基于新型秘密共享方法的高效 RSA 门限签名方案

A New RSA Threshold Group Signature Scheme Based on Modified Shamir's Secret Sharing Solution

针对传统的门限RSA 签名体制中需对剩余环Z_(?)_(N)中元素求逆(而环中元素未必有逆)的问题,该文首先提出一种改进的Shamir 秘密共享方法。该方法通过在整数矩阵中的一系列运算来恢复共享密钥。由于其中涉及的参数均为整数,因此避免了传统方案中由Lagrange 插值公式产生的分数而引起的环Z_(?)_(N)中的求逆运算。然后基于该改进的秘密共享方法给出了一个新型的门限RSA Rivest Shanair Atleman 签名方案。由于该方案无须在任何代数结构(比如Z_(?)_(N)中对任何元素求逆,也无须进行代数扩张,因此在实际应用中更为方便、有效。

In order to avoid computing elements＇ inverses in the ring Zφ（N）since they may not exit, a new RSA threshold group signature scheme based on modified Shamir＇s secret sharing solution is proposed. Differing from the old schemes based on Lagrange interpolation solution in which fraction arithmetic operations leading to the computation of elements＇ inverses in Zφ（N） should be handled, this new scheme reconstructs its group secret key through series of integer arithmetic operations in integral matrixes, by which it can efficiently avoid the computation of any element＇s inverse in any algebraic structure （such as Zφ（N））, and can further avoid algebraic extensions. Therefore, this new scheme is more efficient and convenient than the old ones.