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

Xiaofeng Wang; Chen Xu; Guo Li; Hanling Lin

Paper 2014/528

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.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint. MINOR revision.
Keywords: word problem subgroup membership problem unsolvability Mihailova subgroup
Contact author(s): wangxf @ szu edu cn
History: 2014-07-08: received
Short URL: https://ia.cr/2014/528
License: 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},
      url = {https://eprint.iacr.org/2014/528}
}