Simple Schnorr multi-signatures with applications to Bitcoin View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2019-02-02

AUTHORS

Gregory Maxwell, Andrew Poelstra, Yannick Seurin, Pieter Wuille

ABSTRACT

We describe a new Schnorr-based multi-signature scheme (i.e., a protocol which allows a group of signers to produce a short, joint signature on a common message) called MuSig\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {MuSig}$$\end{document}, provably secure under the Discrete Logarithm assumption and in the plain public-key model (meaning that signers are only required to have a public key, but do not have to prove knowledge of the private key corresponding to their public key to some certification authority or to other signers before engaging the protocol). MuSig\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {MuSig}$$\end{document} improves over the state-of-art scheme of Bellare and Neven (ACM Conference on Computer and Communications Security-CCS 2006) and its variants by Bagherzandi et al. (ACM Conference on Computer and Communications Security-CCS 2008) and Ma et al. (Des Codes Cryptogr 54(2):121–133, 2010) in two respects: (i) it is simple and efficient, having the same key and signature size as standard Schnorr signatures; (ii) it allows key aggregation, which informally means that the joint signature can be verified exactly as a standard Schnorr signature with respect to a single “aggregated” public key which can be computed from the individual public keys of the signers. To the best of our knowledge, this is the first multi-signature scheme provably secure under the Discrete Logarithm assumption in the plain public-key model which allows key aggregation. As an application, we explain how our new multi-signature scheme could improve both performance and user privacy in Bitcoin. More... »

PAGES

2139-2164

References to SciGraph publications

  • 1996. On the risk of disruption in several multiparty signature schemes in ADVANCES IN CRYPTOLOGY — ASIACRYPT '96
  • 2002-12-18. Threshold Signatures, Multisignatures and Blind Signatures Based on the Gap-Diffie-Hellman-Group Signature Scheme in PUBLIC KEY CRYPTOGRAPHY — PKC 2003
  • 2005. Discrete-Log-Based Signatures May Not Be Equivalent to Discrete Log in ADVANCES IN CRYPTOLOGY - ASIACRYPT 2005
  • 2007. The Power of Proofs-of-Possession: Securing Multiparty Signatures against Rogue-Key Attacks in ADVANCES IN CRYPTOLOGY - EUROCRYPT 2007
  • 2002-09-13. GQ and Schnorr Identification Schemes: Proofs of Security against Impersonation under Active and Concurrent Attacks in ADVANCES IN CRYPTOLOGY — CRYPTO 2002
  • 2018-10-27. Compact Multi-signatures for Smaller Blockchains in ADVANCES IN CRYPTOLOGY – ASIACRYPT 2018
  • 2003-05-13. Aggregate and Verifiably Encrypted Signatures from Bilinear Maps in ADVANCES IN CRYPTOLOGY — EUROCRYPT 2003
  • 2016-06-09. Threshold-Optimal DSA/ECDSA Signatures and an Application to Bitcoin Wallet Security in APPLIED CRYPTOGRAPHY AND NETWORK SECURITY
  • 2017-12-23. Escrow Protocols for Cryptocurrencies: How to Buy Physical Goods Using Bitcoin in FINANCIAL CRYPTOGRAPHY AND DATA SECURITY
  • 2012. On the Exact Security of Schnorr-Type Signatures in the Random Oracle Model in ADVANCES IN CRYPTOLOGY – EUROCRYPT 2012
  • 1993. A digital multisignature scheme based on the Fiat-Shamir scheme in ADVANCES IN CRYPTOLOGY — ASIACRYPT '91
  • 1991-01. Efficient signature generation by smart cards in JOURNAL OF CRYPTOLOGY
  • 2004. Sequential Aggregate Signatures from Trapdoor Permutations in ADVANCES IN CRYPTOLOGY - EUROCRYPT 2004
  • 1995. Meta-Multisignature schemes based on the discrete logarithm problem in INFORMATION SECURITY — THE NEXT DECADE
  • 2007-01-01. Unrestricted Aggregate Signatures in AUTOMATA, LANGUAGES AND PROGRAMMING
  • 2009-07-03. Efficient discrete logarithm based multi-signature scheme in the plain public key model in DESIGNS, CODES AND CRYPTOGRAPHY
  • 1993. Provably Secure and Practical Identification Schemes and Corresponding Signature Schemes in ADVANCES IN CRYPTOLOGY — CRYPTO’ 92
  • 2004-07-30. Short Signatures from the Weil Pairing in JOURNAL OF CRYPTOLOGY
  • 2016-07-21. Optimal Security Proofs for Signatures from Identification Schemes in ADVANCES IN CRYPTOLOGY – CRYPTO 2016
  • 2000-03-21. Security Arguments for Digital Signatures and Blind Signatures in JOURNAL OF CRYPTOLOGY
  • 2006. Sequential Aggregate Signatures and Multisignatures Without Random Oracles in ADVANCES IN CRYPTOLOGY - EUROCRYPT 2006
  • 2003-06. The One-More-RSA-Inversion Problems and the Security of Chaum's Blind Signature Scheme in JOURNAL OF CRYPTOLOGY
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s10623-019-00608-x

    DOI

    http://dx.doi.org/10.1007/s10623-019-00608-x

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1111837746


    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/2008/08", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Information and Computing Sciences", 
            "type": "DefinedTerm"
          }, 
          {
            "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"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "San Francisco, USA", 
              "id": "http://www.grid.ac/institutes/None", 
              "name": [
                "San Francisco, USA"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Maxwell", 
            "givenName": "Gregory", 
            "id": "sg:person.014233473557.78", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014233473557.78"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Blockstream, Mountain View, USA", 
              "id": "http://www.grid.ac/institutes/None", 
              "name": [
                "Blockstream, Mountain View, USA"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Poelstra", 
            "givenName": "Andrew", 
            "id": "sg:person.016241362014.54", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016241362014.54"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "ANSSI, Paris, France", 
              "id": "http://www.grid.ac/institutes/None", 
              "name": [
                "ANSSI, Paris, France"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Seurin", 
            "givenName": "Yannick", 
            "id": "sg:person.011724731171.01", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011724731171.01"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Blockstream, Mountain View, USA", 
              "id": "http://www.grid.ac/institutes/None", 
              "name": [
                "Blockstream, Mountain View, USA"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Wuille", 
            "givenName": "Pieter", 
            "id": "sg:person.010473774051.72", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010473774051.72"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/978-3-662-53008-5_2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1015793862", 
              "https://doi.org/10.1007/978-3-662-53008-5_2"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-540-72540-4_13", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1001372793", 
              "https://doi.org/10.1007/978-3-540-72540-4_13"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf00196725", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1043691009", 
              "https://doi.org/10.1007/bf00196725"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/3-540-39200-9_26", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1030846652", 
              "https://doi.org/10.1007/3-540-39200-9_26"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-540-73420-8_37", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1010224437", 
              "https://doi.org/10.1007/978-3-540-73420-8_37"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00145-002-0120-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1038875442", 
              "https://doi.org/10.1007/s00145-002-0120-1"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-540-24676-3_5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1002538471", 
              "https://doi.org/10.1007/978-3-540-24676-3_5"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-030-03329-3_15", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1107870563", 
              "https://doi.org/10.1007/978-3-030-03329-3_15"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/3-540-57332-1_11", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1052110589", 
              "https://doi.org/10.1007/3-540-57332-1_11"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/11761679_28", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1021356577", 
              "https://doi.org/10.1007/11761679_28"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bfb0034859", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1012885523", 
              "https://doi.org/10.1007/bfb0034859"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10623-009-9313-z", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1014195366", 
              "https://doi.org/10.1007/s10623-009-9313-z"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/3-540-48071-4_3", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1039918288", 
              "https://doi.org/10.1007/3-540-48071-4_3"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-0-387-34873-5_11", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1042451236", 
              "https://doi.org/10.1007/978-0-387-34873-5_11"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/11593447_1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1044035450", 
              "https://doi.org/10.1007/11593447_1"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-319-70972-7_18", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1099922858", 
              "https://doi.org/10.1007/978-3-319-70972-7_18"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00145-004-0314-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1000134872", 
              "https://doi.org/10.1007/s00145-004-0314-9"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/3-540-45708-9_11", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1029389964", 
              "https://doi.org/10.1007/3-540-45708-9_11"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-319-39555-5_9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1039225102", 
              "https://doi.org/10.1007/978-3-319-39555-5_9"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/3-540-36288-6_3", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1004411735", 
              "https://doi.org/10.1007/3-540-36288-6_3"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s001450010003", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1018357720", 
              "https://doi.org/10.1007/s001450010003"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-642-29011-4_33", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1019042387", 
              "https://doi.org/10.1007/978-3-642-29011-4_33"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2019-02-02", 
        "datePublishedReg": "2019-02-02", 
        "description": "We describe a new Schnorr-based multi-signature scheme (i.e., a protocol which allows a group of signers to produce a short, joint signature on a common message) called MuSig\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\mathsf {MuSig}$$\\end{document}, provably secure under the Discrete Logarithm assumption and in the plain public-key model (meaning that signers are only required to have a public key, but do not have to prove knowledge of the private key corresponding to their public key to some certification authority or to other signers before engaging the protocol). MuSig\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\mathsf {MuSig}$$\\end{document} improves over the state-of-art scheme of Bellare and Neven (ACM Conference on Computer and Communications Security-CCS 2006) and its variants by Bagherzandi et al. (ACM Conference on Computer and Communications Security-CCS 2008) and Ma et al. (Des Codes Cryptogr 54(2):121\u2013133, 2010) in two respects: (i) it is simple and efficient, having the same key and signature size as standard Schnorr signatures; (ii) it allows key aggregation, which informally means that the joint signature can be verified exactly as a standard Schnorr signature with respect to a single \u201caggregated\u201d public key which can be computed from the individual public keys of the signers. To the best of our knowledge, this is the first multi-signature scheme provably secure under the Discrete Logarithm assumption in the plain public-key model which allows key aggregation. As an application, we explain how our new multi-signature scheme could improve both performance and user privacy in Bitcoin.", 
        "genre": "article", 
        "id": "sg:pub.10.1007/s10623-019-00608-x", 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1136552", 
            "issn": [
              "0925-1022", 
              "1573-7586"
            ], 
            "name": "Designs, Codes and Cryptography", 
            "publisher": "Springer Nature", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "9", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "87"
          }
        ], 
        "keywords": [
          "multi-signature scheme", 
          "plain public key model", 
          "discrete logarithm assumption", 
          "public-key model", 
          "key aggregation", 
          "public key", 
          "Bagherzandi et al", 
          "Schnorr signature", 
          "new multi-signature scheme", 
          "individual public keys", 
          "art schemes", 
          "same key", 
          "signature size", 
          "user privacy", 
          "Schnorr", 
          "joint signature", 
          "Bitcoin", 
          "scheme", 
          "key", 
          "Bellare", 
          "et al", 
          "Ma et al", 
          "privacy", 
          "Neven", 
          "signers", 
          "applications", 
          "assumption", 
          "model", 
          "signatures", 
          "performance", 
          "aggregation", 
          "knowledge", 
          "al", 
          "respect", 
          "state", 
          "variants", 
          "size"
        ], 
        "name": "Simple Schnorr multi-signatures with applications to Bitcoin", 
        "pagination": "2139-2164", 
        "productId": [
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1111837746"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/s10623-019-00608-x"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/s10623-019-00608-x", 
          "https://app.dimensions.ai/details/publication/pub.1111837746"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2022-12-01T06:39", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-springernature-scigraph/baseset/20221201/entities/gbq_results/article/article_814.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://doi.org/10.1007/s10623-019-00608-x"
      }
    ]
     

    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/s10623-019-00608-x'

    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/s10623-019-00608-x'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s10623-019-00608-x'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s10623-019-00608-x'


     

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

    207 TRIPLES      21 PREDICATES      83 URIs      53 LITERALS      6 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/s10623-019-00608-x schema:about anzsrc-for:08
    2 anzsrc-for:0804
    3 schema:author N7388813703fd415e9a830cd75aa0441b
    4 schema:citation sg:pub.10.1007/11593447_1
    5 sg:pub.10.1007/11761679_28
    6 sg:pub.10.1007/3-540-36288-6_3
    7 sg:pub.10.1007/3-540-39200-9_26
    8 sg:pub.10.1007/3-540-45708-9_11
    9 sg:pub.10.1007/3-540-48071-4_3
    10 sg:pub.10.1007/3-540-57332-1_11
    11 sg:pub.10.1007/978-0-387-34873-5_11
    12 sg:pub.10.1007/978-3-030-03329-3_15
    13 sg:pub.10.1007/978-3-319-39555-5_9
    14 sg:pub.10.1007/978-3-319-70972-7_18
    15 sg:pub.10.1007/978-3-540-24676-3_5
    16 sg:pub.10.1007/978-3-540-72540-4_13
    17 sg:pub.10.1007/978-3-540-73420-8_37
    18 sg:pub.10.1007/978-3-642-29011-4_33
    19 sg:pub.10.1007/978-3-662-53008-5_2
    20 sg:pub.10.1007/bf00196725
    21 sg:pub.10.1007/bfb0034859
    22 sg:pub.10.1007/s00145-002-0120-1
    23 sg:pub.10.1007/s00145-004-0314-9
    24 sg:pub.10.1007/s001450010003
    25 sg:pub.10.1007/s10623-009-9313-z
    26 schema:datePublished 2019-02-02
    27 schema:datePublishedReg 2019-02-02
    28 schema:description We describe a new Schnorr-based multi-signature scheme (i.e., a protocol which allows a group of signers to produce a short, joint signature on a common message) called MuSig\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {MuSig}$$\end{document}, provably secure under the Discrete Logarithm assumption and in the plain public-key model (meaning that signers are only required to have a public key, but do not have to prove knowledge of the private key corresponding to their public key to some certification authority or to other signers before engaging the protocol). MuSig\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {MuSig}$$\end{document} improves over the state-of-art scheme of Bellare and Neven (ACM Conference on Computer and Communications Security-CCS 2006) and its variants by Bagherzandi et al. (ACM Conference on Computer and Communications Security-CCS 2008) and Ma et al. (Des Codes Cryptogr 54(2):121–133, 2010) in two respects: (i) it is simple and efficient, having the same key and signature size as standard Schnorr signatures; (ii) it allows key aggregation, which informally means that the joint signature can be verified exactly as a standard Schnorr signature with respect to a single “aggregated” public key which can be computed from the individual public keys of the signers. To the best of our knowledge, this is the first multi-signature scheme provably secure under the Discrete Logarithm assumption in the plain public-key model which allows key aggregation. As an application, we explain how our new multi-signature scheme could improve both performance and user privacy in Bitcoin.
    29 schema:genre article
    30 schema:isAccessibleForFree false
    31 schema:isPartOf N2a13f16eeb3546a5a2de2419a86b1da5
    32 Ne68d526ed9fc491d82b39241e65485f1
    33 sg:journal.1136552
    34 schema:keywords Bagherzandi et al
    35 Bellare
    36 Bitcoin
    37 Ma et al
    38 Neven
    39 Schnorr
    40 Schnorr signature
    41 aggregation
    42 al
    43 applications
    44 art schemes
    45 assumption
    46 discrete logarithm assumption
    47 et al
    48 individual public keys
    49 joint signature
    50 key
    51 key aggregation
    52 knowledge
    53 model
    54 multi-signature scheme
    55 new multi-signature scheme
    56 performance
    57 plain public key model
    58 privacy
    59 public key
    60 public-key model
    61 respect
    62 same key
    63 scheme
    64 signature size
    65 signatures
    66 signers
    67 size
    68 state
    69 user privacy
    70 variants
    71 schema:name Simple Schnorr multi-signatures with applications to Bitcoin
    72 schema:pagination 2139-2164
    73 schema:productId N3315aada78b24a4f99756a2c693526c4
    74 N3e0a0e99063e4abf8628ea355c6c86b8
    75 schema:sameAs https://app.dimensions.ai/details/publication/pub.1111837746
    76 https://doi.org/10.1007/s10623-019-00608-x
    77 schema:sdDatePublished 2022-12-01T06:39
    78 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    79 schema:sdPublisher N0e9e5826d16d456e8600858f991d5d3c
    80 schema:url https://doi.org/10.1007/s10623-019-00608-x
    81 sgo:license sg:explorer/license/
    82 sgo:sdDataset articles
    83 rdf:type schema:ScholarlyArticle
    84 N0e9e5826d16d456e8600858f991d5d3c schema:name Springer Nature - SN SciGraph project
    85 rdf:type schema:Organization
    86 N154271e10968476f89abc3fa20c6691a rdf:first sg:person.011724731171.01
    87 rdf:rest Na3e69c6d7cee434da353bb4c7bed09e6
    88 N2a13f16eeb3546a5a2de2419a86b1da5 schema:volumeNumber 87
    89 rdf:type schema:PublicationVolume
    90 N3315aada78b24a4f99756a2c693526c4 schema:name dimensions_id
    91 schema:value pub.1111837746
    92 rdf:type schema:PropertyValue
    93 N3e0a0e99063e4abf8628ea355c6c86b8 schema:name doi
    94 schema:value 10.1007/s10623-019-00608-x
    95 rdf:type schema:PropertyValue
    96 N7388813703fd415e9a830cd75aa0441b rdf:first sg:person.014233473557.78
    97 rdf:rest Nb0632040ffb94171818af8310187ae48
    98 Na3e69c6d7cee434da353bb4c7bed09e6 rdf:first sg:person.010473774051.72
    99 rdf:rest rdf:nil
    100 Nb0632040ffb94171818af8310187ae48 rdf:first sg:person.016241362014.54
    101 rdf:rest N154271e10968476f89abc3fa20c6691a
    102 Ne68d526ed9fc491d82b39241e65485f1 schema:issueNumber 9
    103 rdf:type schema:PublicationIssue
    104 anzsrc-for:08 schema:inDefinedTermSet anzsrc-for:
    105 schema:name Information and Computing Sciences
    106 rdf:type schema:DefinedTerm
    107 anzsrc-for:0804 schema:inDefinedTermSet anzsrc-for:
    108 schema:name Data Format
    109 rdf:type schema:DefinedTerm
    110 sg:journal.1136552 schema:issn 0925-1022
    111 1573-7586
    112 schema:name Designs, Codes and Cryptography
    113 schema:publisher Springer Nature
    114 rdf:type schema:Periodical
    115 sg:person.010473774051.72 schema:affiliation grid-institutes:None
    116 schema:familyName Wuille
    117 schema:givenName Pieter
    118 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010473774051.72
    119 rdf:type schema:Person
    120 sg:person.011724731171.01 schema:affiliation grid-institutes:None
    121 schema:familyName Seurin
    122 schema:givenName Yannick
    123 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011724731171.01
    124 rdf:type schema:Person
    125 sg:person.014233473557.78 schema:affiliation grid-institutes:None
    126 schema:familyName Maxwell
    127 schema:givenName Gregory
    128 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014233473557.78
    129 rdf:type schema:Person
    130 sg:person.016241362014.54 schema:affiliation grid-institutes:None
    131 schema:familyName Poelstra
    132 schema:givenName Andrew
    133 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016241362014.54
    134 rdf:type schema:Person
    135 sg:pub.10.1007/11593447_1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044035450
    136 https://doi.org/10.1007/11593447_1
    137 rdf:type schema:CreativeWork
    138 sg:pub.10.1007/11761679_28 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021356577
    139 https://doi.org/10.1007/11761679_28
    140 rdf:type schema:CreativeWork
    141 sg:pub.10.1007/3-540-36288-6_3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004411735
    142 https://doi.org/10.1007/3-540-36288-6_3
    143 rdf:type schema:CreativeWork
    144 sg:pub.10.1007/3-540-39200-9_26 schema:sameAs https://app.dimensions.ai/details/publication/pub.1030846652
    145 https://doi.org/10.1007/3-540-39200-9_26
    146 rdf:type schema:CreativeWork
    147 sg:pub.10.1007/3-540-45708-9_11 schema:sameAs https://app.dimensions.ai/details/publication/pub.1029389964
    148 https://doi.org/10.1007/3-540-45708-9_11
    149 rdf:type schema:CreativeWork
    150 sg:pub.10.1007/3-540-48071-4_3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1039918288
    151 https://doi.org/10.1007/3-540-48071-4_3
    152 rdf:type schema:CreativeWork
    153 sg:pub.10.1007/3-540-57332-1_11 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052110589
    154 https://doi.org/10.1007/3-540-57332-1_11
    155 rdf:type schema:CreativeWork
    156 sg:pub.10.1007/978-0-387-34873-5_11 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042451236
    157 https://doi.org/10.1007/978-0-387-34873-5_11
    158 rdf:type schema:CreativeWork
    159 sg:pub.10.1007/978-3-030-03329-3_15 schema:sameAs https://app.dimensions.ai/details/publication/pub.1107870563
    160 https://doi.org/10.1007/978-3-030-03329-3_15
    161 rdf:type schema:CreativeWork
    162 sg:pub.10.1007/978-3-319-39555-5_9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1039225102
    163 https://doi.org/10.1007/978-3-319-39555-5_9
    164 rdf:type schema:CreativeWork
    165 sg:pub.10.1007/978-3-319-70972-7_18 schema:sameAs https://app.dimensions.ai/details/publication/pub.1099922858
    166 https://doi.org/10.1007/978-3-319-70972-7_18
    167 rdf:type schema:CreativeWork
    168 sg:pub.10.1007/978-3-540-24676-3_5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002538471
    169 https://doi.org/10.1007/978-3-540-24676-3_5
    170 rdf:type schema:CreativeWork
    171 sg:pub.10.1007/978-3-540-72540-4_13 schema:sameAs https://app.dimensions.ai/details/publication/pub.1001372793
    172 https://doi.org/10.1007/978-3-540-72540-4_13
    173 rdf:type schema:CreativeWork
    174 sg:pub.10.1007/978-3-540-73420-8_37 schema:sameAs https://app.dimensions.ai/details/publication/pub.1010224437
    175 https://doi.org/10.1007/978-3-540-73420-8_37
    176 rdf:type schema:CreativeWork
    177 sg:pub.10.1007/978-3-642-29011-4_33 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019042387
    178 https://doi.org/10.1007/978-3-642-29011-4_33
    179 rdf:type schema:CreativeWork
    180 sg:pub.10.1007/978-3-662-53008-5_2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1015793862
    181 https://doi.org/10.1007/978-3-662-53008-5_2
    182 rdf:type schema:CreativeWork
    183 sg:pub.10.1007/bf00196725 schema:sameAs https://app.dimensions.ai/details/publication/pub.1043691009
    184 https://doi.org/10.1007/bf00196725
    185 rdf:type schema:CreativeWork
    186 sg:pub.10.1007/bfb0034859 schema:sameAs https://app.dimensions.ai/details/publication/pub.1012885523
    187 https://doi.org/10.1007/bfb0034859
    188 rdf:type schema:CreativeWork
    189 sg:pub.10.1007/s00145-002-0120-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1038875442
    190 https://doi.org/10.1007/s00145-002-0120-1
    191 rdf:type schema:CreativeWork
    192 sg:pub.10.1007/s00145-004-0314-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1000134872
    193 https://doi.org/10.1007/s00145-004-0314-9
    194 rdf:type schema:CreativeWork
    195 sg:pub.10.1007/s001450010003 schema:sameAs https://app.dimensions.ai/details/publication/pub.1018357720
    196 https://doi.org/10.1007/s001450010003
    197 rdf:type schema:CreativeWork
    198 sg:pub.10.1007/s10623-009-9313-z schema:sameAs https://app.dimensions.ai/details/publication/pub.1014195366
    199 https://doi.org/10.1007/s10623-009-9313-z
    200 rdf:type schema:CreativeWork
    201 grid-institutes:None schema:alternateName ANSSI, Paris, France
    202 Blockstream, Mountain View, USA
    203 San Francisco, USA
    204 schema:name ANSSI, Paris, France
    205 Blockstream, Mountain View, USA
    206 San Francisco, USA
    207 rdf:type schema:Organization
     




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


    ...