ZHFE, a New Multivariate Public Key Encryption Scheme View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2014

AUTHORS

Jaiberth Porras , John Baena , Jintai Ding

ABSTRACT

In this paper we propose a new multivariate public key encryption scheme named ZHFE. The public key is constructed using as core map two high rank HFE polynomials. The inversion of the public key is performed using a low degree polynomial of Hamming weight three. This low degree polynomial is obtained from the two high rank HFE polynomials, by means of a special reduction method that uses Hamming weight three polynomials produced from the two high rank HFE polynomials. We show that ZHFE is relatively efficient and that it is secure against the main attacks that have threatened the security of HFE. We also propose parameters for a practical implementation of ZHFE. More... »

PAGES

229-245

References to SciGraph publications

  • 2003. Algebraic Cryptanalysis of Hidden Field Equation (HFE) Cryptosystems Using Gröbner Bases in ADVANCES IN CRYPTOLOGY - CRYPTO 2003
  • 2001. The Security of Hidden Field Equations (HFE) in TOPICS IN CRYPTOLOGY — CT-RSA 2001
  • 2001-07-13. Hidden Fields Equations (HFE) and Isomorphisms of Polynomials (IP): Two New Families of Asymmetric Algorithms in ADVANCES IN CRYPTOLOGY — EUROCRYPT ’96
  • 2013-10. Cryptanalysis of HFE, multi-HFE and variants for odd and even characteristic in DESIGNS, CODES AND CRYPTOGRAPHY
  • 2009. Square, a New Multivariate Encryption Scheme in TOPICS IN CRYPTOLOGY – CT-RSA 2009
  • 2008. Algebraic Attack on HFE Revisited in INFORMATION SECURITY
  • 2004. Comparison Between XL and Gröbner Basis Algorithms in ADVANCES IN CRYPTOLOGY - ASIACRYPT 2004
  • 2008. Kipnis-Shamir Attack on HFE Revisited in INFORMATION SECURITY AND CRYPTOLOGY
  • 1999. Cryptanalysis of the HFE Public Key Cryptosystem by Relinearization in ADVANCES IN CRYPTOLOGY — CRYPTO’ 99
  • 2005-06-10. The computational complexity of some problems of linear algebra in STACS 97
  • 2000. Efficient Algorithms for Solving Overdefined Systems of Multivariate Polynomial Equations in ADVANCES IN CRYPTOLOGY — EUROCRYPT 2000
  • Book

    TITLE

    Post-Quantum Cryptography

    ISBN

    978-3-319-11658-7
    978-3-319-11659-4

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-319-11659-4_14

    DOI

    http://dx.doi.org/10.1007/978-3-319-11659-4_14

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1050834526


    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/2008/0804", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Data Format", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/08", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Information and Computing Sciences", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "National University of Colombia", 
              "id": "https://www.grid.ac/institutes/grid.10689.36", 
              "name": [
                "Universidad Nacional de Colombia, Calle 59A No 63-20, Medellin, Colombia"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Porras", 
            "givenName": "Jaiberth", 
            "id": "sg:person.011352466565.34", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011352466565.34"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "National University of Colombia", 
              "id": "https://www.grid.ac/institutes/grid.10689.36", 
              "name": [
                "Universidad Nacional de Colombia, Calle 59A No 63-20, Medellin, Colombia"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Baena", 
            "givenName": "John", 
            "id": "sg:person.015267600475.09", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015267600475.09"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "University of Cincinnati", 
              "id": "https://www.grid.ac/institutes/grid.24827.3b", 
              "name": [
                "University of Cincinnati, 4199 French Hall West, Cincinnati, OH\u00a045221-0025, USA"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Ding", 
            "givenName": "Jintai", 
            "id": "sg:person.010723403013.04", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010723403013.04"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/3-540-45539-6_27", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1000285811", 
              "https://doi.org/10.1007/3-540-45539-6_27"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/3-540-45353-9_20", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1003163768", 
              "https://doi.org/10.1007/3-540-45353-9_20"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-540-30539-2_24", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1006829906", 
              "https://doi.org/10.1007/978-3-540-30539-2_24"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-540-30539-2_24", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1006829906", 
              "https://doi.org/10.1007/978-3-540-30539-2_24"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-642-00862-7_17", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1009928393", 
              "https://doi.org/10.1007/978-3-642-00862-7_17"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10623-012-9617-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1023616380", 
              "https://doi.org/10.1007/s10623-012-9617-2"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bfb0023480", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1028584092", 
              "https://doi.org/10.1007/bfb0023480"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bfb0023480", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1028584092", 
              "https://doi.org/10.1007/bfb0023480"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1006/jsco.1996.0125", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1036727338"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-540-85886-7_15", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1040695999", 
              "https://doi.org/10.1007/978-3-540-85886-7_15"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-540-85886-7_15", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1040695999", 
              "https://doi.org/10.1007/978-3-540-85886-7_15"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-540-79499-8_31", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1041791996", 
              "https://doi.org/10.1007/978-3-540-79499-8_31"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/3-540-48405-1_2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1045972569", 
              "https://doi.org/10.1007/3-540-48405-1_2"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-540-45146-4_3", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1049476263", 
              "https://doi.org/10.1007/978-3-540-45146-4_3"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-540-45146-4_3", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1049476263", 
              "https://doi.org/10.1007/978-3-540-45146-4_3"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/3-540-68339-9_4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1051894160", 
              "https://doi.org/10.1007/3-540-68339-9_4"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/3-540-68339-9_4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1051894160", 
              "https://doi.org/10.1007/3-540-68339-9_4"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.15446/recolma.v49n1.54163", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1067842919"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2014", 
        "datePublishedReg": "2014-01-01", 
        "description": "In this paper we propose a new multivariate public key encryption scheme named ZHFE. The public key is constructed using as core map two high rank HFE polynomials. The inversion of the public key is performed using a low degree polynomial of Hamming weight three. This low degree polynomial is obtained from the two high rank HFE polynomials, by means of a special reduction method that uses Hamming weight three polynomials produced from the two high rank HFE polynomials. We show that ZHFE is relatively efficient and that it is secure against the main attacks that have threatened the security of HFE. We also propose parameters for a practical implementation of ZHFE.", 
        "editor": [
          {
            "familyName": "Mosca", 
            "givenName": "Michele", 
            "type": "Person"
          }
        ], 
        "genre": "chapter", 
        "id": "sg:pub.10.1007/978-3-319-11659-4_14", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isPartOf": {
          "isbn": [
            "978-3-319-11658-7", 
            "978-3-319-11659-4"
          ], 
          "name": "Post-Quantum Cryptography", 
          "type": "Book"
        }, 
        "name": "ZHFE, a New Multivariate Public Key Encryption Scheme", 
        "pagination": "229-245", 
        "productId": [
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/978-3-319-11659-4_14"
            ]
          }, 
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "f227c78eb8f5a50c2ebace8d01a58b4112f966d326cd0514a002e80a2e417a6b"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1050834526"
            ]
          }
        ], 
        "publisher": {
          "location": "Cham", 
          "name": "Springer International Publishing", 
          "type": "Organisation"
        }, 
        "sameAs": [
          "https://doi.org/10.1007/978-3-319-11659-4_14", 
          "https://app.dimensions.ai/details/publication/pub.1050834526"
        ], 
        "sdDataset": "chapters", 
        "sdDatePublished": "2019-04-15T12:35", 
        "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_8663_00000274.jsonl", 
        "type": "Chapter", 
        "url": "http://link.springer.com/10.1007/978-3-319-11659-4_14"
      }
    ]
     

    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.10.1007/978-3-319-11659-4_14'

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

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-11659-4_14'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-11659-4_14'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-11659-4_14'


     

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

    132 TRIPLES      23 PREDICATES      40 URIs      20 LITERALS      8 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/978-3-319-11659-4_14 schema:about anzsrc-for:08
    2 anzsrc-for:0804
    3 schema:author N7843484daf1448f684098f9988d36568
    4 schema:citation sg:pub.10.1007/3-540-45353-9_20
    5 sg:pub.10.1007/3-540-45539-6_27
    6 sg:pub.10.1007/3-540-48405-1_2
    7 sg:pub.10.1007/3-540-68339-9_4
    8 sg:pub.10.1007/978-3-540-30539-2_24
    9 sg:pub.10.1007/978-3-540-45146-4_3
    10 sg:pub.10.1007/978-3-540-79499-8_31
    11 sg:pub.10.1007/978-3-540-85886-7_15
    12 sg:pub.10.1007/978-3-642-00862-7_17
    13 sg:pub.10.1007/bfb0023480
    14 sg:pub.10.1007/s10623-012-9617-2
    15 https://doi.org/10.1006/jsco.1996.0125
    16 https://doi.org/10.15446/recolma.v49n1.54163
    17 schema:datePublished 2014
    18 schema:datePublishedReg 2014-01-01
    19 schema:description In this paper we propose a new multivariate public key encryption scheme named ZHFE. The public key is constructed using as core map two high rank HFE polynomials. The inversion of the public key is performed using a low degree polynomial of Hamming weight three. This low degree polynomial is obtained from the two high rank HFE polynomials, by means of a special reduction method that uses Hamming weight three polynomials produced from the two high rank HFE polynomials. We show that ZHFE is relatively efficient and that it is secure against the main attacks that have threatened the security of HFE. We also propose parameters for a practical implementation of ZHFE.
    20 schema:editor Ncd22ae2e8ca54185b216a26f62d131f1
    21 schema:genre chapter
    22 schema:inLanguage en
    23 schema:isAccessibleForFree false
    24 schema:isPartOf N9c0a8c1a4f754c4e900d26274ecf2e10
    25 schema:name ZHFE, a New Multivariate Public Key Encryption Scheme
    26 schema:pagination 229-245
    27 schema:productId N82d34b38109e4a7287bb787f66ad3ccc
    28 Nb4eebbfdb99f436299d727b30698aca4
    29 Nf1fd70d39d0349e7a83cc7cc12c4db89
    30 schema:publisher N1e375a16db114f7ba7d1df1917e8748e
    31 schema:sameAs https://app.dimensions.ai/details/publication/pub.1050834526
    32 https://doi.org/10.1007/978-3-319-11659-4_14
    33 schema:sdDatePublished 2019-04-15T12:35
    34 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    35 schema:sdPublisher N6dbe27a25cbb48c495d2f7b148506252
    36 schema:url http://link.springer.com/10.1007/978-3-319-11659-4_14
    37 sgo:license sg:explorer/license/
    38 sgo:sdDataset chapters
    39 rdf:type schema:Chapter
    40 N1e375a16db114f7ba7d1df1917e8748e schema:location Cham
    41 schema:name Springer International Publishing
    42 rdf:type schema:Organisation
    43 N51ae418fd5ef49d3978c623199a6533a rdf:first sg:person.010723403013.04
    44 rdf:rest rdf:nil
    45 N6dbe27a25cbb48c495d2f7b148506252 schema:name Springer Nature - SN SciGraph project
    46 rdf:type schema:Organization
    47 N7843484daf1448f684098f9988d36568 rdf:first sg:person.011352466565.34
    48 rdf:rest Nae3c05d758284e74b0b1b019da58fa6b
    49 N82d34b38109e4a7287bb787f66ad3ccc schema:name readcube_id
    50 schema:value f227c78eb8f5a50c2ebace8d01a58b4112f966d326cd0514a002e80a2e417a6b
    51 rdf:type schema:PropertyValue
    52 N9c0a8c1a4f754c4e900d26274ecf2e10 schema:isbn 978-3-319-11658-7
    53 978-3-319-11659-4
    54 schema:name Post-Quantum Cryptography
    55 rdf:type schema:Book
    56 Nae3c05d758284e74b0b1b019da58fa6b rdf:first sg:person.015267600475.09
    57 rdf:rest N51ae418fd5ef49d3978c623199a6533a
    58 Nb4eebbfdb99f436299d727b30698aca4 schema:name dimensions_id
    59 schema:value pub.1050834526
    60 rdf:type schema:PropertyValue
    61 Ncd22ae2e8ca54185b216a26f62d131f1 rdf:first Ne164946fe0c84a2ebbbcbf1c74aa587b
    62 rdf:rest rdf:nil
    63 Ne164946fe0c84a2ebbbcbf1c74aa587b schema:familyName Mosca
    64 schema:givenName Michele
    65 rdf:type schema:Person
    66 Nf1fd70d39d0349e7a83cc7cc12c4db89 schema:name doi
    67 schema:value 10.1007/978-3-319-11659-4_14
    68 rdf:type schema:PropertyValue
    69 anzsrc-for:08 schema:inDefinedTermSet anzsrc-for:
    70 schema:name Information and Computing Sciences
    71 rdf:type schema:DefinedTerm
    72 anzsrc-for:0804 schema:inDefinedTermSet anzsrc-for:
    73 schema:name Data Format
    74 rdf:type schema:DefinedTerm
    75 sg:person.010723403013.04 schema:affiliation https://www.grid.ac/institutes/grid.24827.3b
    76 schema:familyName Ding
    77 schema:givenName Jintai
    78 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010723403013.04
    79 rdf:type schema:Person
    80 sg:person.011352466565.34 schema:affiliation https://www.grid.ac/institutes/grid.10689.36
    81 schema:familyName Porras
    82 schema:givenName Jaiberth
    83 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011352466565.34
    84 rdf:type schema:Person
    85 sg:person.015267600475.09 schema:affiliation https://www.grid.ac/institutes/grid.10689.36
    86 schema:familyName Baena
    87 schema:givenName John
    88 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015267600475.09
    89 rdf:type schema:Person
    90 sg:pub.10.1007/3-540-45353-9_20 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003163768
    91 https://doi.org/10.1007/3-540-45353-9_20
    92 rdf:type schema:CreativeWork
    93 sg:pub.10.1007/3-540-45539-6_27 schema:sameAs https://app.dimensions.ai/details/publication/pub.1000285811
    94 https://doi.org/10.1007/3-540-45539-6_27
    95 rdf:type schema:CreativeWork
    96 sg:pub.10.1007/3-540-48405-1_2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1045972569
    97 https://doi.org/10.1007/3-540-48405-1_2
    98 rdf:type schema:CreativeWork
    99 sg:pub.10.1007/3-540-68339-9_4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1051894160
    100 https://doi.org/10.1007/3-540-68339-9_4
    101 rdf:type schema:CreativeWork
    102 sg:pub.10.1007/978-3-540-30539-2_24 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006829906
    103 https://doi.org/10.1007/978-3-540-30539-2_24
    104 rdf:type schema:CreativeWork
    105 sg:pub.10.1007/978-3-540-45146-4_3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1049476263
    106 https://doi.org/10.1007/978-3-540-45146-4_3
    107 rdf:type schema:CreativeWork
    108 sg:pub.10.1007/978-3-540-79499-8_31 schema:sameAs https://app.dimensions.ai/details/publication/pub.1041791996
    109 https://doi.org/10.1007/978-3-540-79499-8_31
    110 rdf:type schema:CreativeWork
    111 sg:pub.10.1007/978-3-540-85886-7_15 schema:sameAs https://app.dimensions.ai/details/publication/pub.1040695999
    112 https://doi.org/10.1007/978-3-540-85886-7_15
    113 rdf:type schema:CreativeWork
    114 sg:pub.10.1007/978-3-642-00862-7_17 schema:sameAs https://app.dimensions.ai/details/publication/pub.1009928393
    115 https://doi.org/10.1007/978-3-642-00862-7_17
    116 rdf:type schema:CreativeWork
    117 sg:pub.10.1007/bfb0023480 schema:sameAs https://app.dimensions.ai/details/publication/pub.1028584092
    118 https://doi.org/10.1007/bfb0023480
    119 rdf:type schema:CreativeWork
    120 sg:pub.10.1007/s10623-012-9617-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1023616380
    121 https://doi.org/10.1007/s10623-012-9617-2
    122 rdf:type schema:CreativeWork
    123 https://doi.org/10.1006/jsco.1996.0125 schema:sameAs https://app.dimensions.ai/details/publication/pub.1036727338
    124 rdf:type schema:CreativeWork
    125 https://doi.org/10.15446/recolma.v49n1.54163 schema:sameAs https://app.dimensions.ai/details/publication/pub.1067842919
    126 rdf:type schema:CreativeWork
    127 https://www.grid.ac/institutes/grid.10689.36 schema:alternateName National University of Colombia
    128 schema:name Universidad Nacional de Colombia, Calle 59A No 63-20, Medellin, Colombia
    129 rdf:type schema:Organization
    130 https://www.grid.ac/institutes/grid.24827.3b schema:alternateName University of Cincinnati
    131 schema:name University of Cincinnati, 4199 French Hall West, Cincinnati, OH 45221-0025, USA
    132 rdf:type schema:Organization
     




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


    ...