Post-Quantum Secure Decentralized Random Number Generation Protocol with Two Rounds of Communication in the Standard Model

TL;DR

The paper addresses constructing a DRNG that remains secure against quantum adversaries while operating in the standard model and requiring only two rounds of communication. It achieves this by instantiating a lattice-based PVSS (as in MNSN25) within a DRNG compiler, relying on a one-time common reference string (CRS) to enable public verifiability and post-quantum security without ROM; the design tolerates up to $t < n/2$ dishonest participants. The authors provide a security proof framing pseudorandomness as a reduction to IND2-privacy of the PVSS, and they analyze the complexity in terms of communication and computation, highlighting the two-round round complexity. The work offers a practical path toward robust, publicly verifiable randomness in post-quantum settings, with the CRS serving as a one-off trust anchor that enables repeated, independent randomness generation.

Abstract

Randomness plays a vital role in numerous applications, including simulation, cryptography, distributed systems, and gaming. Consequently, extensive research has been conducted to generate randomness. One such method is to design a decentralized random number generator (DRNG), a protocol that enables multiple participants to collaboratively generate random outputs that must be publicly verifiable. However, existing DRNGs are either not secure against quantum computers or depend on the random oracle model (ROM) to achieve security. In this paper, we design a DRNG based on lattice-based publicly verifiable secret sharing (PVSS) that is post-quantum secure and proven secure in the standard model. Additionally, our DRNG requires only two rounds of communication to generate a single (pseudo)random value and can tolerate up to any t < n/2 dishonest participants. To our knowledge, the proposed DRNG construction is the first to achieve all these properties.

Figures (9)

• Figure 1: Game $\mathbf{Game}^{\mathsf{PVSS}-\mathsf{Correctness}}(\mathcal{A})$
• Figure 2: Game $\mathbf{Game}^{\mathsf{PVSS}-\mathsf{Ver}}(\mathcal{A})$
• Figure 3: Game $\mathbf{Game}^{\mathsf{PVSS}-\mathsf{IND}}_b(\mathcal{A})$ with supporting interactive oracle $\mathcal{O}_{\mathsf{PVSS},\mathcal{A}}(.)$
• Figure 4: Shamir Secret Sharing Scheme
• Figure 5: The ACPS Public Key Encryption Scheme

Theorems & Definitions (17)

• definition thmcounterdefinition: LWE Assumption Re09
• definition thmcounterdefinition: NIZK, Adapted from LNPT20MNSN25
• definition thmcounterdefinition: PVSS, Adapted from MNSN25
• definition thmcounterdefinition: Correctness MNSN25
• definition thmcounterdefinition: Valid Share Language MNSN25
• definition thmcounterdefinition: Verifiability MNSN25
• definition thmcounterdefinition: IND2-Privacy MNSN25
• definition thmcounterdefinition: DRNG, Adapted from MHN23
• definition thmcounterdefinition: Security of DRNG, Adapted from MHN23
• theorem thmcountertheorem