Notes

• Multi-party coin-tossing protocols combine cryptography and game theory to generate unbiased random bits.
• Classical cryptography: strong fairness achievable with honest majority in statistical setting, impossible with dishonest majority.
• Game-theoretic approaches can sometimes circumvent cryptographic lower bounds via weak equilibrium guarantees.
• Main finding: no statistically secure game-theoretic protocol for n parties with t≥n/2 corruptions (except n=4 special case).
• Without broadcast, no computationally secure game-theoretic protocol for t≥n/3 and polynomial rounds (except n=6 special case).
• Work completes the statistical feasibility landscape, defining boundaries of game-theoretic fairness in coin tossing.

• 多方掷币协议研究结合了密码学和博弈论，旨在生成无偏随机比特
• 经典密码学结果：统计设置下，诚实多数可实现强公平性，不诚实多数则不可能
• 博弈论方法有时能通过弱均衡保证规避密码学下界，但在统计设置中优势有限
• 主要结论：对于n方且t≥n/2腐败，不存在统计安全的博弈论掷币协议（除n=4特殊情况）
• 无广播设置下，对于t≥n/3且多项式轮复杂度，不存在计算安全的博弈论协议（除n=6特殊情况）
• 研究完善了统计可行性图景，明确了博弈论公平性在多方掷币中的边界