Elliptic curve cryptosystems and their implementation View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

1993-09

AUTHORS

Alfred J. Menezes, Scott A. Vanstone

ABSTRACT

Elliptic curves have been extensively studied for many years. Recent interest has revolved around their applicability to factoring integers, primality testing, and to cryptography. In this paper we explore the feasibility of implementing in hardware an arithmetic processor for doing elliptic curve computations over finite fields. Of special interest, for practical reasons, are the curves over fields of characteristic 2. The elliptic curve analogue of the ElGamal cryptosystem is also analyzed. More... »

PAGES

209-224

References to SciGraph publications

  • 1986-11. Discrete logarithms inGF(p) in ALGORITHMICA
  • 1991-01. An implementation for a fast public-key cryptosystem in JOURNAL OF CRYPTOLOGY
  • 1992. CM-Curves with Good Cryptographic Properties in ADVANCES IN CRYPTOLOGY — CRYPTO ’91
  • 1985. Discrete logarithms in finite fields and their cryptographic significance in ADVANCES IN CRYPTOLOGY
  • 1987. A Course in Number Theory and Cryptography in NONE
  • 1986. Use of Elliptic Curves in Cryptography in ADVANCES IN CRYPTOLOGY — CRYPTO ’85 PROCEEDINGS
  • 1991-01. Elliptic curve implementation of zero-knowledge blobs in JOURNAL OF CRYPTOLOGY
  • 1991. Constructing Elliptic Curve Cryptosystems in Characteristic 2 in ADVANCES IN CRYPTOLOGY-CRYPT0’ 90
  • 1990. Efficient Identification and Signatures for Smart Cards in ADVANCES IN CRYPTOLOGY — CRYPTO’ 89 PROCEEDINGS
  • 1986. N Using RSA with Low Exponent in a Public Key Network in ADVANCES IN CRYPTOLOGY — CRYPTO ’85 PROCEEDINGS
  • 1993-03. Arithmetic operations inGF(2m) in JOURNAL OF CRYPTOLOGY
  • 1986. The Arithmetic of Elliptic Curves in NONE
  • Journal

    TITLE

    Journal of Cryptology

    ISSUE

    4

    VOLUME

    6

    Related Patents

  • Cryptosystems With Elliptic Curves Chosen By Users
  • Method And Apparatus For Minimizing Differential Power Attacks On Processors
  • Method And System For Generating Implicit Certificates And Applications To Identity-Based Encryption (Ibe)
  • Accelerated Finite Field Operations On An Elliptic Curve
  • Apparatus For Calculating A Result Of A Scalar Multiplication
  • Method And Apparatus For Minimizing Differential Power Attacks On Processors
  • Scheme For Arithmetic Operations In Finite Field And Group Operations Over Elliptic Curves Realizing Improved Computational Speed
  • Method And Apparatus For Minimizing Differential Power Attacks On Processors
  • Elliptic Curve Transformation Device, Utilization Device And Utilization System
  • Method And System For Generating Implicit Certificates And Applications To Identity-Based Encryption (Ibe)
  • Apparatus For Calculating A Result Of A Scalar Multiplication
  • Elliptic Curve Encryption Method And System
  • Countermeasure Procedures In An Electronic Component Implementing An Elliptical Curve Type Public Key Encryption Algorithm
  • Implicit Certificate Scheme
  • Accelerated Finite Field Operations On An Elliptic Curve
  • Signature Verification For Elgamal Schemes
  • Efficient Finite Field Multiplication In Normal Basis
  • Elliptic Curve Encryption Method And System
  • Implicit Certificate Scheme
  • Base Converter Using Ellipse Curvilinear Encryption System, Has Base Converting Unit Which Transforms Calculated Objective Data Into Data Expressed By Second Base Data
  • Strengthened Public Key Protocol
  • Strengthened Public Key Protocol
  • Elliptic Curve Transformation Device, Utilization Device And Utilization System
  • Apparatus For Calculating A Result Of A Scalar Multiplication
  • Key Validation Scheme
  • Cryptosystems With Elliptic Curves Chosen By Users
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf00203817

    DOI

    http://dx.doi.org/10.1007/bf00203817

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1046570674


    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/2008/01", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Mathematical Sciences", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Pure Mathematics", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Department of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada", 
              "id": "http://www.grid.ac/institutes/grid.46078.3d", 
              "name": [
                "Department of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Menezes", 
            "givenName": "Alfred J.", 
            "id": "sg:person.012711653371.43", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012711653371.43"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Department of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada", 
              "id": "http://www.grid.ac/institutes/grid.46078.3d", 
              "name": [
                "Department of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Vanstone", 
            "givenName": "Scott A.", 
            "id": "sg:person.010344544767.07", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010344544767.07"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/bf00196789", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1020123700", 
              "https://doi.org/10.1007/bf00196789"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf00196728", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1023535353", 
              "https://doi.org/10.1007/bf00196728"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/3-540-39757-4_20", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1050029692", 
              "https://doi.org/10.1007/3-540-39757-4_20"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/3-540-39799-x_29", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1047819383", 
              "https://doi.org/10.1007/3-540-39799-x_29"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01840433", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1024039582", 
              "https://doi.org/10.1007/bf01840433"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/3-540-38424-3_11", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1013402407", 
              "https://doi.org/10.1007/3-540-38424-3_11"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-1-4684-0310-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1012143136", 
              "https://doi.org/10.1007/978-1-4684-0310-7"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/3-540-46766-1_22", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1042501449", 
              "https://doi.org/10.1007/3-540-46766-1_22"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/0-387-34805-0_22", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1007631834", 
              "https://doi.org/10.1007/0-387-34805-0_22"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/3-540-39799-x_31", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1022380878", 
              "https://doi.org/10.1007/3-540-39799-x_31"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02620228", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1035105071", 
              "https://doi.org/10.1007/bf02620228"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-1-4757-1920-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1017153141", 
              "https://doi.org/10.1007/978-1-4757-1920-8"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "1993-09", 
        "datePublishedReg": "1993-09-01", 
        "description": "Elliptic curves have been extensively studied for many years. Recent interest has revolved around their applicability to factoring integers, primality testing, and to cryptography. In this paper we explore the feasibility of implementing in hardware an arithmetic processor for doing elliptic curve computations over finite fields. Of special interest, for practical reasons, are the curves over fields of characteristic 2. The elliptic curve analogue of the ElGamal cryptosystem is also analyzed.", 
        "genre": "article", 
        "id": "sg:pub.10.1007/bf00203817", 
        "isAccessibleForFree": true, 
        "isPartOf": [
          {
            "id": "sg:journal.1136278", 
            "issn": [
              "0933-2790", 
              "1432-1378"
            ], 
            "name": "Journal of Cryptology", 
            "publisher": "Springer Nature", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "4", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "6"
          }
        ], 
        "keywords": [
          "elliptic curve computations", 
          "elliptic curve cryptosystem", 
          "elliptic curve analogue", 
          "ElGamal cryptosystem", 
          "primality testing", 
          "arithmetic processor", 
          "elliptic curves", 
          "curve computation", 
          "cryptosystem", 
          "finite field", 
          "cryptography", 
          "hardware", 
          "processors", 
          "computation", 
          "implementation", 
          "recent interest", 
          "interest", 
          "applicability", 
          "feasibility", 
          "field", 
          "integers", 
          "practical reasons", 
          "testing", 
          "special interest", 
          "reasons", 
          "curves", 
          "years", 
          "analogues", 
          "paper"
        ], 
        "name": "Elliptic curve cryptosystems and their implementation", 
        "pagination": "209-224", 
        "productId": [
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1046570674"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/bf00203817"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/bf00203817", 
          "https://app.dimensions.ai/details/publication/pub.1046570674"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2022-09-02T15:48", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-springernature-scigraph/baseset/20220902/entities/gbq_results/article/article_242.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://doi.org/10.1007/bf00203817"
      }
    ]
     

    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/bf00203817'

    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/bf00203817'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/bf00203817'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/bf00203817'


     

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

    141 TRIPLES      21 PREDICATES      66 URIs      46 LITERALS      6 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/bf00203817 schema:about anzsrc-for:01
    2 anzsrc-for:0101
    3 schema:author Nf6b55d0efa3a41619ede5f642ffac8c7
    4 schema:citation sg:pub.10.1007/0-387-34805-0_22
    5 sg:pub.10.1007/3-540-38424-3_11
    6 sg:pub.10.1007/3-540-39757-4_20
    7 sg:pub.10.1007/3-540-39799-x_29
    8 sg:pub.10.1007/3-540-39799-x_31
    9 sg:pub.10.1007/3-540-46766-1_22
    10 sg:pub.10.1007/978-1-4684-0310-7
    11 sg:pub.10.1007/978-1-4757-1920-8
    12 sg:pub.10.1007/bf00196728
    13 sg:pub.10.1007/bf00196789
    14 sg:pub.10.1007/bf01840433
    15 sg:pub.10.1007/bf02620228
    16 schema:datePublished 1993-09
    17 schema:datePublishedReg 1993-09-01
    18 schema:description Elliptic curves have been extensively studied for many years. Recent interest has revolved around their applicability to factoring integers, primality testing, and to cryptography. In this paper we explore the feasibility of implementing in hardware an arithmetic processor for doing elliptic curve computations over finite fields. Of special interest, for practical reasons, are the curves over fields of characteristic 2. The elliptic curve analogue of the ElGamal cryptosystem is also analyzed.
    19 schema:genre article
    20 schema:isAccessibleForFree true
    21 schema:isPartOf N31cfc5baf66b425990e4c37bf45c515b
    22 Nd62393e10dde48fea60b134835a4b15c
    23 sg:journal.1136278
    24 schema:keywords ElGamal cryptosystem
    25 analogues
    26 applicability
    27 arithmetic processor
    28 computation
    29 cryptography
    30 cryptosystem
    31 curve computation
    32 curves
    33 elliptic curve analogue
    34 elliptic curve computations
    35 elliptic curve cryptosystem
    36 elliptic curves
    37 feasibility
    38 field
    39 finite field
    40 hardware
    41 implementation
    42 integers
    43 interest
    44 paper
    45 practical reasons
    46 primality testing
    47 processors
    48 reasons
    49 recent interest
    50 special interest
    51 testing
    52 years
    53 schema:name Elliptic curve cryptosystems and their implementation
    54 schema:pagination 209-224
    55 schema:productId Nd11786a96e5a4e639916ba4876103212
    56 Nead1aa2f080e4c59a3b12dcaeea6c7b9
    57 schema:sameAs https://app.dimensions.ai/details/publication/pub.1046570674
    58 https://doi.org/10.1007/bf00203817
    59 schema:sdDatePublished 2022-09-02T15:48
    60 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    61 schema:sdPublisher N0b98ec99454c49e18bd3cedbe09696de
    62 schema:url https://doi.org/10.1007/bf00203817
    63 sgo:license sg:explorer/license/
    64 sgo:sdDataset articles
    65 rdf:type schema:ScholarlyArticle
    66 N0b98ec99454c49e18bd3cedbe09696de schema:name Springer Nature - SN SciGraph project
    67 rdf:type schema:Organization
    68 N31cfc5baf66b425990e4c37bf45c515b schema:issueNumber 4
    69 rdf:type schema:PublicationIssue
    70 N90a84d823e2949ee93de0062f1530135 rdf:first sg:person.010344544767.07
    71 rdf:rest rdf:nil
    72 Nd11786a96e5a4e639916ba4876103212 schema:name doi
    73 schema:value 10.1007/bf00203817
    74 rdf:type schema:PropertyValue
    75 Nd62393e10dde48fea60b134835a4b15c schema:volumeNumber 6
    76 rdf:type schema:PublicationVolume
    77 Nead1aa2f080e4c59a3b12dcaeea6c7b9 schema:name dimensions_id
    78 schema:value pub.1046570674
    79 rdf:type schema:PropertyValue
    80 Nf6b55d0efa3a41619ede5f642ffac8c7 rdf:first sg:person.012711653371.43
    81 rdf:rest N90a84d823e2949ee93de0062f1530135
    82 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    83 schema:name Mathematical Sciences
    84 rdf:type schema:DefinedTerm
    85 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
    86 schema:name Pure Mathematics
    87 rdf:type schema:DefinedTerm
    88 sg:journal.1136278 schema:issn 0933-2790
    89 1432-1378
    90 schema:name Journal of Cryptology
    91 schema:publisher Springer Nature
    92 rdf:type schema:Periodical
    93 sg:person.010344544767.07 schema:affiliation grid-institutes:grid.46078.3d
    94 schema:familyName Vanstone
    95 schema:givenName Scott A.
    96 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010344544767.07
    97 rdf:type schema:Person
    98 sg:person.012711653371.43 schema:affiliation grid-institutes:grid.46078.3d
    99 schema:familyName Menezes
    100 schema:givenName Alfred J.
    101 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012711653371.43
    102 rdf:type schema:Person
    103 sg:pub.10.1007/0-387-34805-0_22 schema:sameAs https://app.dimensions.ai/details/publication/pub.1007631834
    104 https://doi.org/10.1007/0-387-34805-0_22
    105 rdf:type schema:CreativeWork
    106 sg:pub.10.1007/3-540-38424-3_11 schema:sameAs https://app.dimensions.ai/details/publication/pub.1013402407
    107 https://doi.org/10.1007/3-540-38424-3_11
    108 rdf:type schema:CreativeWork
    109 sg:pub.10.1007/3-540-39757-4_20 schema:sameAs https://app.dimensions.ai/details/publication/pub.1050029692
    110 https://doi.org/10.1007/3-540-39757-4_20
    111 rdf:type schema:CreativeWork
    112 sg:pub.10.1007/3-540-39799-x_29 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047819383
    113 https://doi.org/10.1007/3-540-39799-x_29
    114 rdf:type schema:CreativeWork
    115 sg:pub.10.1007/3-540-39799-x_31 schema:sameAs https://app.dimensions.ai/details/publication/pub.1022380878
    116 https://doi.org/10.1007/3-540-39799-x_31
    117 rdf:type schema:CreativeWork
    118 sg:pub.10.1007/3-540-46766-1_22 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042501449
    119 https://doi.org/10.1007/3-540-46766-1_22
    120 rdf:type schema:CreativeWork
    121 sg:pub.10.1007/978-1-4684-0310-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1012143136
    122 https://doi.org/10.1007/978-1-4684-0310-7
    123 rdf:type schema:CreativeWork
    124 sg:pub.10.1007/978-1-4757-1920-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1017153141
    125 https://doi.org/10.1007/978-1-4757-1920-8
    126 rdf:type schema:CreativeWork
    127 sg:pub.10.1007/bf00196728 schema:sameAs https://app.dimensions.ai/details/publication/pub.1023535353
    128 https://doi.org/10.1007/bf00196728
    129 rdf:type schema:CreativeWork
    130 sg:pub.10.1007/bf00196789 schema:sameAs https://app.dimensions.ai/details/publication/pub.1020123700
    131 https://doi.org/10.1007/bf00196789
    132 rdf:type schema:CreativeWork
    133 sg:pub.10.1007/bf01840433 schema:sameAs https://app.dimensions.ai/details/publication/pub.1024039582
    134 https://doi.org/10.1007/bf01840433
    135 rdf:type schema:CreativeWork
    136 sg:pub.10.1007/bf02620228 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035105071
    137 https://doi.org/10.1007/bf02620228
    138 rdf:type schema:CreativeWork
    139 grid-institutes:grid.46078.3d schema:alternateName Department of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada
    140 schema:name Department of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada
    141 rdf:type schema:Organization
     




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


    ...