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Journal of Applied Mathematics
Volume 2014, Article ID 819182, 7 pages
Research Article

Signature Scheme Using the Root Extraction Problem on Quaternions

1State Key Laboratory of Integrated Service Networks, Xidian University, Xi'an 710071, China
2Guangxi Key Lab of Wireless Wide Band Communication and Signal Processing, Guilin University of Electronic Technology, Guilin 541004, China

Received 6 February 2014; Accepted 19 May 2014; Published 28 May 2014

Academic Editor: Frank Werner

Copyright © 2014 Baocang Wang and Yupu Hu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The root extraction problem over quaternion rings modulo an RSA integer is defined, and the intractability of the problem is examined. A signature scheme is constructed based on the root extraction problem. It is proven that an adversary can forge a signature on a message if and only if he can extract the roots for some quaternion integers. The performance and other security related issues are also discussed.