Paper 2015/584

How to Securely Prolong the Computational Bindingness of Pedersen Commitments

Denise Demirel and Jean Lancrenon

Abstract

Pedersen commitments are important cryptographic primitives. They allow a prover to commit to a certain value without revealing any information about it and without the prover being able to change its mind later on. Since the first property holds unconditionally this is an essential primitive for many schemes providing long-term confidentiality. However, the second property only holds computationally. Hence, in the long run bindingness is lost, making the primitive improper for long-lived systems. Thus in this paper, we describe a protocol that, in a sense, prolongs the bindingness of a given Pedersen commitment. More precisely, we demonstrate how to prove in perfect zero-knowledge that a new Pedersen commitment - generated with a larger security parameter - and a corresponding old commitment both commit to the same value. We stress that this is a non-trivial procedure. Up until now the only known perfect zero-knowledge proof techniques for proving message equivalence of two commitments work when both commitments use isomorphic message spaces. However, as we will show in this work, to prolong the security of Pedersen commitments we cannot tolerate this restriction. Our prolonging technique works for non-isomorphic message spaces, is efficient, can be repeated an arbitrary number of times, maintains unconditional confidentiality, and allows to preserve the format of the Pedersen commitments. This makes the construction presented here an important contribution to long-lived systems. Finally, we illustrate this by discussing how commitments with prolongable bindingness can be used to allow for archiving solutions that provide not only integrity but also confidentiality in the long-term.

Metadata
Available format(s)
PDF
Publication info
Preprint. MINOR revision.
Keywords
unconditionally hiding commitmentslong-term securityperfect zero-knowledge proofsPedersen commitments
Contact author(s)
ddemirel @ cdc informatik tu-darmstadt de
History
2015-06-21: received
Short URL
https://ia.cr/2015/584
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2015/584,
      author = {Denise Demirel and Jean Lancrenon},
      title = {How to Securely Prolong the Computational Bindingness of Pedersen Commitments},
      howpublished = {Cryptology ePrint Archive, Paper 2015/584},
      year = {2015},
      note = {\url{https://eprint.iacr.org/2015/584}},
      url = {https://eprint.iacr.org/2015/584}
}
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