A PTIME solution to the restricted conjugacy problem in generalized Heisenberg groups

Kenneth R. Blaney; Andrey Nikolaev

doi:10.1515/gcc-2016-0003

A PTIME solution to the restricted conjugacy problem in generalized Heisenberg groups

Kenneth R. Blaney
, Andrey Nikolaev

Department of Mathematical Sciences

Stevens Institute of Technology

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

8 Scopus citations

Abstract

We examine the Anshel-Anshel-Goldfeld key exchange protocol with a generalized Heisenberg group, H_m, as a platform. We show that subgroup-restricted simultaneous conjugacy search problem in H_m can be solved in quasi-quintic time, which allows the computation of the private keys of the parties.

Original language	English
Pages (from-to)	69-74
Number of pages	6
Journal	Groups, Complexity, Cryptology
Volume	8
Issue number	1
DOIs	https://doi.org/10.1515/gcc-2016-0003
State	Published - 1 May 2016

Keywords

Anshel-Anshel-Goldfeld protocol
conjugacy problem
generalized Heisenberg group
key establishment

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10.1515/gcc-2016-0003

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title = "A PTIME solution to the restricted conjugacy problem in generalized Heisenberg groups",

abstract = "We examine the Anshel-Anshel-Goldfeld key exchange protocol with a generalized Heisenberg group, Hm, as a platform. We show that subgroup-restricted simultaneous conjugacy search problem in Hm can be solved in quasi-quintic time, which allows the computation of the private keys of the parties.",

keywords = "Anshel-Anshel-Goldfeld protocol, conjugacy problem, generalized Heisenberg group, key establishment",

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AU - Nikolaev, Andrey

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N2 - We examine the Anshel-Anshel-Goldfeld key exchange protocol with a generalized Heisenberg group, Hm, as a platform. We show that subgroup-restricted simultaneous conjugacy search problem in Hm can be solved in quasi-quintic time, which allows the computation of the private keys of the parties.

AB - We examine the Anshel-Anshel-Goldfeld key exchange protocol with a generalized Heisenberg group, Hm, as a platform. We show that subgroup-restricted simultaneous conjugacy search problem in Hm can be solved in quasi-quintic time, which allows the computation of the private keys of the parties.

KW - Anshel-Anshel-Goldfeld protocol

KW - conjugacy problem

KW - generalized Heisenberg group

KW - key establishment

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UR - https://www.scopus.com/pages/publications/84969581305#tab=citedBy

U2 - 10.1515/gcc-2016-0003

DO - 10.1515/gcc-2016-0003

M3 - Article

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SN - 1867-1144

VL - 8

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EP - 74

JO - Groups, Complexity, Cryptology

JF - Groups, Complexity, Cryptology

IS - 1

ER -

A PTIME solution to the restricted conjugacy problem in generalized Heisenberg groups

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Keywords

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