A Lattice-Based Threshold Signature Scheme for IoT Applications
Elizar Kustov · 2025
The advancement of quantum computing threatens classical cryptographic systems, such as RSA and ECDSA, which can be broken by quantum algorithms like Shor's algorithm. This necessitates the development of post-quantum cryptographic systems resistant to quantum attacks. Lattice-based cryptography, particularly the Learning with Errors (LWE) and Learning with Rounding (LWR) problems, is a promising approach. This paper presents a threshold signature scheme based on the Kryzhovnik signature, an adaptation of the Crystals-Dilithium scheme for LWR. The scheme leverages the hardness of the Module Learning with Rounding (MLWR) and Module Short Integer Solution (MSIS) problems to ensure post-quantum security. It allows a group of N participants to collaboratively generate a signature, requiring at least t participants to create a valid signature, preventing forgery by individual participants. The scheme uses Shamir's Secret Sharing, ensuring the shared secret is never stored explicitly. Key advantages include efficiency, security, and threshold-based access control, making it suitable for IoT and other resource-constrained environments.