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Signcryption Schemes Based on the Diffie–Hellman Problem

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Practical Signcryption

Part of the book series: Information Security and Cryptography ((ISC))

Abstract

In this chapter we examine various signcryption schemes based on the Diffie–Hellman problem . Importantly, this set of schemes includes the original signcryption scheme by Zheng [203] and also several constructions with enhanced properties, for example, the scheme by Bao and Deng [15] .

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Notes

  1. 1.

    The latter assumption should not be confused with another assumption introduced by Boneh and Boyen [42] and named “q-Strong Diffie–Hellman.” The assumption of [42] is very different and states the intractability of computing a pair \((c,g^{1/(c+a)})\in \mathbb{Z}_p \times \mathbb{G}\) given \((g,g^a,g^{(a^2)},\ldots,g^{(a^q)})\) for randomly chosen \(a{\stackrel{{\scriptscriptstyle R}}{\leftarrow}} {\mathbb{Z}}_{p}^{*}\). This problem is described in more detail in Chap. 5.

  2. 2.

    Neither did the original specification—given in [203]—of Zheng’s proposal . It was in [12] that the binding information was taken as argument by H for the first time (in order to prove security in the multi-user setting).

  3. 3.

    More hybrid constructions are described in Chap. 7.

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Authors and Affiliations

  1. Architecture and Networking Lab (LARC), Department of Computer and Digital Systems Engineering (PCS), Escola Politécnica, University of São Paulo, São Paulo, Brazil

    Paulo S.L.M. Barreto

  2. Crypto Group, Microelectronics Laboratory, Université Catholique de Louvain, Louvain, Belgium

    Benoît Libert & Jean-Jacques Quisquater

  3. School of Computing, Dublin City University, Dublin, Ireland

    Noel McCullagh

Authors
  1. Paulo S.L.M. Barreto
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  2. Benoît Libert
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  3. Noel McCullagh
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  4. Jean-Jacques Quisquater
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Correspondence to Benoît Libert .

Editor information

Editors and Affiliations

  1. University of London, Information Security Group, Royal Holloway, Egham, Surrey, TW20 0EX, United Kingdom

    Alexander W. Dent

  2. Dept. Software & Information Systems, University of North Carolina, Charlotte, University City Blvd. 9201, Charlotte, 28223, North Carolina, USA

    Yuliang Zheng

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Barreto, P.S., Libert, B., McCullagh, N., Quisquater, JJ. (2010). Signcryption Schemes Based on the Diffie–Hellman Problem. In: Dent, A., Zheng, Y. (eds) Practical Signcryption. Information Security and Cryptography. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89411-7_4

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  • DOI: https://doi.org/10.1007/978-3-540-89411-7_4

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