一个建立在整数环上的秘密共享方案

自A.Shamir和G.R.Blakley于1979年各自独立地提出“秘密共享”的思想及方法以后,现已出现了多种秘密共享方案。这些方案可适应不同的环境要求,然而,这些方案都是在域上建立的,当所面临问题的背景结构不构成域时会遇到麻烦。本文提出了一种新的秘密共享方案,该方案直接在整数环Z上实现,不需要对环Z作任何扩张,因而具有较高的有效性。其安全性基于Hash函数的安全性和大整数分解的难解性。

A Secret Sharing Scheme Defined over the Integer Ring Z

Since the idea and methods of "secret sharing" were proposed independently by Shamir and Blakley in 1979, various schemes of secret sharing have been presented. However, these schemes are all defined over field. When the background structures of the problems we dealt with are not fields, it will meet with troubles to implement the schemes. This paper presented a new secret sharing scheme. This scheme is defined over the integer ring Z, and no extension to the ring Z is needed. Therefore, the scheme presented in this paper is more efficient in a way. The scheme's security is based on the security of Hash functions and the intractability of the problem of decomposed large integers.