Paper 2021/127

Cuproof: A Novel Range Proof with Constant Size

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


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 Bünz 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.

Available format(s)
Cryptographic protocols
Publication info
Preprint. MINOR revision.
BlockchainZero-Knowledge proofRange proofInner-productBulletproofs.
Contact author(s)
mryoulin @ gmail com
2021-05-07: revised
2021-02-05: received
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Creative Commons Attribution


      author = {Cong Deng and Xianghong Tang and Lin You and Gengran Hu and Shuhong Gao},
      title = {Cuproof: A Novel Range Proof with Constant Size},
      howpublished = {Cryptology ePrint Archive, Paper 2021/127},
      year = {2021},
      note = {\url{}},
      url = {}
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