**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 B\"{u}nz 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.

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

**Date: **received 4 Feb 2021

**Contact author: **mryoulin at gmail com

**Available format(s): **PDF | BibTeX Citation

**Version: **20210205:123809 (All versions of this report)

**Short URL: **ia.cr/2021/127

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