Sieve Method for Polynomial Linear Equivalence

Sieve Method for Polynomial Linear Equivalence

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 𝒫=𝒮∘ℒ for given nonlinear polynomial maps 𝒫 and 𝒮 over a finite field 𝔽q. Some cryptographic and algebraic p...

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Main Authors: Baocang Wang, Yupu Hu
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2013/872962
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spelling doaj-5b8b5d493a4d4ba4bd3ef3703cd099972020-11-24T23:45:22ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/872962872962Sieve Method for Polynomial Linear EquivalenceBaocang Wang0Yupu Hu1State Key Laboratory of Integrated Service Networks, Xidian University, Xi'an 710071, ChinaState Key Laboratory of Integrated Service Networks, Xidian University, Xi'an 710071, ChinaWe 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 𝒫=𝒮∘ℒ for given nonlinear polynomial maps 𝒫 and 𝒮 over a finite field 𝔽q. 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.http://dx.doi.org/10.1155/2013/872962
collection DOAJ
language English
format Article
sources DOAJ
author Baocang Wang
Yupu Hu
spellingShingle Baocang Wang
Yupu Hu
Sieve Method for Polynomial Linear Equivalence
Journal of Applied Mathematics
author_facet Baocang Wang
Yupu Hu
author_sort Baocang Wang
title Sieve Method for Polynomial Linear Equivalence
title_short Sieve Method for Polynomial Linear Equivalence
title_full Sieve Method for Polynomial Linear Equivalence
title_fullStr Sieve Method for Polynomial Linear Equivalence
title_full_unstemmed Sieve Method for Polynomial Linear Equivalence
title_sort sieve method for polynomial linear equivalence
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2013-01-01
description 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 𝒫=𝒮∘ℒ for given nonlinear polynomial maps 𝒫 and 𝒮 over a finite field 𝔽q. 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.
url http://dx.doi.org/10.1155/2013/872962
work_keys_str_mv AT baocangwang sievemethodforpolynomiallinearequivalence
AT yupuhu sievemethodforpolynomiallinearequivalence
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