Non-associative key establishment for left distributive systems

Arkadius Kalka, Mina Teicher

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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.

Original languageEnglish
Pages (from-to)169-191
Number of pages23
JournalGroups, Complexity, Cryptology
Issue number2
StatePublished - Nov 2013

Bibliographical note

Funding Information:
The first author acknowledgesfinancial support by the Minerva Foundation of Germany. Parts of the paper were written up during the stay of the first author at University of Queensland, Brisbane. For this stay the first author acknowledgesfinancial support by the Australian Research Council (project DP110101104). The second author acknowledgesfinancial support by The Oswald Veblen Fund.


  • Braid group
  • Conjugacy coset problem
  • Key establishment protocol
  • Left distributive system
  • Magma (groupoid)
  • Non-commutative cryptography
  • Shifted conjugacy


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