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Lecture notes in computer science

Polynomial Commitments from Lattices: Post-quantum Security, Fast Verification and Transparent Setup

Valerio Cini, Giulio Malavolta, Ngoc Khanh Nguyen, Hoeteck Wee

Published Jan 1, 2024• 10 citations
Publisher
DOI
10.1007/978-3-031-68403-6_7

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With the development of large-scale quantum computers, classical cryptographic algorithms such as RSA or ECC can easily be broken by Shor’s algorithm. Consequently, the cryptography community is shifting its focus toward Post-Quantum Cryptography (PQC), developing primitives that are secure against both classical and quantum attacks. In this paper, we propose a novel Verkle-Polynomial Signature (VPS) scheme by combining the lattice-based polynomial commitment scheme of Cini et al. with Verkle trees and a lattice-based One-Time Signature (OTS) engine to achieve post-quantum security. We demonstrate that while sacrificing the operational efficiency and structural maturity of traditional hash-based signatures, our framework provides robust post-quantum security guarantees inherited from standard lattice assumptions.
Post-quantum threshold cryptography requires complete elimination of classical assumptions to achieve genuine quantum resistance. This work presents a fully lattice-based dealerless distributed key generation (DKG) protocol with threshold CRYSTALS–Kyber implementation. We implemented a four-phase DKG protocol using lattice-based primitives: SIS-based commitments for verification, Ring-LWE secret sharing, and secure multi-party key derivation without reconstructing private keys. Our approach eliminates the need for a trusted dealer while maintaining 192-bit post-quantum security through exclusive reliance on lattice problems. Experimental evaluation demonstrates 𝒪(n2) communication complexity for lattice-based DKG setup across 3-20 participants, with secure threshold operations preserving key secrecy. Security analysis provides formal reductions to Ring-LWE and Ring-SIS assumptions, ensuring genuine quantum resistance throughout the protocol stack.