Zero-Knowledge Prover for Fast Verification of Program Execution
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Solution Overview
Problem
Existing zero knowledge proof (ZKP) systems face challenges in efficiently proving the execution of complex computations, particularly in Von Neumann architectures, due to impractical verification times and reliance on non-post-quantum cryptographic primitives, limiting their scalability and practical application.
Innovation Solution
A recursive ZKP system is developed that utilizes zk-STARK-based methods with optimized arithmetic circuits, including efficient representation of processor execution and memory operations, and accelerated cryptographic hashing, such as SHA-256, to enable provable execution of compilable programs in a post-quantum secure manner.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional ZKP systems are used to prove execution of complex computations, then the proof of correctness can be achieved, but the verification time becomes impractically long
Solution Approach 1:
The execution trace is divided into sequential segments representing individual instruction executions. Each segment is independently verified through arithmetic constraints, allowing the verification process to be broken down into manageable units that can be processed efficiently in sequence rather than as one monolithic proof.
Solution Approach 2:
The patent replaces traditional cryptographic verification mechanisms with arithmetic circuit evaluation. By translating the verification problem into polynomial arithmetic over finite fields and using Fast Fourier Transform (FFT) for efficient evaluation, the system achieves sub-linear verification time while maintaining cryptographic security.
2Reliability
If cryptographic primitives are used for security in ZKP systems, then post-quantum security is achieved, but the complexity of the system increases
Solution Approach 1:
The patent extracts and eliminates quantum-vulnerable cryptographic primitives (such as elliptic curve cryptography) from the ZKP system. By designing the system to rely solely on hash functions and polynomial arithmetic over finite fields, it achieves post-quantum security by removing the vulnerable components rather than adding quantum-resistant ones.
Solution Approach 2:
The system changes the cryptographic parameters from traditional discrete logarithm-based primitives to hash function-based constructions. By using SHA-256 and other cryptographic hash functions in place of elliptic curve operations, the system achieves quantum resistance while simplifying the overall cryptographic architecture.
3Reliability
If detailed execution traces are generated for verification, then correctness can be proven, but the amount of data to be processed increases
Solution Approach 1:
The prover pre-computes and commits to the entire execution trace before verification begins. By organizing the trace data in advance and computing commitment values (hashes) for each segment, the verification process can efficiently check correctness without handling the full raw trace data, reducing the effective data volume during verification.
Solution Approach 2:
Instead of transmitting and processing the complete execution trace, the system uses commitment copies (hash commitments) that represent the entire trace. The verifier works with these compact representations and only requests specific portions of the actual trace data when needed for targeted verification, dramatically reducing data transmission and processing requirements.
Data Source
AI summary
Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for implementing a zero knowledge prover are disclosed. In one aspect, a method includes the actions of executing a software program. The method further includes storing an execution trace that includes, for each address in memory, a value at each clock cycle during execution of the software program. The method further includes generating a sorted execution trace by sorting the execution trace. The method further includes determining a constraint for given values in the memory at adjacent clock cycles. The method further includes determining whether the sorted execution trace complies with the constraint and whether the sorted execution trace is a permutation of the execution trace. The method further includes providing, for output, data indicating whether the software program executed correctly while preventing outputting data included in the execution trace or the sorted execution trace.