Modular construction of low complexity parallel multipliers for a class of finite fields GF(2/sup m/)
Structures for parallel multipliers of a class of fields GF(2/sup m/) based on irreducible all one polynomials (AOP) and equally spaced polynomials (ESP) are presented. The structures are simple and modular, which is important for hardware realization. Relationships between an irreducible AOP and th...
Gespeichert in:
| Veröffentlicht in: | IEEE transactions on computers Jg. 41; H. 8; S. 962 - 971 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
IEEE
01.08.1992
|
| Schlagworte: | |
| ISSN: | 0018-9340 |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Abstract | Structures for parallel multipliers of a class of fields GF(2/sup m/) based on irreducible all one polynomials (AOP) and equally spaced polynomials (ESP) are presented. The structures are simple and modular, which is important for hardware realization. Relationships between an irreducible AOP and the corresponding irreducible ESPs have been exploited to construct ESP-based multipliers of large fields by a regular expansion of the basic modules of the AOP-based multiplier of a small field. Some features of the structures also enable a fast implementation of squaring and multiplication algorithms and therefore make fast exponentiation and inversion possible. It is shown that, if for a certain degree, an irreducible AOP as well as an irreducible ESP exist, then from the complexity point of view, it is advantageous to use the ESP-based parallel multiplier.< > |
|---|---|
| AbstractList | Structures for parallel multipliers of a class of fields GF(2/sup m/) based on irreducible all one polynomials (AOP) and equally spaced polynomials (ESP) are presented. The structures are simple and modular, which is important for hardware realization. Relationships between an irreducible AOP and the corresponding irreducible ESPs have been exploited to construct ESP-based multipliers of large fields by a regular expansion of the basic modules of the AOP-based multiplier of a small field. Some features of the structures also enable a fast implementation of squaring and multiplication algorithms and therefore make fast exponentiation and inversion possible. It is shown that, if for a certain degree, an irreducible AOP as well as an irreducible ESP exist, then from the complexity point of view, it is advantageous to use the ESP-based parallel multiplier.< > Structures for parallel multipliers of a class of fields GF(2 super(m)) based on irreducible all one polynomials (AOP) and equally spaced polynomials (ESP) are presented. The structures are simple and modular, which is important for hardware realization. Relationships between an irreducible AOP and the corresponding irreducible ESPs have been exploited to construct ESP-based multipliers of large fields by a regular expansion of the basic modules of the AOP-based multiplier of a small field. Some features of the structures also enable a fast implementation of squaring and multiplication algorithms and therefore make fast exponentiation and inversion possible. It is shown that, if for a certain degree, an irreducible AOP as well as an irreducible ESP exist, then from the complexity point of view, it is advantageous to use the ESP-based parallel multiplier. Structures for parallel multipliers of a class of fields GF(2(m)) based on irreducible all one polynomials (AOP) and equally spaced polynomials (ESP) are presented. The structures are simple and modular, which is important for hardware realization. Relationships between an irreducible AOP and the corresponding irreducible ESPs have been exploited to construct ESP-based multipliers of large fields by a regular expansion of the basic modules of the AOP-based multiplier of a small field. Some features of the structures also enable a fast implementation of squaring and multiplication algorithms and therefore make fast exponentiation and inversion possible. It is shown that, if for a certain degree, an irreducible AOP as well as an irreducible ESP exist, then from the complexity point of view, it is advantageous to use the ESP-based parallel multiplier |
| Author | Hasan, M.A. Bhargava, V.K. Wang, M. |
| Author_xml | – sequence: 1 givenname: M.A. surname: Hasan fullname: Hasan, M.A. organization: Dept. of Electr. & Comput. Eng., Victoria Univ., BC, Canada – sequence: 2 givenname: M. surname: Wang fullname: Wang, M. organization: Dept. of Electr. & Comput. Eng., Victoria Univ., BC, Canada – sequence: 3 givenname: V.K. surname: Bhargava fullname: Bhargava, V.K. organization: Dept. of Electr. & Comput. Eng., Victoria Univ., BC, Canada |
| BookMark | eNqFkD1PwzAQhj0UibYwsDJ5QnRIYztxPkZU0YJUxAJzdE3OkpETB9sR9N-TKkhICInp1d097w3Pgsw62yEhV5ytOWdlzMWay0wm5YzMGeNFVCYpOycL798YY5lg5Zzgk20GA47WtvPBDXXQtqNWUWM_xl3bG_zU4Uh7cGAMGtoOJujeaHSeKuso0NqA96eK0p0OOAaaxtPd9lbEfuhpG68uyJkC4_HyO5fkdXv_snmI9s-7x83dPqqTPA1RgxJQMXEoMM2yLGlYKQAkCiZVCizPJaYNNqqBgyohGwcpVSHTA0_LQmWQLMnN9Ld39n1AH6pW-xqNgQ7t4CtRJBkb4f9BmXM2mhvBeAJrZ713qKpaBzhJCg60qTirTq4rLqrJ9dhY_Wr0Trfgjn-y1xOrEfGHm45fq_mLjw |
| CODEN | ITCOB4 |
| CitedBy_id | crossref_primary_10_1109_TC_2004_52 crossref_primary_10_1016_j_vlsi_2004_10_001 crossref_primary_10_1631_jzus_A0820398 crossref_primary_10_1016_S0167_9260_02_00053_6 crossref_primary_10_1109_12_936239 crossref_primary_10_1109_82_938363 crossref_primary_10_1109_12_859542 crossref_primary_10_1007_s10440_006_9048_z crossref_primary_10_1109_12_926154 crossref_primary_10_1109_12_257715 crossref_primary_10_1007_s10440_006_9047_0 crossref_primary_10_1049_iet_cds_2009_0243 crossref_primary_10_1109_12_508323 crossref_primary_10_1016_S0026_2692_03_00172_1 crossref_primary_10_1109_TC_2004_47 crossref_primary_10_1109_TC_2006_69 crossref_primary_10_2316_Journal_202_2007_4_202_1934 crossref_primary_10_1049_iet_ifs_2009_0160 crossref_primary_10_1109_12_707588 crossref_primary_10_1023_A_1008333132366 crossref_primary_10_1049_ip_cdt_20030061 crossref_primary_10_1109_TC_2002_1004590 crossref_primary_10_1007_s10836_006_7446_9 crossref_primary_10_1109_TC_2002_1004591 crossref_primary_10_1109_TC_2002_1047755 crossref_primary_10_1080_0020716031000079536 crossref_primary_10_1049_ip_cdt_20050165 crossref_primary_10_1109_12_736433 crossref_primary_10_1109_12_980019 crossref_primary_10_1049_iet_ifs_2010_0139 crossref_primary_10_1007_s10440_006_9071_0 crossref_primary_10_1109_TC_2007_70741 crossref_primary_10_1049_iet_cdt_2010_0021 crossref_primary_10_1109_12_863045 crossref_primary_10_1109_12_990131 crossref_primary_10_1109_TC_2007_1076 crossref_primary_10_1023_A_1013860532636 crossref_primary_10_1109_TCSI_2002_800836 crossref_primary_10_1016_j_ffa_2014_10_008 crossref_primary_10_1016_0167_9260_95_00007_3 crossref_primary_10_1109_TCSI_2016_2614309 crossref_primary_10_1109_12_565591 crossref_primary_10_1049_el_19960416 crossref_primary_10_1109_12_888054 crossref_primary_10_1109_TC_2002_1004597 crossref_primary_10_1007_s13389_018_0197_6 crossref_primary_10_1109_TC_2016_2543228 crossref_primary_10_1016_j_compeleceng_2005_09_002 crossref_primary_10_1049_iet_cds_20080122 crossref_primary_10_1109_12_660172 crossref_primary_10_1109_12_663762 crossref_primary_10_1109_12_805153 crossref_primary_10_1016_j_ifacol_2016_12_076 crossref_primary_10_1109_82_877151 crossref_primary_10_1109_12_713313 crossref_primary_10_1109_TC_2007_19 crossref_primary_10_1080_1206212X_2007_11441864 crossref_primary_10_1016_0026_2692_95_98939_O crossref_primary_10_1016_j_ipl_2011_08_004 |
| Cites_doi | 10.1016/0890-5401(89)90045-X 10.1016/0166-218X(89)90001-2 10.1016/0020-0190(91)90219-8 10.1109/TIT.1986.1057178 10.1049/ip-e.1992.0036 10.1109/TC.1985.1676616 10.1016/0890-5401(88)90024-7 10.1109/12.30855 |
| ContentType | Journal Article |
| DBID | AAYXX CITATION 7SC 7SP 8FD JQ2 L7M L~C L~D |
| DOI | 10.1109/12.156539 |
| DatabaseName | CrossRef Computer and Information Systems Abstracts Electronics & Communications Abstracts Technology Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional |
| DatabaseTitle | CrossRef Technology Research Database Computer and Information Systems Abstracts – Academic Electronics & Communications Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional |
| DatabaseTitleList | Technology Research Database Computer and Information Systems Abstracts |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Computer Science |
| EndPage | 971 |
| ExternalDocumentID | 10_1109_12_156539 156539 |
| GroupedDBID | --Z -DZ -~X .55 .DC 0R~ 29I 3EH 3O- 4.4 5GY 5VS 6IK 85S 97E AAJGR AARMG AASAJ AAWTH ABAZT ABFSI ABQJQ ABVLG ACGFO ACIWK ACNCT AENEX AETEA AETIX AGQYO AGSQL AHBIQ AI. AIBXA AKJIK AKQYR ALLEH ALMA_UNASSIGNED_HOLDINGS ASUFR ATWAV BEFXN BFFAM BGNUA BKEBE BPEOZ CS3 DU5 E.L EBS EJD HZ~ H~9 IAAWW IBMZZ ICLAB IEDLZ IFIPE IFJZH IPLJI JAVBF LAI M43 MS~ MVM O9- OCL P2P PQQKQ RIA RIE RNI RNS RXW RZB TAE TN5 TWZ UHB UKR UPT VH1 X7M XJT XOL XZL YXB YYQ YZZ ZCG AAYXX ABUFD CITATION 7SC 7SP 8FD JQ2 L7M L~C L~D |
| ID | FETCH-LOGICAL-c374t-de5aef02b8e46663d092aa5e205f4a0775e4dedfdabf9a6e4d55f854b1498f6a3 |
| IEDL.DBID | RIE |
| ISICitedReferencesCount | 92 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=10_1109_12_156539&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0018-9340 |
| IngestDate | Sun Nov 09 13:29:39 EST 2025 Sat Sep 27 20:36:52 EDT 2025 Sat Nov 29 03:57:01 EST 2025 Tue Nov 18 22:25:52 EST 2025 Wed Aug 27 02:49:05 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 8 |
| Language | English |
| License | https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c374t-de5aef02b8e46663d092aa5e205f4a0775e4dedfdabf9a6e4d55f854b1498f6a3 |
| Notes | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
| PQID | 25710539 |
| PQPubID | 23500 |
| PageCount | 10 |
| ParticipantIDs | ieee_primary_156539 crossref_citationtrail_10_1109_12_156539 proquest_miscellaneous_28360149 proquest_miscellaneous_25710539 crossref_primary_10_1109_12_156539 |
| PublicationCentury | 1900 |
| PublicationDate | 1992-08-01 |
| PublicationDateYYYYMMDD | 1992-08-01 |
| PublicationDate_xml | – month: 08 year: 1992 text: 1992-08-01 day: 01 |
| PublicationDecade | 1990 |
| PublicationTitle | IEEE transactions on computers |
| PublicationTitleAbbrev | TC |
| PublicationYear | 1992 |
| Publisher | IEEE |
| Publisher_xml | – name: IEEE |
| References | ref8 wah (ref4) 1984 ref12 wang (ref9) 1990 hasan (ref7) 1992; 139 ref3 ref6 ref10 ref5 lidl (ref1) 1986 ref2 shanks (ref11) 1962; 1 |
| References_xml | – ident: ref3 doi: 10.1016/0890-5401(89)90045-X – year: 1984 ident: ref4 article-title: Realization and application of the Massey-Omura lock publication-title: ?roc International Zurich Seminar – ident: ref5 doi: 10.1016/0166-218X(89)90001-2 – year: 1990 ident: ref9 article-title: Normal bases and irreducible polynomials in the finite field GF(22r) publication-title: Disc Appl Math – ident: ref10 doi: 10.1016/0020-0190(91)90219-8 – ident: ref6 doi: 10.1109/TIT.1986.1057178 – volume: 139 start-page: 230 year: 1992 ident: ref7 article-title: division and bit-serial multiplication over gf(q/sup m/) publication-title: Computers and Digital Techniques IEE Proceedings- doi: 10.1049/ip-e.1992.0036 – volume: 1 year: 1962 ident: ref11 publication-title: Solved and Unsolved Problems in Number Theory – ident: ref2 doi: 10.1109/TC.1985.1676616 – ident: ref8 doi: 10.1016/0890-5401(88)90024-7 – ident: ref12 doi: 10.1109/12.30855 – year: 1986 ident: ref1 publication-title: Introduction to Finite Fields and Their Applications |
| SSID | ssj0006209 |
| Score | 1.6588197 |
| Snippet | Structures for parallel multipliers of a class of fields GF(2/sup m/) based on irreducible all one polynomials (AOP) and equally spaced polynomials (ESP) are... Structures for parallel multipliers of a class of fields GF(2 super(m)) based on irreducible all one polynomials (AOP) and equally spaced polynomials (ESP) are... Structures for parallel multipliers of a class of fields GF(2(m)) based on irreducible all one polynomials (AOP) and equally spaced polynomials (ESP) are... |
| SourceID | proquest crossref ieee |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 962 |
| SubjectTerms | Arithmetic Complexity theory Cryptography Electrostatic precipitators Error correction Galois fields Hardware Message-oriented middleware Modular construction Polynomials |
| Title | Modular construction of low complexity parallel multipliers for a class of finite fields GF(2/sup m/) |
| URI | https://ieeexplore.ieee.org/document/156539 https://www.proquest.com/docview/25710539 https://www.proquest.com/docview/28360149 |
| Volume | 41 |
| WOSCitedRecordID | wos10_1109_12_156539&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVIEE databaseName: IEEE Xplore Digital Libary (IEL) issn: 0018-9340 databaseCode: RIE dateStart: 19680101 customDbUrl: isFulltext: true dateEnd: 99991231 titleUrlDefault: https://ieeexplore.ieee.org/ omitProxy: false ssIdentifier: ssj0006209 providerName: IEEE |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV07T8MwELZoxQADhQKiPC3EUIa0aRLHyYgQhYWKAaRukR2fpUohqWgL_HzOTtKCqJDYkuich8-P7-LP3xFy5SvwtPJ9h0mGAQpOCQ6iotBJFU_NqhfnUtpkE3w0isbj-KnS2bZ7YQDAks-gZw7tWr4q0oX5VdbHWIP5cYM0OA_LrVrLQTes2Rz4sNgP3EpEaODG_YHXKwv-mHpsLpVfA7CdVYatf73PLtmpwCO9Kb29RzYgb5NWnZiBVv20Tba_qQzuE3gslCGb0rRYycXSQtOs-KCWUg6fiMWpUQHPMshoRTI0SbIpYloqaGowtimiJwajUst7m9H7YdfDpjylr_3rA_IyvHu-fXCq7ApO6vNg7ihgArTryQgCjGF85caeEAw8l-lAGGU8CBQorYTUsQjxhDEdsUBiTBXpUPiHpJkXORwR6nKc6GOhQ8Ux3FShlCLAQFEA3hcRBe-Qbl3xSVpJj5sMGFliQxA3TgZeUlZmh1wuTael3sY6o7ZxxsqgunpROzPBPmIWPkQOxWKW4LCEMPJPC7OXBT_seO2dT8hWydI1vL9T0kRXwRnZTN_nk9nbuW2IX09q3YI |
| linkProvider | IEEE |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LS8NAEB60CurBalWsry7ioR7Spslu0hxFrIpt8aDgLWyysyDERKyvn-_sJq2KInhLwmweO_v4JvvtNwBHvkJPK993RCIoQKEpwSFUFDipClOz6hWGSWKTTYTjcf_uLrqudLbtXhhEtOQz7JhDu5avivTF_CrrUqwh_GgeFgTnnltu1poNu8GUz0GPi3zuVjJCPTfq9rxOWfTb5GOzqfwYgu28Mqj_643WYLWCj-yk9Pc6zGHegPo0NQOremoDVr7oDG4Ajgpl6KYsLT4FY1mhWVa8MUsqx3dC48zogGcZZqyiGZo02YxQLZMsNSjbFNH3BqUyy3ybsPNB26PG_MgeusebcDs4uzm9cKr8Ck7qh_zZUSgkatdL-sgpivGVG3lSCvRcobk02njIFSqtZKIjGdCJELoveEJRVV8H0t-CWl7kuA3MDWmqj6QOVEgBpwqSRHIKFSXSfQlThE1oTys-TivxcZMDI4ttEOJGcc-Ly8pswuHM9LFU3PjNqGGc8WlQXW1NnRlTLzFLHzLH4mUS08BEQPJPC7ObhT5s59c7t2Dp4mY0jIeX46tdWC45u4YFuAc1chvuw2L6-nw_eTqwjfID9qbgyQ |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Modular+construction+of+low+complexity+parallel+multipliers+for+a+class+of+finite+fields+GF%282%28m%29%29&rft.jtitle=IEEE+transactions+on+computers&rft.au=Hasan%2C+M+A&rft.au=Wang%2C+M&rft.au=Bhargava%2C+V+K&rft.date=1992-08-01&rft.issn=0018-9340&rft.volume=41&rft.issue=8&rft.spage=962&rft.epage=971&rft_id=info:doi/10.1109%2F12.156539&rft.externalDBID=NO_FULL_TEXT |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0018-9340&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0018-9340&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0018-9340&client=summon |