Method for anonymity of authenticated messages in SNS

Anonymity in SNS is one of the important things for protecting privacy. We proposed a method in which nouns are replaced with other nouns in consideration of semantic relations. For example, some nouns in the sentence "I go to Tokyo University of Technology with Alice" are replaced such as "I go to university with her". The method prevents the author from leaking privacy of his/her friends to the third party. Levels of obscurity are decided by the relationship between the author and readers. When the relationship is weaker than that in the example above, the message changes such as "I go to school with a friend". In the method, proper nouns and some specific nouns are automatically replaced with other appropriate nouns by hi-speed filtering with Bloom filter. We also proposed an additional method in which messages are authenticated. In the method messages are signed with sanitizable signature since some nouns have possibility to be replaced. The combination of the two proposals provides anonymity and integrity and authentication at the same time. However, I found the latter method has vulnerability. If attackers have knowledge of privacy of victims, original nouns can be specified with one hundred percent correctness. Therefore, in this paper, I propose an improve method for anonymity. The method provides perfect obscurity with anonymity although messages are authenticated.