Distributed Ledger Authentication Systems via Homomorphic Pairwise Verification: Formal Cryptographic Analysis and Zero-Knowledge Constructions

We present a comprehensive cryptographic framework for distributed ledger-based authentication that achieves perfect zero-knowledge privacy preservation through homomorphic pairwise verification based on Elliptic Curve ElGamal encryption. Our construction extends the theoretical foundations of homomorphic authentication to practical distributed systems by introducing novel public zero-detection protocols based on bilinear pairings over elliptic curves and threshold secret sharing mechanisms. The system guarantees that authentication succeeds if and only if encrypted credential differences equal the point at infinity, while maintaining computational indistinguishability of authentication transcripts from random distributions. We provide rigorous security proofs demonstrating the system's resistance to adaptive chosen-message attacks, replay attacks, and node compromise scenarios under standard cryptographic assumptions including the Elliptic Curve Discrete Logarithm Problem and the Bilinear Diffie-Hellman assumption. Our performance analysis shows sub-100 millisecond authentication latency with linear scalability properties, making the system suitable for enterprise-grade deployment. The construction enables perfect forward secrecy, unlinkable authentication sessions, and cryptographically verifiable audit trails without compromising user privacy.