International Association
for Cryptologic Research

Zero-knowledge range arguments are a fundamental cryptographic primitive that allows a prover to convince a verifier of the knowledge of a secret value lying within a predefined range. They have been utilized in diverse applications, such as confidential transactions, proofs of solvency and anonymous credentials. Range arguments with a transparent setup dispense with any trusted setup to eliminate security backdoor and enhance transparency. They are increasingly deployed in diverse decentralized applications on blockchains. One of the major concerns of practical deployment of range arguments on blockchains is the incurred gas cost and high computational overhead associated with blockchain miners. Hence, it is crucial to optimize the verification efficiency in range arguments to alleviate the deployment cost on blockchains and other decentralized platforms. In this paper, we present VeRange with several new zero-knowledge range arguments in the discrete logarithm setting, requiring only $c \sqrt{N/\log N}$ group exponentiations for verification, where $N$ is the number of bits to represent a range and $c$ is a small constant, making them concretely efficient for blockchain deployment with a very low gas cost. Furthermore, VeRange is aggregable, allowing a prover to simultaneously prove $T$ range arguments in a single argument, requiring only $O(\sqrt{TN/\log (TN)}) + T$ group exponentiations for verification. We deployed {\tt VeRange} on Ethereum and measured the empirical gas cost, achieving the fastest verification runtime and the lowest gas cost among the discrete-logarithm-based range arguments in practice.