Pedersen Commitment Encryption for Faster Zero-Knowledge Proofs
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Solution Overview
Problem
Existing zero-knowledge proof algorithms like zk-SNARK require complex cryptographic operations, increasing circuit size and proof generation time, which hampers practicality in encryption technologies.
Innovation Solution
An encryption method using Pedersen commitment to generate cypher texts and a decryption method utilizing pairing functions to efficiently decrypt messages, leveraging Pedersen commitments and zero-knowledge proofs for rapid verification.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If complex cryptographic operations are used in encryption technologies, then security and privacy are improved, but circuit size increases and proof generation time increases
Solution Approach 1:
The patent changes the cryptographic parameters by using Pedersen commitment scheme with specific group elements (g1, g2, h1, h2) and pairing-friendly curves. This parameter selection enables the encryption to achieve security while maintaining circuit efficiency and reducing proof generation time through optimized cryptographic operations.
Solution Approach 2:
The patent replaces traditional complex cryptographic mechanisms with a pairing-based cryptographic system. By using bilinear pairings and Pedersen commitments, the system achieves the same security goals with simpler circuit operations and faster proof generation, substituting the mechanical complexity of traditional encryption with more efficient mathematical operations.
2Reliability
If complex cryptographic operations are used in encryption technologies, then security and privacy are improved, but proof generation time increases
Solution Approach 1:
The patent optimizes proof generation time by carefully selecting cryptographic parameters including pairing-friendly curves and Pedersen commitment parameters. These parameter choices enable faster verification and generation of zero-knowledge proofs while maintaining security, directly addressing the time efficiency requirement.
Solution Approach 2:
The patent substitutes traditional time-consuming cryptographic verification mechanisms with pairing-based verification. The use of bilinear pairings allows for efficient verification of encrypted data and zero-knowledge proofs, significantly reducing proof generation and verification time compared to conventional cryptographic approaches.
3Loss of time
If Pedersen commitment is used in encryption, then proof generation time is reduced, but cryptographic operation complexity remains
Solution Approach 1:
The patent makes the Pedersen commitment scheme serve multiple functions simultaneously: it provides encryption, enables zero-knowledge proofs, and facilitates efficient verification. By designing the system where the same commitment structure serves multiple cryptographic purposes, the patent reduces overall complexity despite the advanced mathematical operations required.
Solution Approach 2:
The patent merges the encryption operation with the commitment scheme, so that the Pedersen commitment serves as both the encryption mechanism and the basis for zero-knowledge proofs. This consolidation eliminates the need for separate encryption and proof-generation systems, reducing overall cryptographic operation complexity while maintaining fast proof generation.
Data Source
AI summary
The present invention is an encryption method based on identification using a Pedersen commitment and a decryption method corresponding to the same. An encryption method of a message based on identification, performed by at least one processor, includes steps of receiving a public parameter and a public key, randomly determining an encryption constant, parsing a plurality of parameters from the public parameter, calculating a first cypher text and a second cypher text by using the plurality of parameters, the encryption constant, and the message, parsing an ID value including a plurality of bits from the public key, calculating a third cypher text by using the ID value, and outputting the first cypher text, the second cypher text, and the third cypher text. At least one of the first cypher text, the second cypher text, and the third cypher text has a Pedersen commitment format.