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Efficiency Improvement in Group Signature Scheme with Probabilistic Revocation

In group signature schemes, one of the important issues is the member revocation, and lots of revocable schemes have been proposed. Recently, a Group Signature scheme with Probabilistic Revocation (GSPR) is proposed. In GSPR, by employing a novel notion of probabilistic revocation, the computation cost of the revocation check is drastically reduced, although the correctness of the check is with a certain probability. However, in the GSPR scheme, there is another problem: m alias tokens are embedded into the certificate of a member. Then, in signing, each token is used, and O(m) exponentiations are needed to prove that the used token is embedded in the certificate. When m is large, this signing cost including O(m) exponentiations becomes a big problem for powerless mobile devices. In this paper, we propose an extended GSPR scheme where the signing cost is reduced, but the revocation mechanism is exactly the same as the original GSPR scheme. Our main idea is to utilize an efficient pairing-based accumulator with multiplications to embed lots of alias tokens in a certificate. Thus, in the proposed scheme, the signing cost is reduced to only O(m) multiplications instead of O(m) exponentiations.