Cryptanalysis of some schemes applying automorphisms

V. A. Romankov

Prikladnaâ diskretnaâ matematika, no. 3 (2013), pp. 35-51

Résumé

Some methods are given for cryptanalysis of encryption schemes and key establishment protocols based on a group (loop) algebra or on a graded algebra with multiplicative base and proposed by Rososhek; Mihalev et. al.; Mahalanobis, etc. These cryptosystems have a common feature that all of them (except the scheme of Mihalev) use automorphisms. Also, a cryptanalysis of the key exchange protocol proposed by Megreleshvili and Djindjihadze is given. An original approach is described to find a secret message or a shared key based on usual tools of linear algebra assuming that platform can be chosen as a finite dimensional algebra, e.g., a matrix algebra over a field. The approach does not suppose to find the secret automorphism used in protocol. A theoretical foundation of this approach and a series of attacks on some cryptosystems based on different generalizations of discrete logarithm and Diffie–Hellman's ideas to noncommutative groups are described by the author earlier. Here the approach is developed by presenting its new applications in cryptanalysis of different schemes and protocols.

Détail

Keywords: cryptographic scheme, group algebra, loop algebra, graded algebra, discrete logarithm, generalized discrete logarithm, Diffie–Hellman scheme
Mots-clés : matrix algebra, El Gamal protocol, automorphism.