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 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.

• Fecha de publicación: 2014
• Institución: Universidad del Rosario
• Repositorio: Repositorio EdocUR - U. Rosario
• Idioma: eng
• 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
• 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); Code-based cryptography; Distinguisher; Generalized Reed-Solomon codes; Homomorphic encryption; Key-recovery
• License: Abierto (Texto Completo)