Pedersen Commitment Encryption for Zero-Knowledge Proof Speed
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Solution Overview
Problem
Existing zero-knowledge proof algorithms like zk-SNARK require complex cryptographic operations, leading to increased circuit size and prolonged proof generation times, which hampers practicality in encryption processes.
Innovation Solution
An encryption method using Pedersen commitment to generate cypher texts and a decryption method utilizing pairing functions to efficiently decrypt messages, leveraging identification-based keys and zero-knowledge proofs for rapid verification.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If complex cryptographic operations are used in encryption, then security is improved, but proof generation time increases linearly with circuit size
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 circuit to be optimized for faster proof generation while maintaining security through the mathematical properties of the Pedersen commitment and pairing operations.
Solution Approach 2:
The encryption process is segmented into distinct cryptographic operations: Pedersen commitment calculation, pairing function applications, and exponentiation operations. By dividing the encryption circuit into these modular segments, the patent enables parallel computation and optimization of each segment, reducing the overall proof generation time while maintaining security.
2Reliability
If complex cryptographic operations are used in encryption, then encryption security is improved, but device complexity increases
Solution Approach 1:
The patent uses universal pairing-friendly cryptographic primitives that can serve multiple functions: Pedersen commitment for hiding, pairing operations for verification, and exponentiation for key derivation. This multi-functionality reduces the need for separate cryptographic circuits, thereby reducing overall device complexity while maintaining strong encryption security.
Solution Approach 2:
The patent leverages the mathematical copying properties of pairing operations where the same pairing function can be applied to different input combinations (e.g., e(g1, g2), e(h1, h2), e(g1, h2)) to derive multiple cryptographic values. This allows the circuit to reuse the same computational structure multiple times, reducing complexity compared to implementing separate circuits for each cryptographic operation.
Data Source
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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.