Distinguisher-based attacks on public-key cryptosystems using Reed-Solomon codes
Because of their interesting algebraic properties, several authors promote the use of generalized Reed-Solomon codes in cryptography. Niederreiter was the first to suggest an instantiation of his cryptosystem with them but Sidelnikov and Shestakov showed that this choice is insecure. Wieschebrink pr...
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2014
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ir-10336-238452022-05-02T12:37:16Z Distinguisher-based attacks on public-key cryptosystems using Reed-Solomon codes Couvreur, Alain Gaborit, Philippe Gauthier-Umaña, Valérie Otmani, Ayoub Tillich, Jean-Pierre Matrix algebra Public key cryptography Recovery Reed-Solomon codes Code-based cryptography Distinguishers Generalized reed-solomon codes Ho-momorphic encryptions Key-recovery Codes (symbols) Code-based cryptography Distinguisher Generalized Reed-Solomon codes Homomorphic encryption Key-recovery Because of their interesting algebraic properties, several authors promote the use of generalized Reed-Solomon codes in cryptography. Niederreiter was the first to suggest an instantiation of his cryptosystem with them but Sidelnikov and Shestakov showed that this choice is insecure. Wieschebrink proposed a variant of the McEliece cryptosystem which consists in concatenating a few random columns to a generator matrix of a secretly chosen generalized Reed-Solomon code. More recently, new schemes appeared which are the homomorphic encryption scheme proposed by Bogdanov and Lee, and a variation of the McEliece cryptosystem proposed by Baldi et al. which hides the generalized Reed-Solomon code by means of matrices of very low rank. In this work, we show how to mount key-recovery attacks against these public-key encryption schemes. We use the concept of distinguisher which aims at detecting a behavior different from the one that one would expect from a random code. All the distinguishers we have built are based on the notion of component-wise product of codes. It results in a powerful tool that is able to recover the secret structure of codes when they are derived from generalized Reed-Solomon codes. Lastly, we give an alternative to Sidelnikov and Shestakov attack by building a filtration which enables to completely recover the support and the non-zero scalars defining the secret generalized Reed-Solomon code. © 2014 Springer Science+Business Media New York. 2014 2020-05-26T00:05:58Z info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion 09251022 15737586 https://repository.urosario.edu.co/handle/10336/23845 https://doi.org/10.1007/s10623-014-9967-z eng info:eu-repo/semantics/openAccess application/pdf Kluwer Academic Publishers instname:Universidad del Rosario |
institution |
EdocUR - Universidad del Rosario |
collection |
DSpace |
language |
Inglés (English) |
topic |
Matrix algebra Public key cryptography Recovery Reed-Solomon codes Code-based cryptography Distinguishers Generalized reed-solomon codes Ho-momorphic encryptions Key-recovery Codes (symbols) Code-based cryptography Distinguisher Generalized Reed-Solomon codes Homomorphic encryption Key-recovery |
spellingShingle |
Matrix algebra Public key cryptography Recovery Reed-Solomon codes Code-based cryptography Distinguishers Generalized reed-solomon codes Ho-momorphic encryptions Key-recovery Codes (symbols) Code-based cryptography Distinguisher Generalized Reed-Solomon codes Homomorphic encryption Key-recovery Couvreur, Alain Gaborit, Philippe Gauthier-Umaña, Valérie Otmani, Ayoub Tillich, Jean-Pierre Distinguisher-based attacks on public-key cryptosystems using Reed-Solomon codes |
description |
Because of their interesting algebraic properties, several authors promote the use of generalized Reed-Solomon codes in cryptography. Niederreiter was the first to suggest an instantiation of his cryptosystem with them but Sidelnikov and Shestakov showed that this choice is insecure. Wieschebrink proposed a variant of the McEliece cryptosystem which consists in concatenating a few random columns to a generator matrix of a secretly chosen generalized Reed-Solomon code. More recently, new schemes appeared which are the homomorphic encryption scheme proposed by Bogdanov and Lee, and a variation of the McEliece cryptosystem proposed by Baldi et al. which hides the generalized Reed-Solomon code by means of matrices of very low rank. In this work, we show how to mount key-recovery attacks against these public-key encryption schemes. We use the concept of distinguisher which aims at detecting a behavior different from the one that one would expect from a random code. All the distinguishers we have built are based on the notion of component-wise product of codes. It results in a powerful tool that is able to recover the secret structure of codes when they are derived from generalized Reed-Solomon codes. Lastly, we give an alternative to Sidelnikov and Shestakov attack by building a filtration which enables to completely recover the support and the non-zero scalars defining the secret generalized Reed-Solomon code. © 2014 Springer Science+Business Media New York. |
format |
Artículo (Article) |
author |
Couvreur, Alain Gaborit, Philippe Gauthier-Umaña, Valérie Otmani, Ayoub Tillich, Jean-Pierre |
author_facet |
Couvreur, Alain Gaborit, Philippe Gauthier-Umaña, Valérie Otmani, Ayoub Tillich, Jean-Pierre |
author_sort |
Couvreur, Alain |
title |
Distinguisher-based attacks on public-key cryptosystems using Reed-Solomon codes |
title_short |
Distinguisher-based attacks on public-key cryptosystems using Reed-Solomon codes |
title_full |
Distinguisher-based attacks on public-key cryptosystems using Reed-Solomon codes |
title_fullStr |
Distinguisher-based attacks on public-key cryptosystems using Reed-Solomon codes |
title_full_unstemmed |
Distinguisher-based attacks on public-key cryptosystems using Reed-Solomon codes |
title_sort |
distinguisher-based attacks on public-key cryptosystems using reed-solomon codes |
publisher |
Kluwer Academic Publishers |
publishDate |
2014 |
url |
https://repository.urosario.edu.co/handle/10336/23845 https://doi.org/10.1007/s10623-014-9967-z |
_version_ |
1740172318909399040 |
score |
12,131701 |