SSE Implementation of Multivariate PKCs on Modern x86 CPUs View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2009

AUTHORS

Anna Inn-Tung Chen , Ming-Shing Chen , Tien-Ren Chen , Chen-Mou Cheng , Jintai Ding , Eric Li-Hsiang Kuo , Frost Yu-Shuang Lee , Bo-Yin Yang

ABSTRACT

Multivariate Public Key Cryptosystems (MPKCs) are often touted as future-proofing against Quantum Computers. It also has been known for efficiency compared to “traditional” alternatives. However, this advantage seems to erode with the increase of arithmetic resources in modern CPUs and improved algorithms, especially with respect to Elliptic Curve Cryptography (ECC). In this paper, we show that hardware advances do not just favor ECC. Modern commodity CPUs also have many small integer arithmetic/logic resources, embodied by SSE2 or other vector instruction sets, that are useful for MPKCs. In particular, Intel’s SSSE3 instructions can speed up both public and private maps over prior software implementations of Rainbow-type systems up to 4×. Furthermore, MPKCs over fields of relatively small odd prime characteristics can exploit SSE2 instructions, supported by most modern 64-bit Intel and AMD CPUs. For example, Rainbow over \({\mathbb F}_{31}\) can be up to 2× faster than prior implementations of similarly-sized systems over \({\mathbb F}_{16}\). Here a key advance is in using Wiedemann (as opposed to Gauss) solvers to invert the small linear systems in the central maps. We explain the techniques and design choices in implementing our chosen MPKC instances over fields such as \({\mathbb F}_{31}\), \({\mathbb F}_{16}\) and \({\mathbb F}_{256}\). We believe that our results can easily carry over to modern FPGAs, which often contain a large number of small multipliers, usable by odd-field MPKCs. More... »

PAGES

33-48

References to SciGraph publications

  • 2008. New Differential-Algebraic Attacks and Reparametrization of Rainbow in ROBOCUP 2001: ROBOT SOCCER WORLD CUP V
  • 1986. Algebraic methods for constructing asymmetric cryptosystems in ALGEBRAIC ALGORITHMS AND ERROR-CORRECTING CODES
  • 2000. Cryptanalysis of the TTM Cryptosystem in ADVANCES IN CRYPTOLOGY — ASIACRYPT 2000
  • 2008. Could SFLASH be Repaired? in AUTOMATA, LANGUAGES AND PROGRAMMING
  • 1988. Public Quadratic Polynomial-Tuples for Efficient Signature-Verification and Message-Encryption in ADVANCES IN CRYPTOLOGY — EUROCRYPT ’88
  • 2008. Algebraic Attack on HFE Revisited in INFORMATION SECURITY
  • 2007. Practical Cryptanalysis of SFLASH in ADVANCES IN CRYPTOLOGY - CRYPTO 2007
  • 1999-04-15. Unbalanced Oil and Vinegar Signature Schemes in ADVANCES IN CRYPTOLOGY — EUROCRYPT ’99
  • 2006. Inoculating Multivariate Schemes Against Differential Attacks in PUBLIC KEY CRYPTOGRAPHY - PKC 2006
  • 2008. Ultra High Performance ECC over NIST Primes on Commercial FPGAs in CRYPTOGRAPHIC HARDWARE AND EMBEDDED SYSTEMS – CHES 2008
  • 2006. Inverting HFE Is Quasipolynomial in ADVANCES IN CRYPTOLOGY - CRYPTO 2006
  • 2007. Efficient Implementations of Multivariate Quadratic Systems in SELECTED AREAS IN CRYPTOGRAPHY
  • 2005. Rainbow, a New Multivariable Polynomial Signature Scheme in ROBOCUP 2005: ROBOT SOCCER WORLD CUP IX
  • 2005. Finding Collisions in the Full SHA-1 in ADVANCES IN CRYPTOLOGY – CRYPTO 2005
  • Book

    TITLE

    Cryptographic Hardware and Embedded Systems - CHES 2009

    ISBN

    978-3-642-04137-2
    978-3-642-04138-9

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-642-04138-9_3

    DOI

    http://dx.doi.org/10.1007/978-3-642-04138-9_3

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1016599588


    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/2008/0802", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Computation Theory and Mathematics", 
            "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 Taiwan University", 
              "id": "https://www.grid.ac/institutes/grid.19188.39", 
              "name": [
                "National Taiwan University, Taipei, Taiwan"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Chen", 
            "givenName": "Anna Inn-Tung", 
            "id": "sg:person.011042211073.83", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011042211073.83"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Academia Sinica", 
              "id": "https://www.grid.ac/institutes/grid.28665.3f", 
              "name": [
                "Academia Sinica, Taipei, Taiwan"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Chen", 
            "givenName": "Ming-Shing", 
            "id": "sg:person.015621036433.28", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015621036433.28"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Academia Sinica", 
              "id": "https://www.grid.ac/institutes/grid.28665.3f", 
              "name": [
                "Academia Sinica, Taipei, Taiwan"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Chen", 
            "givenName": "Tien-Ren", 
            "id": "sg:person.010700761157.16", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010700761157.16"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "National Taiwan University", 
              "id": "https://www.grid.ac/institutes/grid.19188.39", 
              "name": [
                "National Taiwan University, Taipei, Taiwan"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Cheng", 
            "givenName": "Chen-Mou", 
            "id": "sg:person.014013613551.99", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014013613551.99"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "University of Cincinnati", 
              "id": "https://www.grid.ac/institutes/grid.24827.3b", 
              "name": [
                "University of Cincinnati, Cincinnati, Ohio, 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"
          }, 
          {
            "affiliation": {
              "alternateName": "Academia Sinica", 
              "id": "https://www.grid.ac/institutes/grid.28665.3f", 
              "name": [
                "Academia Sinica, Taipei, Taiwan"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Kuo", 
            "givenName": "Eric Li-Hsiang", 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "National Taiwan University", 
              "id": "https://www.grid.ac/institutes/grid.19188.39", 
              "name": [
                "National Taiwan University, Taipei, Taiwan"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Lee", 
            "givenName": "Frost Yu-Shuang", 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Academia Sinica", 
              "id": "https://www.grid.ac/institutes/grid.28665.3f", 
              "name": [
                "Academia Sinica, Taipei, Taiwan"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Yang", 
            "givenName": "Bo-Yin", 
            "id": "sg:person.010017213117.39", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010017213117.39"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/11535218_2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1002819603", 
              "https://doi.org/10.1007/11535218_2"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/11535218_2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1002819603", 
              "https://doi.org/10.1007/11535218_2"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/3-540-16776-5_713", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1003206244", 
              "https://doi.org/10.1007/3-540-16776-5_713"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-540-74462-7_13", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1003248823", 
              "https://doi.org/10.1007/978-3-540-74462-7_13"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-540-74462-7_13", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1003248823", 
              "https://doi.org/10.1007/978-3-540-74462-7_13"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1080/00927879908826559", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1008867318"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/11745853_19", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1020186349", 
              "https://doi.org/10.1007/11745853_19"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/11745853_19", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1020186349", 
              "https://doi.org/10.1007/11745853_19"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/3-540-48910-x_15", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1020614953", 
              "https://doi.org/10.1007/3-540-48910-x_15"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/3-540-48910-x_15", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1020614953", 
              "https://doi.org/10.1007/3-540-48910-x_15"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-540-74143-5_1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1029272780", 
              "https://doi.org/10.1007/978-3-540-74143-5_1"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-540-74143-5_1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1029272780", 
              "https://doi.org/10.1007/978-3-540-74143-5_1"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-540-70583-3_56", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1030446339", 
              "https://doi.org/10.1007/978-3-540-70583-3_56"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/11496137_12", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1033985068", 
              "https://doi.org/10.1007/11496137_12"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/11496137_12", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1033985068", 
              "https://doi.org/10.1007/11496137_12"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/11496137_12", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1033985068", 
              "https://doi.org/10.1007/11496137_12"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-540-68914-0_15", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1034340313", 
              "https://doi.org/10.1007/978-3-540-68914-0_15"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-540-68914-0_15", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1034340313", 
              "https://doi.org/10.1007/978-3-540-68914-0_15"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1145/178243.178249", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1035011364"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/3-540-45961-8_39", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1035601256", 
              "https://doi.org/10.1007/3-540-45961-8_39"
            ], 
            "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": "https://doi.org/10.1145/232973.232983", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1041464587"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/11818175_20", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1048753453", 
              "https://doi.org/10.1007/11818175_20"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/11818175_20", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1048753453", 
              "https://doi.org/10.1007/11818175_20"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-540-85053-3_5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1051927548", 
              "https://doi.org/10.1007/978-3-540-85053-3_5"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/3-540-44448-3_4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1052740197", 
              "https://doi.org/10.1007/3-540-44448-3_4"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1109/mm.2009.9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1061408686"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2009", 
        "datePublishedReg": "2009-01-01", 
        "description": "Multivariate Public Key Cryptosystems (MPKCs) are often touted as future-proofing against Quantum Computers. It also has been known for efficiency compared to \u201ctraditional\u201d alternatives. However, this advantage seems to erode with the increase of arithmetic resources in modern CPUs and improved algorithms, especially with respect to Elliptic Curve Cryptography (ECC). In this paper, we show that hardware advances do not just favor ECC. Modern commodity CPUs also have many small integer arithmetic/logic resources, embodied by SSE2 or other vector instruction sets, that are useful for MPKCs. In particular, Intel\u2019s SSSE3 instructions can speed up both public and private maps over prior software implementations of Rainbow-type systems up to 4\u00d7. Furthermore, MPKCs over fields of relatively small odd prime characteristics can exploit SSE2 instructions, supported by most modern 64-bit Intel and AMD CPUs. For example, Rainbow over \\({\\mathbb F}_{31}\\) can be up to 2\u00d7 faster than prior implementations of similarly-sized systems over \\({\\mathbb F}_{16}\\). Here a key advance is in using Wiedemann (as opposed to Gauss) solvers to invert the small linear systems in the central maps. We explain the techniques and design choices in implementing our chosen MPKC instances over fields such as \\({\\mathbb F}_{31}\\), \\({\\mathbb F}_{16}\\) and \\({\\mathbb F}_{256}\\). We believe that our results can easily carry over to modern FPGAs, which often contain a large number of small multipliers, usable by odd-field MPKCs.", 
        "editor": [
          {
            "familyName": "Clavier", 
            "givenName": "Christophe", 
            "type": "Person"
          }, 
          {
            "familyName": "Gaj", 
            "givenName": "Kris", 
            "type": "Person"
          }
        ], 
        "genre": "chapter", 
        "id": "sg:pub.10.1007/978-3-642-04138-9_3", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": true, 
        "isPartOf": {
          "isbn": [
            "978-3-642-04137-2", 
            "978-3-642-04138-9"
          ], 
          "name": "Cryptographic Hardware and Embedded Systems - CHES 2009", 
          "type": "Book"
        }, 
        "name": "SSE Implementation of Multivariate PKCs on Modern x86 CPUs", 
        "pagination": "33-48", 
        "productId": [
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/978-3-642-04138-9_3"
            ]
          }, 
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "4f1791ae8b74c84c02e22270049fcb8fa10468d9f39b398b5a6499ccc17c167a"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1016599588"
            ]
          }
        ], 
        "publisher": {
          "location": "Berlin, Heidelberg", 
          "name": "Springer Berlin Heidelberg", 
          "type": "Organisation"
        }, 
        "sameAs": [
          "https://doi.org/10.1007/978-3-642-04138-9_3", 
          "https://app.dimensions.ai/details/publication/pub.1016599588"
        ], 
        "sdDataset": "chapters", 
        "sdDatePublished": "2019-04-15T16:59", 
        "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_8678_00000028.jsonl", 
        "type": "Chapter", 
        "url": "http://link.springer.com/10.1007/978-3-642-04138-9_3"
      }
    ]
     

    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.10.1007/978-3-642-04138-9_3'

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

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-3-642-04138-9_3'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-3-642-04138-9_3'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-3-642-04138-9_3'


     

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

    191 TRIPLES      23 PREDICATES      45 URIs      20 LITERALS      8 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/978-3-642-04138-9_3 schema:about anzsrc-for:08
    2 anzsrc-for:0802
    3 schema:author N531a8d93f5354796bad2a18f70abda8d
    4 schema:citation sg:pub.10.1007/11496137_12
    5 sg:pub.10.1007/11535218_2
    6 sg:pub.10.1007/11745853_19
    7 sg:pub.10.1007/11818175_20
    8 sg:pub.10.1007/3-540-16776-5_713
    9 sg:pub.10.1007/3-540-44448-3_4
    10 sg:pub.10.1007/3-540-45961-8_39
    11 sg:pub.10.1007/3-540-48910-x_15
    12 sg:pub.10.1007/978-3-540-68914-0_15
    13 sg:pub.10.1007/978-3-540-70583-3_56
    14 sg:pub.10.1007/978-3-540-74143-5_1
    15 sg:pub.10.1007/978-3-540-74462-7_13
    16 sg:pub.10.1007/978-3-540-85053-3_5
    17 sg:pub.10.1007/978-3-540-85886-7_15
    18 https://doi.org/10.1080/00927879908826559
    19 https://doi.org/10.1109/mm.2009.9
    20 https://doi.org/10.1145/178243.178249
    21 https://doi.org/10.1145/232973.232983
    22 schema:datePublished 2009
    23 schema:datePublishedReg 2009-01-01
    24 schema:description Multivariate Public Key Cryptosystems (MPKCs) are often touted as future-proofing against Quantum Computers. It also has been known for efficiency compared to “traditional” alternatives. However, this advantage seems to erode with the increase of arithmetic resources in modern CPUs and improved algorithms, especially with respect to Elliptic Curve Cryptography (ECC). In this paper, we show that hardware advances do not just favor ECC. Modern commodity CPUs also have many small integer arithmetic/logic resources, embodied by SSE2 or other vector instruction sets, that are useful for MPKCs. In particular, Intel’s SSSE3 instructions can speed up both public and private maps over prior software implementations of Rainbow-type systems up to 4×. Furthermore, MPKCs over fields of relatively small odd prime characteristics can exploit SSE2 instructions, supported by most modern 64-bit Intel and AMD CPUs. For example, Rainbow over \({\mathbb F}_{31}\) can be up to 2× faster than prior implementations of similarly-sized systems over \({\mathbb F}_{16}\). Here a key advance is in using Wiedemann (as opposed to Gauss) solvers to invert the small linear systems in the central maps. We explain the techniques and design choices in implementing our chosen MPKC instances over fields such as \({\mathbb F}_{31}\), \({\mathbb F}_{16}\) and \({\mathbb F}_{256}\). We believe that our results can easily carry over to modern FPGAs, which often contain a large number of small multipliers, usable by odd-field MPKCs.
    25 schema:editor N20ec713af0fc4172953ecf195b76c4ed
    26 schema:genre chapter
    27 schema:inLanguage en
    28 schema:isAccessibleForFree true
    29 schema:isPartOf N7b0185b898ac4508a5138a3f98fd7ba1
    30 schema:name SSE Implementation of Multivariate PKCs on Modern x86 CPUs
    31 schema:pagination 33-48
    32 schema:productId N54a2fe0e1c1945b1b9a9645b84d656a3
    33 N76fb9685e7394fba8ee9b0605024a753
    34 Nc511ef88db6c41e49ef68204a7c58756
    35 schema:publisher N687c85f88f2a41deaa611b37b972a857
    36 schema:sameAs https://app.dimensions.ai/details/publication/pub.1016599588
    37 https://doi.org/10.1007/978-3-642-04138-9_3
    38 schema:sdDatePublished 2019-04-15T16:59
    39 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    40 schema:sdPublisher N777800fdbbf64c37b42911f720c9190e
    41 schema:url http://link.springer.com/10.1007/978-3-642-04138-9_3
    42 sgo:license sg:explorer/license/
    43 sgo:sdDataset chapters
    44 rdf:type schema:Chapter
    45 N0a09d7eae3ab4813bb3dfbe58ab9d5c2 rdf:first sg:person.010723403013.04
    46 rdf:rest N2371931a69ef4ae4933d0e70cd502010
    47 N1286cb4707754cada95f1703fe5ab682 schema:familyName Gaj
    48 schema:givenName Kris
    49 rdf:type schema:Person
    50 N20ec713af0fc4172953ecf195b76c4ed rdf:first Ne851a2c21e4b413892755fd4a3ba1534
    51 rdf:rest N2fa368dcb7e541d3b210149569e7106d
    52 N2371931a69ef4ae4933d0e70cd502010 rdf:first Na64973f9af0f4b45b2f6f04301e63468
    53 rdf:rest Nabbcecd5c1124087b766ecc2bed7376d
    54 N2fa368dcb7e541d3b210149569e7106d rdf:first N1286cb4707754cada95f1703fe5ab682
    55 rdf:rest rdf:nil
    56 N41b33a0876ad4d3187a29b0796b528bf schema:affiliation https://www.grid.ac/institutes/grid.19188.39
    57 schema:familyName Lee
    58 schema:givenName Frost Yu-Shuang
    59 rdf:type schema:Person
    60 N43939daf0a154faeb19a24301909c88d rdf:first sg:person.010017213117.39
    61 rdf:rest rdf:nil
    62 N531a8d93f5354796bad2a18f70abda8d rdf:first sg:person.011042211073.83
    63 rdf:rest Nf3ac0fde5fb6436993368059fad8d3bd
    64 N54a2fe0e1c1945b1b9a9645b84d656a3 schema:name dimensions_id
    65 schema:value pub.1016599588
    66 rdf:type schema:PropertyValue
    67 N687c85f88f2a41deaa611b37b972a857 schema:location Berlin, Heidelberg
    68 schema:name Springer Berlin Heidelberg
    69 rdf:type schema:Organisation
    70 N76fb9685e7394fba8ee9b0605024a753 schema:name doi
    71 schema:value 10.1007/978-3-642-04138-9_3
    72 rdf:type schema:PropertyValue
    73 N777800fdbbf64c37b42911f720c9190e schema:name Springer Nature - SN SciGraph project
    74 rdf:type schema:Organization
    75 N7b0185b898ac4508a5138a3f98fd7ba1 schema:isbn 978-3-642-04137-2
    76 978-3-642-04138-9
    77 schema:name Cryptographic Hardware and Embedded Systems - CHES 2009
    78 rdf:type schema:Book
    79 N973cd9efe18248f293c6a694d15fffab rdf:first sg:person.010700761157.16
    80 rdf:rest Nd052db25bd194c3b94f3e7e78bcf75fd
    81 Na64973f9af0f4b45b2f6f04301e63468 schema:affiliation https://www.grid.ac/institutes/grid.28665.3f
    82 schema:familyName Kuo
    83 schema:givenName Eric Li-Hsiang
    84 rdf:type schema:Person
    85 Nabbcecd5c1124087b766ecc2bed7376d rdf:first N41b33a0876ad4d3187a29b0796b528bf
    86 rdf:rest N43939daf0a154faeb19a24301909c88d
    87 Nc511ef88db6c41e49ef68204a7c58756 schema:name readcube_id
    88 schema:value 4f1791ae8b74c84c02e22270049fcb8fa10468d9f39b398b5a6499ccc17c167a
    89 rdf:type schema:PropertyValue
    90 Nd052db25bd194c3b94f3e7e78bcf75fd rdf:first sg:person.014013613551.99
    91 rdf:rest N0a09d7eae3ab4813bb3dfbe58ab9d5c2
    92 Ne851a2c21e4b413892755fd4a3ba1534 schema:familyName Clavier
    93 schema:givenName Christophe
    94 rdf:type schema:Person
    95 Nf3ac0fde5fb6436993368059fad8d3bd rdf:first sg:person.015621036433.28
    96 rdf:rest N973cd9efe18248f293c6a694d15fffab
    97 anzsrc-for:08 schema:inDefinedTermSet anzsrc-for:
    98 schema:name Information and Computing Sciences
    99 rdf:type schema:DefinedTerm
    100 anzsrc-for:0802 schema:inDefinedTermSet anzsrc-for:
    101 schema:name Computation Theory and Mathematics
    102 rdf:type schema:DefinedTerm
    103 sg:person.010017213117.39 schema:affiliation https://www.grid.ac/institutes/grid.28665.3f
    104 schema:familyName Yang
    105 schema:givenName Bo-Yin
    106 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010017213117.39
    107 rdf:type schema:Person
    108 sg:person.010700761157.16 schema:affiliation https://www.grid.ac/institutes/grid.28665.3f
    109 schema:familyName Chen
    110 schema:givenName Tien-Ren
    111 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010700761157.16
    112 rdf:type schema:Person
    113 sg:person.010723403013.04 schema:affiliation https://www.grid.ac/institutes/grid.24827.3b
    114 schema:familyName Ding
    115 schema:givenName Jintai
    116 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010723403013.04
    117 rdf:type schema:Person
    118 sg:person.011042211073.83 schema:affiliation https://www.grid.ac/institutes/grid.19188.39
    119 schema:familyName Chen
    120 schema:givenName Anna Inn-Tung
    121 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011042211073.83
    122 rdf:type schema:Person
    123 sg:person.014013613551.99 schema:affiliation https://www.grid.ac/institutes/grid.19188.39
    124 schema:familyName Cheng
    125 schema:givenName Chen-Mou
    126 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014013613551.99
    127 rdf:type schema:Person
    128 sg:person.015621036433.28 schema:affiliation https://www.grid.ac/institutes/grid.28665.3f
    129 schema:familyName Chen
    130 schema:givenName Ming-Shing
    131 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015621036433.28
    132 rdf:type schema:Person
    133 sg:pub.10.1007/11496137_12 schema:sameAs https://app.dimensions.ai/details/publication/pub.1033985068
    134 https://doi.org/10.1007/11496137_12
    135 rdf:type schema:CreativeWork
    136 sg:pub.10.1007/11535218_2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002819603
    137 https://doi.org/10.1007/11535218_2
    138 rdf:type schema:CreativeWork
    139 sg:pub.10.1007/11745853_19 schema:sameAs https://app.dimensions.ai/details/publication/pub.1020186349
    140 https://doi.org/10.1007/11745853_19
    141 rdf:type schema:CreativeWork
    142 sg:pub.10.1007/11818175_20 schema:sameAs https://app.dimensions.ai/details/publication/pub.1048753453
    143 https://doi.org/10.1007/11818175_20
    144 rdf:type schema:CreativeWork
    145 sg:pub.10.1007/3-540-16776-5_713 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003206244
    146 https://doi.org/10.1007/3-540-16776-5_713
    147 rdf:type schema:CreativeWork
    148 sg:pub.10.1007/3-540-44448-3_4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052740197
    149 https://doi.org/10.1007/3-540-44448-3_4
    150 rdf:type schema:CreativeWork
    151 sg:pub.10.1007/3-540-45961-8_39 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035601256
    152 https://doi.org/10.1007/3-540-45961-8_39
    153 rdf:type schema:CreativeWork
    154 sg:pub.10.1007/3-540-48910-x_15 schema:sameAs https://app.dimensions.ai/details/publication/pub.1020614953
    155 https://doi.org/10.1007/3-540-48910-x_15
    156 rdf:type schema:CreativeWork
    157 sg:pub.10.1007/978-3-540-68914-0_15 schema:sameAs https://app.dimensions.ai/details/publication/pub.1034340313
    158 https://doi.org/10.1007/978-3-540-68914-0_15
    159 rdf:type schema:CreativeWork
    160 sg:pub.10.1007/978-3-540-70583-3_56 schema:sameAs https://app.dimensions.ai/details/publication/pub.1030446339
    161 https://doi.org/10.1007/978-3-540-70583-3_56
    162 rdf:type schema:CreativeWork
    163 sg:pub.10.1007/978-3-540-74143-5_1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1029272780
    164 https://doi.org/10.1007/978-3-540-74143-5_1
    165 rdf:type schema:CreativeWork
    166 sg:pub.10.1007/978-3-540-74462-7_13 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003248823
    167 https://doi.org/10.1007/978-3-540-74462-7_13
    168 rdf:type schema:CreativeWork
    169 sg:pub.10.1007/978-3-540-85053-3_5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1051927548
    170 https://doi.org/10.1007/978-3-540-85053-3_5
    171 rdf:type schema:CreativeWork
    172 sg:pub.10.1007/978-3-540-85886-7_15 schema:sameAs https://app.dimensions.ai/details/publication/pub.1040695999
    173 https://doi.org/10.1007/978-3-540-85886-7_15
    174 rdf:type schema:CreativeWork
    175 https://doi.org/10.1080/00927879908826559 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008867318
    176 rdf:type schema:CreativeWork
    177 https://doi.org/10.1109/mm.2009.9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1061408686
    178 rdf:type schema:CreativeWork
    179 https://doi.org/10.1145/178243.178249 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035011364
    180 rdf:type schema:CreativeWork
    181 https://doi.org/10.1145/232973.232983 schema:sameAs https://app.dimensions.ai/details/publication/pub.1041464587
    182 rdf:type schema:CreativeWork
    183 https://www.grid.ac/institutes/grid.19188.39 schema:alternateName National Taiwan University
    184 schema:name National Taiwan University, Taipei, Taiwan
    185 rdf:type schema:Organization
    186 https://www.grid.ac/institutes/grid.24827.3b schema:alternateName University of Cincinnati
    187 schema:name University of Cincinnati, Cincinnati, Ohio, USA
    188 rdf:type schema:Organization
    189 https://www.grid.ac/institutes/grid.28665.3f schema:alternateName Academia Sinica
    190 schema:name Academia Sinica, Taipei, Taiwan
    191 rdf:type schema:Organization
     




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


    ...