Often the correctness of a piece of information, is not easily verified; Alice holds an encryption of Bob's secret and in the absence of Bob's key she must trust that Bob shared the correct encryption with her. In a cryptographic setting it is assumed that some, possibly all, parties participating are untrustworthy adversaries. An important generalized adversary is an Honest-but-Curious (HBC) adversary, a legitimate participant in an interactive protocol, requiring two or more participants, who will not deviate from the defined protocol but will attempt to gain as much knowledge from legitimately received messages. In security-critical applications, it is likely that participants are not acting honestly (regarded as malicious). A zero-knowledge proof (ZKP) is a tool that enables the verification that all parties acted honestly (provided well formed messages). One fundamental ZKP is the Schnorr protocol for knowledge of a discrete logarithm (DL); the Schnorr Σ-protocol is a three-move public coin protocol between two named parties, the Prover (\Prover) and the Verifier (\Verifier). The class of all Σ-protocols has well-established analysis techniques enabling secure composition both in parallel and sequential applications. Scaling Σ-protocols efficiently is challenging, and techniques to reduce the cost of conjunctive composition of the same Σ-protocols exist in the form of batch verification and batched proofs. Batched proof techniques trade bits of security for speed and efficiency. Batching non-conjunctive logic with Σ-protocols forms the contribution of this work.