The emergence of quantum computing poses unprecedented challenges to contemporary cryptographic systems, particularly those relying on integer factorization and discrete logarithm assumptions. While the National Institute of Standards and Technology (NIST) has standardized post-quantum cryptographic algorithms including Dilithium for digital signatures, existing verification processes often involve computationally intensive operations unsuitable for resource-constrained environments. This paper presents Dilion, a novel digital signature scheme that synergistically combines the quantum-resistant foundation of Dilithium with an innovative homomorphic pairwise verification mechanism. Unlike conventional signature schemes requiring expensive decryption operations during verification, Dilion performs verification directly on encrypted data through elliptic curve-based homomorphic encryption. Our approach introduces a lightweight verification protocol that leverages Dilithium's challenge-response structure while incorporating cryptographically secure pairwise identity binding. Comprehensive experimental evaluation demonstrates that Dilion maintains equivalent security guarantees to standard Dilithium while achieving approximately 40% reduction in verification computational complexity. We provide rigorous security proofs demonstrating that Dilion achieves existential unforgeability under chosen message attacks, context-binding security, and privacy preservation under standard cryptographic assumptions.
Lee et al. (Thu,) studied this question.