OmegaProtocol_EHDSABasedZeroKnowledgeFrameworkforPrivacyPreservingDigitalSignatures

We introduce the ω-Protocol, a zero-knowledge proof framework for the verification of elliptic curve–based homomorphic digital signatures. The protocol is constructed on top of the Elliptic Curve Homomorphic Digital Signature Algorithm (EHDSA) and enables zero-knowledge verification of signature validity while preserving signer privacy. The core contribution of the ω-Protocol is a signature-integrated zero-knowledge construction that combines homomorphic properties of EHDSA with algebraic commitment mechanisms over elliptic curve groups. We formalize the protocol model and define security notions capturing zero-knowledge, soundness, and unlinkability of signature verification. Under standard cryptographic assumptions over elliptic curve groups, we prove that the ω-Protocol achieves zero-knowledge and unforgeability-preserving verification without revealing signature components or ephemeral key material. We further analyze the computational complexity of the protocol and show that it incurs only minimal overhead compared to standard EHDSA verification. Our results establish a principled cryptographic framework for zero-knowledge verification of homomorphic digital signatures and provide a foundation applicable to privacy-preserving authentication and verification protocols.