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Perfect Hiding and Perfect Binding Universally Composable Commitment Schemes with Constant Expansion Factor

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Part of the book series:Lecture Notes in Computer Science ((LNCS,volume 2442))

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Abstract

Canetti and Fischlin have recently proposed the security notionuniversal composability for commitment schemes and provided two examples. This new notion is very strong. It guarantees that security is maintained even when an unbounded number of copies of the scheme are running concurrently, also it guarantees non-malleability and security against adaptive adversaries. Both proposed schemes use Θ(k) bits to commit to one bit and can be based on the existence of trapdoor commitments and non-malleable encryption.

We present new universally composable commitment (UCC) schemes based on extractableq one-way homomorphisms. These in turn exist based on the Paillier cryptosystem, the Okamoto-Uchiyama cryptosystem, or the DDH assumption. The schemes are efficient: to commit tok bits, they use a constant number of modular exponentiations and communicatesO(k) bits. Furthermore the scheme can be instantiated in either perfectly hiding or perfectly binding versions. These are the first schemes to show that constant expansion factor, perfect hiding, and perfect binding can be obtained for universally composable commitments.

We also show how the schemes can be applied to do efficient zeroknowledge proofs of knowledge that are universally composable.

Basic Research in Computer Science, Centre of the Danish National Research Foundation.

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Authors and Affiliations

  1. BRICS Department of Computer Science, University of Aarhus, Ny Munkegade, DK-8000, Arhus C, Denmark

    Ivan Damgård & Jesper Buus Nielsen

Authors
  1. Ivan Damgård
  2. Jesper Buus Nielsen

Editor information

Editors and Affiliations

  1. Department of Computer Science, Columbia University, 450 Computer Science Building 1214 Amsterdam Ave., 10027, NewYork, N.Y., USA

    Moti Yung

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© 2002 Springer-Verlag Berlin Heidelberg

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Damgård, I., Nielsen, J.B. (2002). Perfect Hiding and Perfect Binding Universally Composable Commitment Schemes with Constant Expansion Factor. In: Yung, M. (eds) Advances in Cryptology — CRYPTO 2002. CRYPTO 2002. Lecture Notes in Computer Science, vol 2442. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45708-9_37

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