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Issuing CL-Signatures on Speed: Signing with a Constant Number of Exponentiations

Lookup NU author(s): Professor Thomas Gross



This is the final published version of a report that has been published in its final definitive form by School of Computing Science, University of Newcastle upon Tyne, 2014.

For re-use rights please refer to the publisher's terms and conditions.


In SCN 2002, Jan Camenisch and Anna Lysyanskaya have proposed the Strong RSA version of their Camenisch-Lysyanskaya (CL) signature scheme [8], a fundamental cryptographic building block to compute a digital signature on hidden committed messages and allow zero-knowledge proofs of knowledge on them. Ever since, the CL signature scheme has been adopted for different applications, such as anonymous credential systems, Direct Anonymous Attestation, and different prototypes for smart cards. Unfortunately, CL signatures place a significant workload on the issuer, as the signature generation requires a number of modular exponentiations linear in the number of message blocks signed, which, in turn, constitutes a significant obstacle for the broad adoption of the scheme. In this work, we propose a variant of the Strong RSA CL-signature scheme, which computes the signature with a constant number of modular exponentiations, that is, independent of the number of message blocks involved. In fact, we show that issuer can compute a commitment on an arbitrary number of message blocks with one modular exponentiation and complete the signature generation with five modular exponentiations. All the issuer needs to do is store n group elements readily available from the standard key generation with its private key and use this knowledge in the signature generation. The output of the optimized CL-issuing is fully wire-format compatible to the standard CL-issuing. We provide a comprehensive performance analysis of the optimized issuing approach, which shows that signatures with strong security parameters and even with tens of thousands of message blocks can be computed in the order of one hundred milliseconds. ---------

Publication metadata

Author(s): Gross T

Publication type: Report

Publication status: Published

Series Title: School of Computing Science Technical Report Series

Year: 2014

Pages: 16

Print publication date: 01/05/2014

Acceptance date: 03/03/2014

Report Number: 1418

Institution: School of Computing Science, University of Newcastle upon Tyne

Place Published: Newcastle upon Tyne