Non-associative key establishment for left distributive systems

Arkadius Kalka; Mina Teicher

doi:10.1515/gcc-2013-0009

Non-associative key establishment for left distributive systems

Arkadius Kalka, Mina Teicher

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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.

Original language	English
Pages (from-to)	169-191
Number of pages	23
Journal	Groups, Complexity, Cryptology
Volume	5
Issue number	2
DOIs	https://doi.org/10.1515/gcc-2013-0009
State	Published - 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.

Keywords

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

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10.1515/gcc-2013-0009

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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.",

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author = "Arkadius Kalka and Mina Teicher",

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year = "2013",

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doi = "10.1515/gcc-2013-0009",

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AB - 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.

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KW - Conjugacy coset problem

KW - Key establishment protocol

KW - Left distributive system

KW - Magma (groupoid)

KW - Non-commutative cryptography

KW - Shifted conjugacy

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ER -

Non-associative key establishment for left distributive systems

Abstract

Bibliographical note

Keywords

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