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Journal of Applied Mathematics
Volume 2013, Article ID 872962, 8 pages
http://dx.doi.org/10.1155/2013/872962
Research Article

Sieve Method for Polynomial Linear Equivalence

Baocang Wang1,2 and Yupu Hu1,3

1State Key Laboratory of Integrated Service Networks, Xidian University, Xi'an 710071, China
2Guangxi Experiment Center of Information Science, Guilin University of Electronic Technology, Guilin, Guangxi 541004, China
3Guangxi Key Lab of Wireless Wide Band Communication and Signal Processing, Guilin University of Electronic Technology, Guilin 541004, China

Received 5 August 2013; Accepted 2 November 2013

Academic Editor: Jacek Rokicki

Copyright © 2013 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.

Abstract

We consider the polynomial linear equivalence (PLE) problem arising from the multivariate public key cryptography, which is defined as to find an invertible linear transformation satisfying for given nonlinear polynomial maps and over a finite field . Some cryptographic and algebraic properties of PLE are discussed, and from the properties we derive three sieves called multiplicative, differential, and additive sieves. By combining the three sieves, we propose a sieve method for the PLE problem. As an application of our sieve method, we show that it is infeasible to construct public key encryption schemes from the PLE problem.