Collaboration Encouraging Quantum Secret Sharing Scheme with Seal Property (2409.07863v1)

Abstract: A new concept of quantum secret sharing is introduced, in which collaboration among participants are encourage. And the dealer can ask the participants to send back their share and revoke the secret before a predefined date or event, i.e. so-called seal property. We also give two concrete constructions of CE-QSS-Seal (Collaboration-Encouraging Quantum Secret Sharing with Seal property) scheme. The first one is unconditional secure and achieve the optimal bound of a seal scheme. The second one improve the optimal bound of seal by introducing post-quantum secure computational assumption.

• The paper introduces a quantum secret sharing scheme that integrates collaboration incentives with a unique seal property.
• It details two constructions: one achieving unconditional security via GHZ-like states and another using public key encryption for post-quantum security.
• The scheme enhances cheat detection and revocability, thereby advancing secure and practical quantum communication protocols.

Analyzing the Collaboration-Encouraging Quantum Secret Sharing Scheme with Seal Property

The paper "Collaboration Encouraging Quantum Secret Sharing Scheme with Seal Property" by Xiaogang Cheng and Ren Guo brings forth innovative advancements in the domain of quantum secret sharing (QSS) by combining concepts of collaboration encouragement and the quintessential seal property. This essay explores the key contributions and the underlying implications of this work within the context of contemporary developments in quantum cryptography.

Introduction to Quantum Secret Sharing (QSS)

Secret sharing (SS) is a cryptographic technique where a secret is divided into multiple shares, distributed among participants, such that only specified subsets of participants (access structure) can reconstruct the secret. Recent research has extended SS to quantum secret sharing (QSS), which leverages quantum particles to encode shares enabling properties unattainable in classical SS due to the non-cloning theorem in quantum mechanics.

The Concept of CE-QSS-Seal Scheme

The authors propose a novel QSS framework termed as Collaboration-Encouraging Quantum Secret Sharing with Seal property (CE-QSS-Seal). This scheme introduces two distinctive properties:

1. Collaboration Encouragement (CE): The reconstruction of the secret becomes easier with increased participation, thus incentivizing collaborative behavior among parties.
2. Seal Property: The dealer has the ability to revoke the secret before a predetermined date or event by requiring participants to return their shares, which can confirm their honesty.

Construction of CE-QSS-Seal Scheme

Two specific constructions of CE-QSS-Seal are presented in the paper:

1. First Construction - Unconditional Security:
   • The scheme is based on generating an $n$-qubit quantum entangled state (GHZ-like state), where the secret can be reconstructed by measuring the entangled state in the computational basis.
   • The security bound achieved in this construction ensures that the probability of successful reconstruction diminishes exponentially with the number of missing participants. If any dishonest behavior is detected, the dealer can catch it with a probability of 50%, which is the optimal bound for quantum seals as noted in related research literature.
2. Second Construction - Post-Quantum Security:
   • This construction utilizes public key encryption (PKE) with certified deletion to enhance security beyond the conventional limits.
   • It significantly improves the honesty-checking mechanism, achieving nearly 100% probability of detecting dishonest behavior. This enhancement is achieved at the cost of relying on post-quantum cryptographic assumptions, thereby sacrificing unconditional security for computational security.

Theoretical and Practical Implications

Theoretical Implications:

• This work addresses the optimal bound of cheat-detection probability for quantum seals, providing both a matching unconditional secure scheme and an exceeding post-quantum secure scheme.
• The concept of CE in secret sharing could spearhead new research into collaborative cryptographic protocols where group efficacy is paramount.

Practical Implications:

• Enhanced security in practical implementations of quantum communication systems, especially in scenarios where revoking secrets might be necessary before critical deadlines.
• The potential application of post-quantum cryptographic techniques in other domains where quantum security paradigms are being adopted.

Future Directions

The authors hint at potential future work to extend their CE-QSS-Seal scheme beyond its current form. Specifically:

• Threshold Secret Sharing: Integrating CE-QSS-Seal into threshold secret sharing systems to improve their robustness and security.
• Efficiency and Security Enhancements: Refining the existing constructions to balance between performance overhead and security guarantees, especially within varied deployment environments.

Conclusion

In summary, the paper proposes a robust framework of CE-QSS-Seal that advances the domain of quantum cryptography by merging secret sharing with enhanced collaborative and seal properties. The introduction of post-quantum cryptographic techniques to improve security metrics while maintaining practical feasibility marks a significant step forward that future research can build upon to develop even more resilient and efficient cryptographic protocols.