Cryptology ePrint Archive: Report 2014/528

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

Xiaofeng Wang and Chen Xu and 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_2F_2 with finite number of generators are given. Where Mihailova subgroup of F_2F_2 enjoys the unsolvable subgroup membership problem.One then can use the presentation to create entities' private key in a public key cryptsystem.

Category / Keywords: foundations / word problem, subgroup membership problem, unsolvability, Mihailova subgroup

Date: received 7 Jul 2014, last revised 7 Jul 2014

Contact author: wangxf at szu edu cn

Available format(s): PDF | BibTeX Citation

Note: In this paper, we give an explicit countable presentation of Mihailova subgroup of F_2F_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.

Version: 20140708:063620 (All versions of this report)

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