Anonymity of identity-based encryption (IBE) means that given a ciphertext, one cannot distinguish the target identity from a random identity. In this paper, we thoroughly discuss the anonymity of IBE systems. We found that the current definition of anonymity is obscure to describe some IBE systems, such as Gentry IBE system. Furthermore, current definition cannot express the degree of anonymity. So we divide the degree of anonymity into weak anonymity and strong anonymity based on indistinguishability between different games. For weakly anonymous IBE systems, the target identity in a ciphertext cannot be distinguished from a random identity. For strongly anonymous IBE systems, the whole ciphertext cannot be distinguished from a random tuple. We also discuss the type of anonymity and divide it into two types. Type 1 means that a random tuple can be seen as a valid ciphertext, while type 2 cannot. Based on our new definitions, we show that three famous IBE systems, Gentry IBE system, Boyen-Waters IBE system, and Lewko IBE system, have strong but different types of anonymity.
Song Luo. Ning Hu. "On the Anonymity of Identity-Based Encryption." J. Appl. Math. 2013 1 - 9, 2013. https://doi.org/10.1155/2013/217480