In the implicit certification model, the process of verifying the validity of the signer's public key is combined with the verification of the signature itself. When compared to traditional, explicit certificates, the main advantage of the implicit approach lies in the shorter public key validation data. This property is particularly important in resource-constrained scenarios where public key validation is performed very often, which is common in vehicular communications (V2X) that employ pseudonym certificates. In this article, show that an alternative, Schnorr-based implicit certification procedure can improve the efficiency of a popular V2X-oriented Vehicular Public Key Infrastructure (VPKI), the Security Credential Management System (SCMS). As an additional contribution, we show that SCMS's underlying certificate provisioning procedure, based on butterfly keys, is vulnerable to existential forgery attacks under certain conditions. We then discuss how this issue can be fixed in an effective and efficient manner.