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Experimental asymmetric relativistic zero-knowledge proofs with unconditional security.
Chen-Xun Weng1,2,3, Ming-Yang Li1,2, Nai-Rui Xu4
1National Laboratory of Solid State Microstructures and School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, China.
Nature Communications
|May 26, 2026
Summary
We developed an efficient quantum-safe zero-knowledge proof (ZKP) using relativity, improving practical feasibility for secure digital transactions. This new relativistic ZKP protocol offers robust privacy against quantum attacks in the internet environment.
Area of Science:
- Cryptography
- Quantum Information Science
- Theoretical Computer Science
Background:
- Zero-knowledge proofs (ZKPs) are crucial for privacy in digital economies but classical methods face quantum threats.
- Existing quantum-sound ZKPs are computationally intensive and impractical due to high round complexity.
- Relativistic ZKPs offer a potential solution but require efficient protocol designs.
Purpose of the Study:
- To develop an efficient asymmetric relativistic zero-knowledge proof (ZKP) protocol.
- To ensure quantum soundness for cryptographic applications in distrustful environments.
- To enhance the practical feasibility of ZKPs against quantum attacks.
Main Methods:
- Developed an asymmetric relativistic ZKP protocol utilizing relativistic bit commitments.
- Proved quantum soundness by establishing a connection to the nonlocal Clauser-Horne-Shimony-Holt (CHSH) game.
- Implemented a proof-of-principle experiment to demonstrate practical performance.
Main Results:
- The protocol exhibits a linear relationship between round complexity and the number of edges, enhancing feasibility.
- Experimental results show interactive rounds completed in approximately 0.22 seconds.
- The experiment required an overall randomness cost of 430.81 MB.
Conclusions:
- The developed relativistic ZKP protocol is efficient and quantum-sound, offering practical cryptographic solutions.
- Integrating special relativity and quantum theory shows significant potential for trustless cryptography.
- This work paves the way for robust, quantum-resistant applications in the internet environment.
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