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Nowadays, Internet becomes a part of the peoples' life. The authors can make use of numerous services with personal computer, laptop, tablet, smart phone or smart TV. These devices with network make one enjoy ubiquitous computing life. Sometimes, online services request one authentication or identification for access control and authorization, and PKI technology is widely used because of its security. However, the possibility of privacy invasion will increase, if the people identified with same certificate in many services and these identification data are accumulated. For privacy-preserving authentication or anonymous authentication, there have been many researches such as group signatures, anonymous credentials, etc. Among these researches, group signatures are very practical because they provide unlinkability and traceability as well as anonymity.
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