DiLizium: A Two-Party Lattice-Based Signature Scheme

Area of Science:

• Cryptography
• Post-Quantum Cryptography
• Digital Signatures

Background:

• Existing signature schemes face threats from quantum computing.
• Efficient two-party signature schemes are crucial for secure multi-user systems.
• Crystals-Dilithium offers post-quantum security but can be complex for two-party implementations.

Purpose of the Study:

• To propose DiLizium, a new lattice-based two-party signature scheme.
• To enhance the efficiency of two-party signature generation compared to existing schemes.
• To ensure post-quantum security against quantum adversaries.

Main Methods:

• Construction of a new signature scheme based on a variant of Crystals-Dilithium.
• Derivation of security from Module Learning With Errors (M-LWE) and Module Short Integer Solution (M-SIS) problems.
• Detailed protocol description and security proof against classical adversaries.

Main Results:

• DiLizium achieves more efficient two-party implementation than the original scheme.
• The scheme's post-quantum security is rooted in established lattice-based problems.
• A security proof against classical adversaries is provided for the two-party signature computation.

Conclusions:

• DiLizium presents an efficient and secure lattice-based two-party signature scheme.
• The scheme offers a practical solution for post-quantum secure digital signatures in two-party settings.
• Further research is needed to extend the security proof to quantum adversaries.