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      Practical threshold signatures with linear secret sharing schemes

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      Author(s)
      Bozkurt, İlker Nadi
      Kaya, Kamer
      Selçuk, Ali Aydın
      Date
      2009-06
      Source Title
      International Conference on Cryptology in Africa. AFRICACRYPT 2009: Progress in Cryptology
      Publisher
      Springer
      Pages
      167 - 178
      Language
      English
      Type
      Conference Paper
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      Abstract
      Function sharing deals with the problem of distribution of the computation of a function (such as decryption or signature) among several parties. The necessary values for the computation are distributed to the participating parties using a secret sharing scheme (SSS). Several function sharing schemes have been proposed in the literature, with most of them using Shamir secret sharing as the underlying SSS. In this paper, we investigate how threshold cryptography can be conducted with any linear secret sharing scheme and present a function sharing scheme for the RSA cryptosystem. The challenge is that constructing the secret in a linear SSS requires the solution of a linear system, which normally involves computing inverses, while computing an inverse modulo φ(N) cannot be tolerated in a threshold RSA system in any way. The threshold RSA scheme we propose is a generalization of Shoup's Shamir-based scheme. It is similarly robust and provably secure under the static adversary model. At the end of the paper, we show how this scheme can be extended to other public key cryptosystems and give an example on the Paillier cryptosystem. © 2009 Springer Berlin Heidelberg.
      Keywords
      Function sharing
      Linear secret sharing
      Threshold cryptography
      Adversary models
      Paillier cryptosystem
      Provably secure
      Public key cryptosystems
      RSA cryptosystems
      Secret sharing
      Secret sharing schemes
      Sharing schemes
      Threshold RSA
      Threshold signature
      Linear systems
      Public key cryptography
      Computer science
      Permalink
      http://hdl.handle.net/11693/28698
      Published Version (Please cite this version)
      http://dx.doi.org/10.1007/978-3-642-02384-2_11
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      • Department of Computer Engineering 1435
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