXiv   pre-print
A recent paper by Coggia and Couvreur presents a polynomial time key-recovery attack on Loidreau's encryption scheme, based on rank-metric codes, for some parameters.  ...  The secret matrix component of Loidreau's scheme is chosen over a defining subspace of the field associated with the rank-metric code.  ...  Acknowledgements The author would like to thank Arnab Chakraborty and Mridul Nandi for several helpful discussions.  ... 
arXiv:2007.07354v1 fatcat:pou4w44zxff5xcna7y2v7kvmf4

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 this paper, we suggest a code-based public key encryption scheme, called McNie.  ...  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.  ...  A polynomial time attack against algebraic geometry code based public key cryptosystems. In Information Theory (ISIT), 2014 IEEE International Symposium on (pp. 1446-1450). IEEE. 11.  ... 
arXiv:1812.05008v2 fatcat:wsagwr4tofd3fdn2cxpp3vogte

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.  ...  Acknowledgement The first author is supported by the Swiss National Science Foundation grant number 195290.  ... 
arXiv:2201.07119v3 fatcat:oo53emg22jdxtmsevemlit7hlm