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29 March 2024
 
  » arxiv » math.GR/0506180

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Constructions in public-key cryptography over matrix groups
Dimitri Grigoriev ; Ilia Ponomarenko ;
Date 10 Jun 2005
Subject Group Theory; Cryptography and Security | math.GR cs.CR math-ph math.MP
AffiliationIRMAR
AbstractThe 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.
Source arXiv, math.GR/0506180
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