Efficient revocable group signature schemes using primes

Group signature schemes with membership revocation have been intensively researched. In this paper, we propose revocable group signature schemes with less computational costs for signing/verification than an existing scheme without the update of the signer's secret keys. The key idea is the use of a small prime number embedded in the signer's secret key. By using simple prime integer relations between the secret prime and the public product of primes for valid or invalid members, the revocation is efficiently ensured. To show the practicality, we implemented the schemes and measured the signing/verification times in a common PC (Core2 DUO 2.13 GHz). The times are all less than 0.5 seconds even for relatively large groups (10,000 members), and thus our schemes are sufficiently practical.