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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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/872962 |
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| author | Baocang Wang Yupu Hu |
| author_facet | Baocang Wang Yupu Hu |
| author_sort | Baocang Wang |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-5b8b5d493a4d4ba4bd3ef3703cd09997 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-5b8b5d493a4d4ba4bd3ef3703cd099972025-02-03T01:23:12ZengWileyJournal 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 |
| spellingShingle | Baocang Wang Yupu Hu Sieve Method for Polynomial Linear Equivalence Journal of Applied Mathematics |
| title | 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_short | Sieve Method for Polynomial Linear Equivalence |
| title_sort | sieve method for polynomial linear equivalence |
| url | http://dx.doi.org/10.1155/2013/872962 |
| work_keys_str_mv | AT baocangwang sievemethodforpolynomiallinearequivalence AT yupuhu sievemethodforpolynomiallinearequivalence |