Publication: IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences Publication Date: 2010/06/01 Vol. E93-ANo. 6pp. 1122-1131 Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications) Category: Cryptography and Information Security Keyword: secret handshake with multiple groups, privacy preserving authentication, anonymity, monotone condition,