This work formalizes Publicly Auditable Conditional Blind Signatures (PACBS), a new cryptographic primitive that allows the verifiable issuance of blind signatures, the validity of which is contingent upon a predicate and decided by a designated verifier. In particular, when a user requests the signing of a message, blinded to protect her privacy, the signer embeds data in the signature that makes it valid if and only if a condition holds. A verifier, identified by a private key, can check the signature and learn the value of the predicate. Auditability mechanisms in the form of non-interactive zero-knowledge proofs are provided, so that a cheating signer cannot issue arbitrary signatures and a cheating verifier cannot ignore the embedded condition. The security properties of this new primitive are defined using cryptographic games. A proof-of-concept construction, based on the Okamoto–Schnorr blind signatures infused with a plaintext equivalence test is presented and its security is analyzed.