Distinguisher-based attacks on public-key cryptosystems using Reed-Solomon codes

作者：Couvreur Alain; Gaborit Philippe; Gauthier Umana Valerie; Otmani Ayoub^*; Tillich Jean Pierre

来源：Designs, Codes and Cryptography, 2014, 73(2): 641-666.

DOI：10.1007/s10623-014-9967-z

• Code-based cryptography
• Generalized Reed-Solomon codes
• Key-recovery
• Distinguisher
• Homomorphic encryption

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.

• 出版日期2014-11