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How to Securely Prolong the Computational Bindingness of Pedersen Commitments

Demirel, Denise and Lancrenon, Jean :
How to Securely Prolong the Computational Bindingness of Pedersen Commitments.

[Report] , (2015)

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.

Item Type: Report
Erschienen: 2015
Creators: Demirel, Denise and Lancrenon, Jean
Title: How to Securely Prolong the Computational Bindingness of Pedersen Commitments
Language: English
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.

Uncontrolled Keywords: Secure Data;Solutions;S6;PRISMACLOUD;unconditionally hiding commitments, long-term security, perfect zero-knowledge proofs, Pedersen commitments
Divisions: DFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres > CRC 1119: CROSSING – Cryptography-Based Security Solutions: Enabling Trust in New and Next Generation Computing Environments
Department of Computer Science > Theoretical Computer Science - Cryptography and Computer Algebra
LOEWE > LOEWE-Zentren > CASED – Center for Advanced Security Research Darmstadt
Department of Computer Science > Theoretical Computer Science - Cryptography and Computer Algebra > Long-term Security
Profile Areas > Cybersecurity (CYSEC)
Department of Computer Science > Theoretical Computer Science - Cryptography and Computer Algebra > Post-Quantum Cryptography
LOEWE > LOEWE-Zentren
DFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres
Department of Computer Science
Profile Areas
LOEWE
DFG-Collaborative Research Centres (incl. Transregio)
Date Deposited: 15 Nov 2016 23:15
Identification Number: TUD-CS-2015-0140
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