Paper 2025/1233

Improved Constant-Sized Polynomial Commitment Schemes Without Trusted Setup

Abstract

Argument systems are a fundamental ingredient in many cryptographic constructions. The best-performing argument systems to date largely rely on a trusted setup, which is undesirable in trust-minimized applications. While transparent argument systems avoid this trust assumption, they have historically been inefficient, typically exhibiting polylogarithmic proof sizes compared to their trusted counterparts. In 2023, Arun et al. (PKC 2023) constructed the first transparent constant-sized polynomial commitment scheme (PCS), leading to transparent constant-sized arguments. However, the evaluation proof still comprises 66 group elements in a group of unknown order (GUO), rendering it rather impractical. In this work, we address this challenge by presenting a set of novel batching and aggregation techniques tailored for proofs of knowledge of ranges in GUOs. These techniques may also be of independent interest and are readily applicable to enhance and shorten other existing schemes in GUOs. Consequently, by applying these techniques, we immediately achieve an improved PCS with an evaluation proof consisting of only 10 group elements---an impressive 85% reduction. To our knowledge, this represents the shortest PCS in the transparent setting. Thus compiling known information-theoretic proof systems using our improved PCS yields highly compact transparent argument systems when instantiated in a class group, which is more practical than prior constant-sized schemes.