Abstract
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 [CL02]. It is obtained by integrating a novel dynamic accumulator with the scheme by Ateniese, et al. [ACJT00].
In this paper, we construct a dynamic accumulator that accumulates composites, as opposed to previous accumulators that accumulated 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 common auxiliary string model and offers two important benefits: 1) the 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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Tsudik, G., Xu, S.: Accumulating Composites and Improved Group Signing. Extended version of this paper available at, http://eprint.iacr.org/2003/112/
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Tsudik, G., Xu, S. (2003). Accumulating Composites and Improved Group Signing. In: Laih, CS. (eds) Advances in Cryptology - ASIACRYPT 2003. ASIACRYPT 2003. Lecture Notes in Computer Science, vol 2894. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40061-5_16
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