基于二元多项式的秘密分享技术研究

摘要

At present most secret sharing schemes follow the realization idea of classic Shamir scheme, namely the unary polynomial based (k, n) threshold scheme. Such schemes inherit many advantages of Shamir scheme, such as simple thought, easy implementation, harmony of perfection and idealness and so on. However, still there is a defect in these schemes that their access structure is not rich enough, so that the popularization of secret sharing technology in practical applications is seriously limited. In view of this situation, the paper proposes a bivariate polynomial based secret sharing scheme. Besides possessing the various advantages of Shamir scheme, the access structure of the new scheme is greatly enriched. In addition, the new scheme can easily be introduced to image secret sharing, audio secret sharing as well as other fields.%当前大多数秘密分享方案的设计沿用了经典Shamir方案的实现思路,即基于一元多项式的(k,n)门限方案.此类方案继承了Shamir方案的诸多优点,如思路简洁便于实现、兼有完备性(Perfect)和理想性(Ideal)等.然而,这一类方案也有着准入结构不够丰富的缺陷,极大地限制了秘密分享技术在实际应用中的推广.针对这一情况,提出一种基于二元多项式的秘密分享方案,该方案兼有Shamir方案的诸多优点,而准入结构又得到了极大的丰富.此外,新方案很容易推广到图像秘密分享、音频秘密分享等领域.