Paper 2021/127

Cuproof: A Novel Range Proof with Constant Size

Cong Deng and Xianghong Tang and Lin You and Gengran Hu

Abstract

By combining inner-product and Lagrange's four-square theorem, we structure a range proof scheme which is called Cuproof. The scheme of Cuproof would make a range proof to prove that a secret number $v \in [a,b]$ without exposing redundant information of $v$. In Cuproof, the communication cost and the proof time is constant. Once the interval of range proof is large, the scheme of Cuproof would show better. Zero-knowledge proof is widely used in blockchain. For example, zk-SNARK is used by Zcash as its core technology in identifying transactions. Up to now, various range proofs have been proposed as well their efficiency and range-flexibility are enhanced. Bootle et al. firstly used inner product method and recursion to an efficient zero-knowledge proof. Then, Benediky Bünz et al. came up with an efficient zero-knowledge argument called Bulletproofs which convinces the verifier that a secret number lies in $[0,\, 2^{n}]$. The scheme of Cuproof is based on the scheme of Bulletproofs.