Paper 2003/112

Accumulating Composites and Improved Group Signing

Gene Tsudik and Shouhuai Xu


Constructing practical and provably secure group signature schemes has been a very active research topic in recent years. A group signature can be viewed as a digital signature with certain extra properties. Notably, anyone can verify that a signature is generated by a legitimate group member, while the actual signer can only be identified (and linked) by a designated entity called a group manager. Currently, the most efficient group signature scheme available is due to Camenisch and Lysyanskaya \cite{CL02}. It is obtained by integrating a novel dynamic accumulator with the scheme by Ateniese, et al. \cite{ACJT00}. In this paper, we construct a dynamic accumulator that accumulates \emph{composites}, as opposed to previous accumulators that accumulated \emph{primes}. We also present an efficient method for proving knowledge of factorization of a committed value. Based on these (and other) techniques we design a novel provably secure group signature scheme. It operates in the \emph{common auxiliary string} model and offers two important benefits: 1) the {\sf Join} process is very efficient: a new member computes only a single exponentiation, and 2) the (unoptimized) cost of generating a group signature is 17 exponentiations which is appreciably less than the state-of-the-art.

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Published elsewhere. Unknown where it was published
Accumulatorgroup signatureidentity escrow
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shxu @ ics uci edu
2003-06-03: received
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      author = {Gene Tsudik and Shouhuai Xu},
      title = {Accumulating Composites and Improved Group Signing},
      howpublished = {Cryptology ePrint Archive, Paper 2003/112},
      year = {2003},
      note = {\url{}},
      url = {}
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