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...
| Autores: | , , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2014 |
| País: | Colombia |
| Institución: | Universidad del Rosario |
| Repositorio: | Repositorio EdocUR - U. Rosario |
| Idioma: | inglés |
| OAI Identifier: | oai:repository.urosario.edu.co:10336/23845 |
| Acceso en línea: | https://doi.org/10.1007/s10623-014-9967-z https://repository.urosario.edu.co/handle/10336/23845 |
| Access Level: | acceso abierto |
| Palabra clave: | Matrix algebra Public key cryptography Recovery Reed-Solomon codes Code-based cryptography Distinguishers Generalized reed-solomon codes Ho-momorphic encryptions Key-recovery Codes (symbols) Distinguisher Generalized Reed-Solomon codes Homomorphic encryption |
| Sumario: | 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. |
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