A Hidden Vector Encryption (HVE) scheme is a special type of anonymous identity-based encryption (IBE) scheme where the attribute string associated with the ciphertext or the user secret key can contain wildcards. In this paper, we introduce two constant-size ciphertext-policy hidden vector encryption (CP-HVE) schemes. Our first scheme is constructed on composite order bilinear groups, while the second one is built on prime order bilinear groups. Both schemes are proven secure in a selective security model which captures plaintext (or payload) and attribute hiding. To the best of our knowledge, our schemes are the first HVE constructions that can achieve constant-size ciphertext among all the existing HVE schemes. 2014 Springer International Publishing Switzerland.