2005/06/10 by Dimitri Grigoriev, Grigoriev, Dimitri, Ilia Ponomarenko +1
Computer Science · Mathematics · Physics and Astronomy · #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Group Theory (math.GR) #Mathematical Physics (math-ph) #cs.CR #math-ph #math.GR #math.MP
paper · pdf · doi:10.48550/arxiv.math/0506180
arxiv created 2005/06/10 · arxiv updated 2009/12/01
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.