An Efficient Algorithm for Computing Inverses in GF(2m) Using Dual Bases View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2003

AUTHORS

Hyeong Seon Yoo , Seok Ung Yoon , Eui Sun Kim

ABSTRACT

This paper propose a new multiplicative inverse algorithm for Galois field GF(2n) whose elements are represented by optimal normal bases type II. The efficiency of the arithmetic algorithms depends on the basis and many foregoing papers use either polynomial or optimal normal basis. A normal basis element is always possible to rewrite canonical basis form. The proposed algorithm combines normal basis and canonical basis. It is shown that the suggested algorithm is suitable for implementation and reduces the computation time to 5–10 % of the normal basis algorithm. More... »

PAGES

994-999

References to SciGraph publications

  • 1998-04. Montgomery Multiplication in GF(2k) in DESIGNS, CODES AND CRYPTOGRAPHY
  • 2002-02. Itoh-Tsujii Inversion in Standard Basis and Its Application in Cryptography and Codes in DESIGNS, CODES AND CRYPTOGRAPHY
  • Book

    TITLE

    Computational Science — ICCS 2003

    ISBN

    978-3-540-40197-1
    978-3-540-44864-8

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/3-540-44864-0_103

    DOI

    http://dx.doi.org/10.1007/3-540-44864-0_103

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1042374423


    Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
    Incoming Citations Browse incoming citations for this publication using opencitations.net

    JSON-LD is the canonical representation for SciGraph data.

    TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

    [
      {
        "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
        "about": [
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0103", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Numerical and Computational Mathematics", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Mathematical Sciences", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Inha University", 
              "id": "https://www.grid.ac/institutes/grid.202119.9", 
              "name": [
                "Department of Computer Science, Inha University, Incheon, 402-751, Korea"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Yoo", 
            "givenName": "Hyeong Seon", 
            "id": "sg:person.010724721532.32", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010724721532.32"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Inha University", 
              "id": "https://www.grid.ac/institutes/grid.202119.9", 
              "name": [
                "Department of Computer Science, Inha University, Incheon, 402-751, Korea"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Yoon", 
            "givenName": "Seok Ung", 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Inha University", 
              "id": "https://www.grid.ac/institutes/grid.202119.9", 
              "name": [
                "Department of Computer Science, Inha University, Incheon, 402-751, Korea"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Kim", 
            "givenName": "Eui Sun", 
            "id": "sg:person.012210665661.13", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012210665661.13"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1023/a:1008208521515", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1002824065", 
              "https://doi.org/10.1023/a:1008208521515"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1023/a:1013860532636", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1011834051", 
              "https://doi.org/10.1023/a:1013860532636"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0166-218x(88)90090-x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1025417667"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1109/12.257715", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1061087795"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2003", 
        "datePublishedReg": "2003-01-01", 
        "description": "This paper propose a new multiplicative inverse algorithm for Galois field GF(2n) whose elements are represented by optimal normal bases type II. The efficiency of the arithmetic algorithms depends on the basis and many foregoing papers use either polynomial or optimal normal basis. A normal basis element is always possible to rewrite canonical basis form. The proposed algorithm combines normal basis and canonical basis. It is shown that the suggested algorithm is suitable for implementation and reduces the computation time to 5\u201310 % of the normal basis algorithm.", 
        "editor": [
          {
            "familyName": "Sloot", 
            "givenName": "Peter M. A.", 
            "type": "Person"
          }, 
          {
            "familyName": "Abramson", 
            "givenName": "David", 
            "type": "Person"
          }, 
          {
            "familyName": "Bogdanov", 
            "givenName": "Alexander V.", 
            "type": "Person"
          }, 
          {
            "familyName": "Gorbachev", 
            "givenName": "Yuriy E.", 
            "type": "Person"
          }, 
          {
            "familyName": "Dongarra", 
            "givenName": "Jack J.", 
            "type": "Person"
          }, 
          {
            "familyName": "Zomaya", 
            "givenName": "Albert Y.", 
            "type": "Person"
          }
        ], 
        "genre": "chapter", 
        "id": "sg:pub.10.1007/3-540-44864-0_103", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": true, 
        "isPartOf": {
          "isbn": [
            "978-3-540-40197-1", 
            "978-3-540-44864-8"
          ], 
          "name": "Computational Science \u2014 ICCS 2003", 
          "type": "Book"
        }, 
        "name": "An Efficient Algorithm for Computing Inverses in GF(2m) Using Dual Bases", 
        "pagination": "994-999", 
        "productId": [
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/3-540-44864-0_103"
            ]
          }, 
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "c9d9330bf21cf5f5ff05e58a1a02ee918e1f6c62f906cd28897d94bddb5008b7"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1042374423"
            ]
          }
        ], 
        "publisher": {
          "location": "Berlin, Heidelberg", 
          "name": "Springer Berlin Heidelberg", 
          "type": "Organisation"
        }, 
        "sameAs": [
          "https://doi.org/10.1007/3-540-44864-0_103", 
          "https://app.dimensions.ai/details/publication/pub.1042374423"
        ], 
        "sdDataset": "chapters", 
        "sdDatePublished": "2019-04-15T13:30", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000001_0000000264/records_8664_00000269.jsonl", 
        "type": "Chapter", 
        "url": "http://link.springer.com/10.1007/3-540-44864-0_103"
      }
    ]
     

    Download the RDF metadata as:  json-ld nt turtle xml License info

    HOW TO GET THIS DATA PROGRAMMATICALLY:

    JSON-LD is a popular format for linked data which is fully compatible with JSON.

    curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/3-540-44864-0_103'

    N-Triples is a line-based linked data format ideal for batch operations.

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/3-540-44864-0_103'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/3-540-44864-0_103'

    RDF/XML is a standard XML format for linked data.

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/3-540-44864-0_103'


     

    This table displays all metadata directly associated to this object as RDF triples.

    117 TRIPLES      23 PREDICATES      31 URIs      20 LITERALS      8 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/3-540-44864-0_103 schema:about anzsrc-for:01
    2 anzsrc-for:0103
    3 schema:author N8d1469fec5034f5fbc1c92bb47501c58
    4 schema:citation sg:pub.10.1023/a:1008208521515
    5 sg:pub.10.1023/a:1013860532636
    6 https://doi.org/10.1016/0166-218x(88)90090-x
    7 https://doi.org/10.1109/12.257715
    8 schema:datePublished 2003
    9 schema:datePublishedReg 2003-01-01
    10 schema:description This paper propose a new multiplicative inverse algorithm for Galois field GF(2n) whose elements are represented by optimal normal bases type II. The efficiency of the arithmetic algorithms depends on the basis and many foregoing papers use either polynomial or optimal normal basis. A normal basis element is always possible to rewrite canonical basis form. The proposed algorithm combines normal basis and canonical basis. It is shown that the suggested algorithm is suitable for implementation and reduces the computation time to 5–10 % of the normal basis algorithm.
    11 schema:editor Nfc9ad1f5d19748e08729aed9c3becd61
    12 schema:genre chapter
    13 schema:inLanguage en
    14 schema:isAccessibleForFree true
    15 schema:isPartOf N07b9305b84554025bb08531509a06add
    16 schema:name An Efficient Algorithm for Computing Inverses in GF(2m) Using Dual Bases
    17 schema:pagination 994-999
    18 schema:productId N9677a2ce769642a8bab89e9df68feb97
    19 Naca79052aaa240588fb44c05b09e81b1
    20 Nb2da4b1d330840a8b818d227bda71d46
    21 schema:publisher N0ad46d71e0f24e1798af9b6c3170e2ad
    22 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042374423
    23 https://doi.org/10.1007/3-540-44864-0_103
    24 schema:sdDatePublished 2019-04-15T13:30
    25 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    26 schema:sdPublisher N460e756f2ec948079cbddf4624fcc94a
    27 schema:url http://link.springer.com/10.1007/3-540-44864-0_103
    28 sgo:license sg:explorer/license/
    29 sgo:sdDataset chapters
    30 rdf:type schema:Chapter
    31 N07b9305b84554025bb08531509a06add schema:isbn 978-3-540-40197-1
    32 978-3-540-44864-8
    33 schema:name Computational Science — ICCS 2003
    34 rdf:type schema:Book
    35 N0ad46d71e0f24e1798af9b6c3170e2ad schema:location Berlin, Heidelberg
    36 schema:name Springer Berlin Heidelberg
    37 rdf:type schema:Organisation
    38 N0ce60eca50e247aa9f3776452aa37b50 schema:familyName Sloot
    39 schema:givenName Peter M. A.
    40 rdf:type schema:Person
    41 N151d9914e6ee4c75b0da6d12d66daeda rdf:first sg:person.012210665661.13
    42 rdf:rest rdf:nil
    43 N2262300742e14161b18d23c3e8080d40 schema:affiliation https://www.grid.ac/institutes/grid.202119.9
    44 schema:familyName Yoon
    45 schema:givenName Seok Ung
    46 rdf:type schema:Person
    47 N38f2787e9dec4dc0875c3a9e89dcaa2b rdf:first Ncc8b3252e93a4edfb225ff8c9889c43a
    48 rdf:rest rdf:nil
    49 N430b408c4b374f2590661d1eff6233ac schema:familyName Bogdanov
    50 schema:givenName Alexander V.
    51 rdf:type schema:Person
    52 N460e756f2ec948079cbddf4624fcc94a schema:name Springer Nature - SN SciGraph project
    53 rdf:type schema:Organization
    54 N489cdef8e4d34fa394a5160237e2c659 rdf:first Na986591dd7f04b2da6a8eddcb9236d68
    55 rdf:rest Nc20d323127a848f3bd857a0ba6aadc03
    56 N4dab9f37d9a84d3f902a3381c95f6776 rdf:first N2262300742e14161b18d23c3e8080d40
    57 rdf:rest N151d9914e6ee4c75b0da6d12d66daeda
    58 N7cedb44b8f6d47e18ba0f287af67e737 rdf:first Nac3b8212168e4188b73775e6181ef96d
    59 rdf:rest N9ae79a5cdd3e437381feefb000892c9b
    60 N8d1469fec5034f5fbc1c92bb47501c58 rdf:first sg:person.010724721532.32
    61 rdf:rest N4dab9f37d9a84d3f902a3381c95f6776
    62 N9677a2ce769642a8bab89e9df68feb97 schema:name readcube_id
    63 schema:value c9d9330bf21cf5f5ff05e58a1a02ee918e1f6c62f906cd28897d94bddb5008b7
    64 rdf:type schema:PropertyValue
    65 N9ae79a5cdd3e437381feefb000892c9b rdf:first Nbb2757420768453d9e24d8521e8858e3
    66 rdf:rest N38f2787e9dec4dc0875c3a9e89dcaa2b
    67 Na986591dd7f04b2da6a8eddcb9236d68 schema:familyName Abramson
    68 schema:givenName David
    69 rdf:type schema:Person
    70 Nac3b8212168e4188b73775e6181ef96d schema:familyName Gorbachev
    71 schema:givenName Yuriy E.
    72 rdf:type schema:Person
    73 Naca79052aaa240588fb44c05b09e81b1 schema:name doi
    74 schema:value 10.1007/3-540-44864-0_103
    75 rdf:type schema:PropertyValue
    76 Nb2da4b1d330840a8b818d227bda71d46 schema:name dimensions_id
    77 schema:value pub.1042374423
    78 rdf:type schema:PropertyValue
    79 Nbb2757420768453d9e24d8521e8858e3 schema:familyName Dongarra
    80 schema:givenName Jack J.
    81 rdf:type schema:Person
    82 Nc20d323127a848f3bd857a0ba6aadc03 rdf:first N430b408c4b374f2590661d1eff6233ac
    83 rdf:rest N7cedb44b8f6d47e18ba0f287af67e737
    84 Ncc8b3252e93a4edfb225ff8c9889c43a schema:familyName Zomaya
    85 schema:givenName Albert Y.
    86 rdf:type schema:Person
    87 Nfc9ad1f5d19748e08729aed9c3becd61 rdf:first N0ce60eca50e247aa9f3776452aa37b50
    88 rdf:rest N489cdef8e4d34fa394a5160237e2c659
    89 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    90 schema:name Mathematical Sciences
    91 rdf:type schema:DefinedTerm
    92 anzsrc-for:0103 schema:inDefinedTermSet anzsrc-for:
    93 schema:name Numerical and Computational Mathematics
    94 rdf:type schema:DefinedTerm
    95 sg:person.010724721532.32 schema:affiliation https://www.grid.ac/institutes/grid.202119.9
    96 schema:familyName Yoo
    97 schema:givenName Hyeong Seon
    98 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010724721532.32
    99 rdf:type schema:Person
    100 sg:person.012210665661.13 schema:affiliation https://www.grid.ac/institutes/grid.202119.9
    101 schema:familyName Kim
    102 schema:givenName Eui Sun
    103 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012210665661.13
    104 rdf:type schema:Person
    105 sg:pub.10.1023/a:1008208521515 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002824065
    106 https://doi.org/10.1023/a:1008208521515
    107 rdf:type schema:CreativeWork
    108 sg:pub.10.1023/a:1013860532636 schema:sameAs https://app.dimensions.ai/details/publication/pub.1011834051
    109 https://doi.org/10.1023/a:1013860532636
    110 rdf:type schema:CreativeWork
    111 https://doi.org/10.1016/0166-218x(88)90090-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1025417667
    112 rdf:type schema:CreativeWork
    113 https://doi.org/10.1109/12.257715 schema:sameAs https://app.dimensions.ai/details/publication/pub.1061087795
    114 rdf:type schema:CreativeWork
    115 https://www.grid.ac/institutes/grid.202119.9 schema:alternateName Inha University
    116 schema:name Department of Computer Science, Inha University, Incheon, 402-751, Korea
    117 rdf:type schema:Organization
     




    Preview window. Press ESC to close (or click here)


    ...