Game Theory-Based Rational Secret Sharing Scheme with Quantum Resistant

Traditional threshold secret sharing scheme provides a mechanism to prevent the over-concentration of secrets while allowing for flexibility through the distribution and reconstruction of sub-secrets. However, this approach often simplifies participant behavior into categories of complete honesty or continuous deceit, neglecting the nuances of rational decision-making. To address this limitation, the rational secret sharing scheme merges threshold secret sharing with game theory, where each participant is considered rational and acts solely in self-interest. Nonetheless, existing schemes encounter challenges such as the prisoner's dilemma and the inability to reconstruct secrets due to the prioritization of individual interests. To mitigate these issues, our proposed scheme integrates a reward and punishment mechanism that balances short-term gains with long-term incentives, effectively deterring malicious behavior among participants. Moreover, traditional solutions based on elliptic curves and bilinear pairs lack resilience against quantum attacks. In response, our solution incorporates lattice-based cryptography to enhance security in the face of quantum threats. Additionally, we introduce an attribute access control tree to empower secret dealers in selecting suitable participants based on attribute restrictions, ensuring a more flexible, convenient, and secure rational secret sharing plan. This comprehensive approach improves participant selection and strengthens security measures in secret sharing scenarios.