Analysis of Rabin's irreducibility test for polynomials over finite fields
Resumen:
We give a precise average-case analysis of Rabin's algorithm for testing the irreducibility of polynomials over finite fields. The main technical contribution of the paper is the study of the probability that a random polynomial of degree n contains an irreducible factor of degree dividing several maximal divisors of the degree n. We study the expected value and the variance of the number of operations performed by the algorithm. We present a exact analysis when n=p1 and n=p1p2 for p1,p2 prime numbers, and as asymptotic analysis for the general case. Our method generalizes to other algorithms that deal with similar divisor conditions. In particular, we analyze the average-case number of operations for two variants of Rabin's algorithm, and determine the ordering of prime divisors of n that minimizes the leading factor.
| 2001 | |
|
RANDOM POLYNOMIALS FINITE FIELDS ALGORITHMS |
|
| Universidad de la República | |
| COLIBRI | |
| http://hdl.handle.net/20.500.12008/3455 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución – No Comercial – Sin Derivadas (CC BY-NC-ND 4.0) |
| _version_ | 1807522943373148160 |
|---|---|
| author | Panario, Daniel |
| author2 | Pittel, Boris Richmond, Bruce Viola, Alfredo |
| author2_role | author author author |
| author_facet | Panario, Daniel Pittel, Boris Richmond, Bruce Viola, Alfredo |
| author_role | author |
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| collection | COLIBRI |
| dc.creator.none.fl_str_mv | Panario, Daniel Pittel, Boris Richmond, Bruce Viola, Alfredo |
| dc.date.accessioned.none.fl_str_mv | 2014-12-02T16:06:17Z |
| dc.date.available.none.fl_str_mv | 2014-12-02T16:06:17Z |
| dc.date.issued.es.fl_str_mv | 2001 |
| dc.date.submitted.es.fl_str_mv | 20141202 |
| dc.description.abstract.none.fl_txt_mv | We give a precise average-case analysis of Rabin's algorithm for testing the irreducibility of polynomials over finite fields. The main technical contribution of the paper is the study of the probability that a random polynomial of degree n contains an irreducible factor of degree dividing several maximal divisors of the degree n. We study the expected value and the variance of the number of operations performed by the algorithm. We present a exact analysis when n=p1 and n=p1p2 for p1,p2 prime numbers, and as asymptotic analysis for the general case. Our method generalizes to other algorithms that deal with similar divisor conditions. In particular, we analyze the average-case number of operations for two variants of Rabin's algorithm, and determine the ordering of prime divisors of n that minimizes the leading factor. |
| dc.format.extent.es.fl_str_mv | 30 p. |
| dc.format.mimetype.es.fl_str_mv | application/pdf |
| dc.identifier.citation.es.fl_str_mv | PANARIO, D., PITTEL, B., RICHMOND, B., y otros. "Analysis of Rabin's irreducibility test for polynomials over finite fields". Reportes Técnicos 01-16. UR. FI – INCO, 2001. |
| dc.identifier.issn.es.fl_str_mv | 0797-6410 |
| dc.identifier.uri.none.fl_str_mv | http://hdl.handle.net/20.500.12008/3455 |
| dc.language.iso.none.fl_str_mv | in |
| dc.publisher.es.fl_str_mv | UR. FI – INCO. |
| dc.relation.ispartof.es.fl_str_mv | Reportes Técnicos 01-16 |
| dc.rights.license.none.fl_str_mv | Licencia Creative Commons Atribución – No Comercial – Sin Derivadas (CC BY-NC-ND 4.0) |
| dc.rights.none.fl_str_mv | info:eu-repo/semantics/openAccess |
| dc.source.none.fl_str_mv | reponame:COLIBRI instname:Universidad de la República instacron:Universidad de la República |
| dc.subject.es.fl_str_mv | RANDOM POLYNOMIALS FINITE FIELDS ALGORITHMS |
| dc.title.none.fl_str_mv | Analysis of Rabin's irreducibility test for polynomials over finite fields |
| dc.type.es.fl_str_mv | Reporte técnico |
| dc.type.none.fl_str_mv | info:eu-repo/semantics/report |
| dc.type.version.none.fl_str_mv | info:eu-repo/semantics/publishedVersion |
| description | We give a precise average-case analysis of Rabin's algorithm for testing the irreducibility of polynomials over finite fields. The main technical contribution of the paper is the study of the probability that a random polynomial of degree n contains an irreducible factor of degree dividing several maximal divisors of the degree n. We study the expected value and the variance of the number of operations performed by the algorithm. We present a exact analysis when n=p1 and n=p1p2 for p1,p2 prime numbers, and as asymptotic analysis for the general case. Our method generalizes to other algorithms that deal with similar divisor conditions. In particular, we analyze the average-case number of operations for two variants of Rabin's algorithm, and determine the ordering of prime divisors of n that minimizes the leading factor. |
| eu_rights_str_mv | openAccess |
| format | report |
| id | COLIBRI_e3373a2dd96fc1a81478d336d15484f7 |
| identifier_str_mv | PANARIO, D., PITTEL, B., RICHMOND, B., y otros. "Analysis of Rabin's irreducibility test for polynomials over finite fields". Reportes Técnicos 01-16. UR. FI – INCO, 2001. 0797-6410 |
| instacron_str | Universidad de la República |
| institution | Universidad de la República |
| instname_str | Universidad de la República |
| language_invalid_str_mv | in |
| network_acronym_str | COLIBRI |
| network_name_str | COLIBRI |
| oai_identifier_str | oai:colibri.udelar.edu.uy:20.500.12008/3455 |
| publishDate | 2001 |
| reponame_str | COLIBRI |
| repository.mail.fl_str_mv | mabel.seroubian@seciu.edu.uy |
| repository.name.fl_str_mv | COLIBRI - Universidad de la República |
| repository_id_str | 4771 |
| rights_invalid_str_mv | Licencia Creative Commons Atribución – No Comercial – Sin Derivadas (CC BY-NC-ND 4.0) |
| spelling | 2014-12-02T16:06:17Z2014-12-02T16:06:17Z200120141202PANARIO, D., PITTEL, B., RICHMOND, B., y otros. "Analysis of Rabin's irreducibility test for polynomials over finite fields". Reportes Técnicos 01-16. UR. FI – INCO, 2001.0797-6410http://hdl.handle.net/20.500.12008/3455We give a precise average-case analysis of Rabin's algorithm for testing the irreducibility of polynomials over finite fields. The main technical contribution of the paper is the study of the probability that a random polynomial of degree n contains an irreducible factor of degree dividing several maximal divisors of the degree n. We study the expected value and the variance of the number of operations performed by the algorithm. We present a exact analysis when n=p1 and n=p1p2 for p1,p2 prime numbers, and as asymptotic analysis for the general case. Our method generalizes to other algorithms that deal with similar divisor conditions. In particular, we analyze the average-case number of operations for two variants of Rabin's algorithm, and determine the ordering of prime divisors of n that minimizes the leading factor.Made available in DSpace on 2014-12-02T16:06:17Z (GMT). No. of bitstreams: 5 TR0116.pdf: 329604 bytes, checksum: b3a9f170b891ec9efc3606e49319d7e2 (MD5) license_text: 21936 bytes, checksum: 9833653f73f7853880c94a6fead477b1 (MD5) license_url: 49 bytes, checksum: 4afdbb8c545fd630ea7db775da747b2f (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) license.txt: 4244 bytes, checksum: 528b6a3c8c7d0c6e28129d576e989607 (MD5) Previous issue date: 200130 p.application/pdfinUR. FI – INCO.Reportes Técnicos 01-16Las obras depositadas en el Repositorio se rigen por la Ordenanza de los Derechos de la Propiedad Intelectual de la Universidad De La República. (Res. Nº 91 de C.D.C. de 8/III/1994 – D.O. 7/IV/1994) y por la Ordenanza del Repositorio Abierto de la Universidad de la República (Res. Nº 16 de C.D.C. de 07/10/2014)info:eu-repo/semantics/openAccessLicencia Creative Commons Atribución – No Comercial – Sin Derivadas (CC BY-NC-ND 4.0)RANDOM POLYNOMIALSFINITE FIELDSALGORITHMSAnalysis of Rabin's irreducibility test for polynomials over finite fieldsReporte técnicoinfo:eu-repo/semantics/reportinfo:eu-repo/semantics/publishedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaPanario, DanielPittel, BorisRichmond, BruceViola, AlfredoLICENSElicense.txttext/plain4244http://localhost:8080/xmlui/bitstream/20.500.12008/3455/5/license.txt528b6a3c8c7d0c6e28129d576e989607MD55CC-LICENSElicense_textapplication/octet-stream21936http://localhost:8080/xmlui/bitstream/20.500.12008/3455/2/license_text9833653f73f7853880c94a6fead477b1MD52license_urlapplication/octet-stream49http://localhost:8080/xmlui/bitstream/20.500.12008/3455/3/license_url4afdbb8c545fd630ea7db775da747b2fMD53license_rdfapplication/octet-stream23148http://localhost:8080/xmlui/bitstream/20.500.12008/3455/4/license_rdf9da0b6dfac957114c6a7714714b86306MD54ORIGINALTR0116.pdfapplication/pdf329604http://localhost:8080/xmlui/bitstream/20.500.12008/3455/1/TR0116.pdfb3a9f170b891ec9efc3606e49319d7e2MD5120.500.12008/34552016-05-03 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- Universidad de la Repúblicafalse |
| spellingShingle | Analysis of Rabin's irreducibility test for polynomials over finite fields Panario, Daniel RANDOM POLYNOMIALS FINITE FIELDS ALGORITHMS |
| status_str | publishedVersion |
| title | Analysis of Rabin's irreducibility test for polynomials over finite fields |
| title_full | Analysis of Rabin's irreducibility test for polynomials over finite fields |
| title_fullStr | Analysis of Rabin's irreducibility test for polynomials over finite fields |
| title_full_unstemmed | Analysis of Rabin's irreducibility test for polynomials over finite fields |
| title_short | Analysis of Rabin's irreducibility test for polynomials over finite fields |
| title_sort | Analysis of Rabin's irreducibility test for polynomials over finite fields |
| topic | RANDOM POLYNOMIALS FINITE FIELDS ALGORITHMS |
| url | http://hdl.handle.net/20.500.12008/3455 |
