### Groups With Two Generators Having Unsolvable Word Problem And Presentations of Mihailova Subgroups

Xiaofeng Wang, Chen Xu, Guo Li, and Hanling Lin

##### Abstract

A presentation of a group with two generators having unsolvable word problem and an explicit countable presentation of Mihailova subgroup of F_2×F_2 with finite number of generators are given. Where Mihailova subgroup of F_2×F_2 enjoys the unsolvable subgroup membership problem.One then can use the presentation to create entities' private key in a public key cryptsystem.

Note: In this paper, we give an explicit countable presentation of Mihailova subgroup of F_2×F_2 with finite number of generators which has unsolvable subgroup membership problem. Followed we know that in a braid group B_n with n \geq 6, there are some such subgroups. Thus one possibly can use this property to set up highly secured public key cryptsystems.

Available format(s)
Category
Foundations
Publication info
Preprint. Minor revision.
Keywords
word problemsubgroup membership problemunsolvabilityMihailova subgroup
Contact author(s)
wangxf @ szu edu cn
History
Short URL
https://ia.cr/2014/528

CC BY

BibTeX

@misc{cryptoeprint:2014/528,
author = {Xiaofeng Wang and Chen Xu and Guo Li and Hanling Lin},
title = {Groups With Two Generators Having Unsolvable Word Problem And Presentations of Mihailova Subgroups},
howpublished = {Cryptology ePrint Archive, Paper 2014/528},
year = {2014},
note = {\url{https://eprint.iacr.org/2014/528}},
url = {https://eprint.iacr.org/2014/528}
}

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