An Attribute-based signature (ABS), is a cryptographic scheme where someone can sign a message using any kind of predicates verified by the attributes he owns. For such scheme, it is expected to be impossible for users to collude to sign a message if none of them is originally able to sign the message on his own. The main advantage of such a solution is that the signer can remain anonymous in the set of users fulfilling the chosen predicate. It can then be used for anonymous authentication for instance. In this paper, our main contribution is a new designated verifier attribute based signature scheme. In other words, the signer is using his attributes to authenticate a message according to a predicate, and while doing so he can pick another policy such that only users owning attributes fulfilling this policy can check the validity of the signature. It can be used to extend anonymous authentication, ensuring that the designated verifier cannot prove to anyone that a valid authentication has been performed. In addition to classical anonymity, this also increases the privacy of users as no further statistics on valid connection can be deduced. To do so, we first propose a generic construction of this primitive using standard cryptographic building blocks. An instantiation of this primitive is then described and proved through security games under the Symmetric External Diffie-Hellman (SXDH) assumption. This main contribution is compared to state-of-the-art solutions in terms of both security and efficiency.