Paper 2024/737

Mutable Batch Arguments and Applications

Abstract

Non-interactive batch arguments (BARGs) let a prover compute a single proof $\pi$ proving validity of a `batch' of $k$ $\mathbf{NP}$ statements $x_1, \ldots, x_{k}$. The two central features of BARGs are succinctness and soundness. Succinctness states that proof size, $|\pi|$ does not grow with $k$; while soundness states a polytime cheating prover cannot create an accepting proof for any invalid batch of statements. In this work, we put forth a new concept of mutability for batch arguments, called mutable batch arguments. Our goal is to re-envision how we think about and use BARGs. Traditionally, a BARG proof string $\pi$ is an immutable encoding of $k$ $\mathbf{NP}$ witness $\omega_1, \ldots, \omega_{k}$. In a mutable BARG system, each proof string $\pi$ is a mutable encoding of original witnesses. Thus, a mutable BARG captures and enables computations over a batch proof $\pi$. We also study new privacy notions for mutable BARGs, guaranteeing that a mutated proof hides all non-trivial information. Such mutable BARGs are a naturally good fit for many privacy sensitive applications. Our main contributions can be summarized as introducing the general concept of mutable BARGs, identifying new non-trivial classes of feasible mutations over BARGs, designing new constructions for mutable BARGs satisfying mutation privacy for these classes from standard cryptographic assumptions, and developing applications of mutable BARGs to advanced signatures such as homomorphic signatures, redactable signatures, and aggregate signatures. Our results improve state-of-the-art known for many such signature systems either in terms of functionality, efficiency, security, or versatility (in terms of cryptographic assumptions).