## Cryptology ePrint Archive: Report 2021/127

Cuproof: A Novel Range Proof with Constant Size

Cong Deng and Xianghong Tang and Lin You and Gengran Hu and Shuhong Gao

Abstract: Zero-knowledge proof is widely used in blockchains. For example, zk-SNARK is used by Zcash as its core technology in identifying transactions. Up to now, various range proofs have been proposed, and their efficiency and range-flexibility are enhanced. Bootle et al. used inner product method and recursion to make an efficient zero-knowledge proof. Then, Benediky B\"{u}nz et al. came up with an efficient zero-knowledge proof scheme called Bulletproofs which can convince the verifier that a secret number lies in $[0,2^{\kappa}-1]$. 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, all the communication cost, the proving time and the verification time are constant. When the interval of the range proof is large, our Cuproof would show much better.

Category / Keywords: cryptographic protocols / Blockchain, Zero-Knowledge proof, Range proof, Inner-product, Bulletproofs.

Date: received 4 Feb 2021, last revised 7 May 2021

Contact author: mryoulin at gmail com

Available format(s): PDF | BibTeX Citation

Short URL: ia.cr/2021/127

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