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**2014/528**

**Title:**

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

**Authors:**
Xiaofeng Wang, Chen Xu, Guo Li, 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.

**ePrint:**
https://eprint.iacr.org/2014/528

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