基于中国剩余定理的秘密共享方案

摘要

利用中国剩余定理、椭圆曲线离散对数问题(ECDLP)、双线性变换和强RSA假设,提出了一种新的可验证秘密共享方案.该方案具有能够检测出秘密分发者和可信中心的诚实性,检测出系统中参与者的欺诈行为;利用椭圆曲线,结合双线性对技术,不仅降低了系统的计算成本,而且实现了方案的可验证性;利用强RSA假设,实现方案的前向安全性,即使敌手掌握第j个时间段的子秘密,也无法获取之前时间段关于共享秘密的任何信息,增强了系统的安全性.%By utilizing the Chinese remainder theorem, elliptic curve discrete logarithm problem (ECDLP), bilinear transformation and strong RSA hypothesis, a new verifiable secret sharing scheme is proposed. The scheme is capable of detecting the integrity of secret distributors, trusted centers and fraudulent behavior in the system; by using elliptic curve and bilinear pair technology, the computational cost of the system could be reduced and the verification of the scheme realized; by using strong RSA assumption the forward security of the scheme be achieved, even if the opponent grasps the sub-secret of the j-th time period, he can't get any information about the shared secret in the previous time period, thus enhancing the security of the system.