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Non-associative key establishment for left distributive systems
-
Arkadius Kalka
and
Mina Teicher
Published/Copyright:
October 15, 2013
Abstract.
We construct non-associative key establishment protocols for all left self-distributive (LD), multi-LD-, and other left distributive systems. Instantiations of these protocols using generalized shifted conjugacy in braid groups lead to instances of a natural and apparently new group-theoretic problem, which we call the (subgroup) conjugacy coset problem.
Keywords: Non-commutative cryptography; key establishment protocol; magma (groupoid); left distributive system; braid group; shifted conjugacy; conjugacy coset problem
Received: 2013-05-07
Revised: 2013-09-15
Published Online: 2013-10-15
Published in Print: 2013-11-01
© 2013 by Walter de Gruyter Berlin Boston
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- Masthead
- Another look at non-uniformity
- An asymmetric generalisation of Artin monoids
- Non-associative key establishment for left distributive systems
- On the dimension of matrix representations of finitely generated torsion free nilpotent groups
- On the intersection of subgroups in free groups: Echelon subgroups are inert
- A secret sharing scheme based on the Closest Vector Theorem and a modification to a private key cryptosystem
Keywords for this article
Non-commutative cryptography;
key establishment protocol;
magma (groupoid);
left distributive system;
braid group;
shifted conjugacy;
conjugacy coset problem
Articles in the same Issue
- Masthead
- Another look at non-uniformity
- An asymmetric generalisation of Artin monoids
- Non-associative key establishment for left distributive systems
- On the dimension of matrix representations of finitely generated torsion free nilpotent groups
- On the intersection of subgroups in free groups: Echelon subgroups are inert
- A secret sharing scheme based on the Closest Vector Theorem and a modification to a private key cryptosystem
