KiloNova: Non-Uniform PCD with Zero-Knowledge Property from Generic Folding Schemes

Most existing accumulation/folding schemes focus on implementing Incrementally Verifiable Computation (IVC). Proof-carrying Data (PCD), as a generalization of IVC, enables sequential computation performance by multiple distrusting parties, thereby offering a robust primitive tool in real-world applications. However, building non-uniform PCD from folding schemes faces many technical challenges, particularly in handling cross items and preserving zero knowledge. This paper introduces KiloNova, a non-uniform PCD system with zero-knowledge properties derived from generic folding schemes. Motivated by HyperNova (Kothapalli et al. ePrint 2023), we derive a variant of the Customizable Constraint System with linear claims on circuits and inputs to avoid cross items. With the new constraint system, we propose a generic folding scheme for multiple instances of different circuits and ensure the zero-knowledge property with various effective methods. Consequently, we build a non-uniform ZK-PCD scheme from the generic folding scheme and improve its performance with some optimization techniques, such as circuit aggregation and decoupling. We propose a new construction for ZK-PCD that does not use a ZK argument system and has little influence on the complexity. The theoretical evaluation shows our non-uniform ZK-PCD scheme outperforms previous models. A single multi-scalar multiplication dominates the prover cost at each step. The recursive circuit is dominated by $O(\log(n))$ random-oracle-like hashes and $O(k)$ scalar multiplications, where $n$ is the circuit input length and $k$ is the instance number at each step