Anonymous hierarchical identity based encryption (HIBE) is an extension of identity based encryption (IBE) that can use an arbitrary string like an e-mail address for a public key, and it additionally provide the anonymity of identity in ciphertexts. Using the anonymous HIBE schemes, it is possible to construct anonymous communication systems and public key encryption with keyword search. This paper presents an anonymous HIBE scheme with constant size ciphertexts under prime order symmetric bilinear groups, and shows that it is secure under the selective security model. Previous anonymous HIBE schemes were constructed to have linear size ciphertexts, to use composite order bilinear groups, or to use asymmetric bilinear groups that is a special type of bilinear groups. Our construction is the first efficient anonymous HIBE scheme that has constant size ciphertexts and that uses prime order symmetric bilinear groups. Compared to the previous scheme of composite order bilinear groups, ours is ten times faster. To achieve our construction, we first devise a novel cancelable random blinding technique. The random blinding property of our technique provides the anonymity of our construction, and the cancellation property of our technique enables decryption.