## Journal of Applied Mathematics

### Sieve Method for Polynomial Linear Equivalence

#### 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 $ℒ$ satisfying $\mathrm{𝒫}=\mathrm{𝒮}\circ ℒ$ for given nonlinear polynomial maps $\mathrm{𝒫}$ and $\mathrm{𝒮}$ over a finite field ${\mathrm{𝔽}}_{q}$. 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.

#### Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 872962, 8 pages.

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1394808286

Digital Object Identifier
doi:10.1155/2013/872962

Zentralblatt MATH identifier
1270.16008

#### Citation

Wang, Baocang; Hu, Yupu. Sieve Method for Polynomial Linear Equivalence. J. Appl. Math. 2013 (2013), Article ID 872962, 8 pages. doi:10.1155/2013/872962. https://projecteuclid.org/euclid.jam/1394808286

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