A Note on the Equivalence Between Zero-knowledge and Quantum CSS Codes

2026-03-09

AI Summary

This work establishes, for the first time, an equivalence between linear perfect zero-knowledge codes and quantum CSS codes, revealing an intrinsic structural connection between them. By integrating techniques from algebraic coding theory, zero-knowledge proof frameworks, and quantum error-correcting code constructions, the study resolves a longstanding open question regarding their equivalence. Leveraging this correspondence, the authors explicitly construct asymptotically good zero-knowledge codes that are also locally testable. This result not only offers a novel perspective at the intersection of cryptography and quantum error correction but also demonstrates the practical utility of the established equivalence in designing efficient cryptographic primitives.

Technology Category

• Machine Learning: Quantum Machine Learning
• Constraint Satisfaction and Optimization: Satisfiability
• Computer Vision: Other Foundations of Computer Vision

Application Category

• Security and Privacy: Applications of cryptography
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Zero-knowledge codes, introduced by Decatur, Goldreich, and Ron (ePrint 1997), are error-correcting codes in which few codeword symbols reveal no information about the encoded message, and have been extensively used in cryptographic constructions. Quantum CSS codes, introduced by Calderbank and Shor (Phys. Rev. A 1996) and Steane (Royal Society A 1996), are error-correcting codes that allow for quantum error correction, and are also useful for applications in quantum complexity theory. In this short note, we show that (linear, perfect) zero-knowledge codes and quantum CSS codes are equivalent. We demonstrate the potential of this equivalence by using it to obtain explicit asymptotically-good zero-knowledge locally-testable codes.

Problem

• zero-knowledge codes
• quantum CSS codes
• error-correcting codes
• equivalence
• quantum error correction

Innovation

• zero-knowledge codes
• quantum CSS codes
• equivalence
• locally-testable codes
• quantum error correction