This paper presents an anonymous certification (AC) scheme, built over an attribute based signature (ABS). After identifying properties and core building blocks of anonymous certification schemes, we identify ABS limitations to fulfill AC properties, and we propose a new system model along with a concrete mathematical construction based on standard assumptions and the random oracle model. Our solution has several advantages. First, it provides a data minimization cryptographic scheme, permitting the user to reveal only required information to any service provider. Second, it ensures unlinkability between the different authentication sessions, while preserving the anonymity of the user. Third, the derivation of certified attributes by the issuing authority relies on a non interactive protocol which provides an interesting communication overhead