【摘要】 在经典的Shamir秘密共享方案中,秘密分发者把秘密s分为n个影子秘密并分发给持有者;其中任意不少于t个影子秘密均能恢复秘密s,少于t个影子秘密则得不到秘密s的任何信息。现实的秘密恢复过程中可能存在超过t个参与者的情形。因此,在Shamir的秘密共享方案基础上讨论此种情形下秘密共享问题,通过引入影子秘密的线性组合——拉格朗日因子来恢复秘密,并进一步将其扩展为一个多秘密共享方案。理论分析与仿真实验表明:改进算法在同样复杂度条件下既保证影子秘密的安全,又能阻止欺骗者得到秘密,提高了整体安全性。更多还原

【Abstract】 In Shamir’s secret sharing scheme,the dealer divided the secret s into n shadows and distributed it to shareholders in such a way that any t or more than t shadows can recover this secret,while fewer than t shadows cannot obtain any information about the secret s.During the actual secret recovery process,there exist other cases with more than t participants.The case of secret sharing problem was discussed based on Shamir’s secret sharing scheme and reconstructs the secret by introducing a linear combination of shadows—Lagrange factor.Then,the improved algorithm of key distribution and recovery was proposed and extended to a multi-secret sharing scheme.Theoretical analysis and simulation show that the improved scheme improves its security under the same conditions of complexity.更多还原