Cuproof: Range Proof with Constant Size.

Area of Science:

• Cryptography
• Blockchain Technology
• Information Security

Background:

• Zero-Knowledge Proofs (ZKPs) are crucial for privacy in blockchains, exemplified by zk-SNARKs in Zcash.
• Existing range proofs, like Bulletproofs, offer improved efficiency but can still have communication overhead.
• The need for efficient and flexible range proofs remains a key challenge in privacy-preserving technologies.

Purpose of the Study:

• To propose Cuproof, a new range proof scheme for Zero-Knowledge Proofs.
• To demonstrate Cuproof's ability to prove a secret number within a specified range [a,b] without revealing the number.
• To achieve constant communication, proving, and verification times, surpassing existing schemes like Bulletproofs.

Main Methods:

• Combining the inner-product technique with Lagrange's four-square theorem.
• Developing a novel range proof scheme, termed Cuproof.
• Analyzing communication costs, proving time, and verification time.

Main Results:

• Cuproof enables proving a secret number 'v' lies within a range [a,b] without exposing 'v'.
• Achieved constant communication cost, independent of the range size or security parameters.
• Demonstrated constant proving and verification times, significantly improving upon schemes like Bulletproofs (6+2logκ).

Conclusions:

• Cuproof presents a practical and efficient method for enhancing privacy and information security in blockchain applications.
• The constant-time properties of Cuproof make it highly suitable for resource-constrained environments and large-scale deployments.
• This scheme offers a significant advancement in the field of Zero-Knowledge Proofs and privacy-preserving computations.