Constructions in public-key cryptography over matrix groups
<|reference_start|>Constructions in public-key cryptography over matrix groups: 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.<|reference_end|>
@article{grigoriev2005constructions,
    title={Constructions in public-key cryptography over matrix groups},
    author={Dimitri Grigoriev (IRMAR), Ilia Ponomarenko},
    journal={arXiv preprint arXiv:math/0506180},
    year={2005},
    number={2005-19},
    archivePrefix={arXiv},
    eprint={math/0506180},
    primaryClass={math.GR cs.CR math-ph math.MP}
}