Constructions in public-key cryptography over matrix groups

Dima Grigoriev (1) , Ilia Ponomarenko (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 Institut des Mathématiques. Saint Petersburg

The purpose of the paper is to give new key agreement protocols (a multi-party extension of the protocol due to Anshel-Anshel-Goldfeld and a generalization of the Diffie-Hellman protocol from abelian to solvable groups) and a new homomorphic public-key cryptosystem. They rely on difficulty of the conjugacy and membership problems for subgroups of a given group. To support these and other known cryptographic schemes we present a general technique to produce a family of instances being matrix groups (over finite commutative rings) which play a role for these schemes similar to the groups $Z_n^*$ in the existing cryptographic constructions like RSA or discrete logarithm.

Mots clés: public-key cryptosystems; matrix groups

Domaines: Théorie des groupes [math.GR]; Cryptographie et sécurité [cs.CR]

Dima Grigoriev, Ilia Ponomarenko. Constructions in public-key cryptography over matrix groups. International Workshop on Algebraic Methods in Cryptography, Nov 2005, Bochum, Germany. pp.103-119. ⟨hal-00005317⟩