Revocable Group Signature Schemes with Constant Costs for Signing and Verifying

Authors:
Toru Nakanishi;Hiroki Fujii;Yuta Hira;Nobuo Funabiki
Affiliations:
Department of Communication Network Engineering, Okayama University, Okayama, Japan 700-8530;Department of Communication Network Engineering, Okayama University, Okayama, Japan 700-8530;Department of Communication Network Engineering, Okayama University, Okayama, Japan 700-8530;Department of Communication Network Engineering, Okayama University, Okayama, Japan 700-8530
Venue:
Irvine Proceedings of the 12th International Conference on Practice and Theory in Public Key Cryptography: PKC '09
Year:
2009

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Abstract

Lots of revocable group signature schemes have been proposed so far. In one type of revocable schemes, signing and/or verifying algorithms have O (N ) or O (R ) complexity, where N is the group size and R is the number of revoked members. On the other hand, in Camenisch-Lysyanskaya scheme and the followers, signing and verifying algorithms have O (1) complexity. However, before signing, updates of the secret key are required. The complexity is O (R ) in the worst case. In this paper, we propose a revocable scheme with signing and verifying of O (1) complexity, where no updates of secret key are required. The compensation is the long public key of O (N ). In addition, we extend it to the scheme with $O(\sqrt{N})$-size public key, where signing and verifying have constant extra costs.