Homomorphic Encryption for Zero-Knowledge Proof Efficiency
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Solution Overview
Problem
The existing succinct non-interactive zero-knowledge proof (zk-SNARK) systems face inefficiencies due to the inclusion of complex cryptographic operations in the ciphertext generation process, leading to impractical proof times and large proof key sizes, as they require all circuit inputs for both attribute proof and ciphertext generation.
Innovation Solution
A homomorphic encryption method is developed that separates the encryption process from the zero-knowledge proof circuit input, dividing messages into blocks, generating ciphertext through exponentiation of a generator, and using a common reference string to facilitate efficient proof verification and rerandomization, thereby enabling efficient zero-knowledge proof without exposing secret keys.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the ciphertext generation process is included in the zero-knowledge proof circuit input, then the attribute proof can be verified, but the proof time and proof key size increase significantly
Solution Approach 1:
The patent segments the encryption process into a separate setup phase and a proof phase. The setup phase generates encryption keys and a common reference string (CRS) offline, while the proof phase only processes the actual message and generates the zero-knowledge proof. This segmentation separates the heavy cryptographic operations from the proof generation, reducing proof time while maintaining verification reliability.
Solution Approach 2:
The patent performs preliminary actions by pre-generating the common reference string (CRS) and encryption keys before the actual zero-knowledge proof is needed. The CRS is generated once during setup and can be reused for multiple proofs, eliminating the need to recompute encryption operations for each proof, thus significantly reducing proof time.
2Reliability
If the ciphertext generation process is included in the zero-knowledge proof circuit input, then the attribute proof can be verified, but the proof key size becomes impractically large
Solution Approach 1:
The patent divides the cryptographic components into two separate sets: a public CRS that is shared and reused, and a private key that is kept secret. The CRS includes public parameters that can be verified without including the full ciphertext generation process, reducing the proof key size while maintaining verification capability.
Solution Approach 2:
The common reference string (CRS) serves multiple functions: it is used for setting up the encryption scheme, verifying zero-knowledge proofs, and validating ciphertexts. By making the CRS universal and reusable across multiple operations, the patent eliminates the need to include redundant encryption parameters in each proof, significantly reducing proof key size.
3Reliability
If all circuit inputs including ciphertext generation are included in zk-SNARK, then complete proof can be provided, but the system becomes impractical due to large proof key size and long proof time
Solution Approach 1:
The patent extracts the ciphertext generation process from the zero-knowledge proof circuit. Instead of including all encryption operations in the proof circuit, the patent separates the encryption setup (key generation and CRS creation) from the proof generation. This extraction removes the complex ciphertext generation operations from the circuit input, making the system practical while maintaining complete proof capability through the separated CRS and key mechanisms.
Data Source
AI summary
Disclosed are homomorphic encryption method and apparatus specialized for zero-knowledge proof. The homomorphic encryption method specialized for zero-knowledge proof includes (a) dividing a message M into n message blocks; (b) generating a ciphertext CT by encrypting the n message blocks, wherein the ciphertext CT includes each encryption block for each of the n message blocks, and each encryption block includes the message block in the form Gim<sub2>i </sub2>of an exponentiation of a generator G; and (c) generating a zero-knowledge proof key π for the n message blocks by applying the n message blocks as inputs to a preset zero-knowledge proof algorithm.