We present a novel homomorphic pairwise authentication protocol that achieves strong privacy guarantees by leveraging the additive homomorphic properties of EC-ElGamal encryption for secure credential comparison. Our key innovation is the homomorphic difference verification mechanism: instead of comparing credentials directly, we compute the homomorphic difference between stored and presented encrypted credentials, then verify whether this difference encrypts the identity element (zero). This approach ensures that authentication reveals only credential validity while completely hiding credential values, achieving information-theoretic privacy for the authentication decision. The protocol eliminates plaintext credential exposure at all stages while maintaining practical efficiency with authentication times under 1.2 milliseconds and communication overhead of only 128 bytes per session. We provide formal security proofs demonstrating semantic security, unlinkability, and perfect zero-knowledge properties under the Decisional Diffie-Hellman assumption, along with practical extensions for multi-credential scenarios and threshold authentication systems.