基于Hermite插值的门限多秘密共享方案

Hermite Interpolation-Based Threshold Multi-Secret Sharing Scheme

(t,n)门限共享方案是在n个参与者之间分发信息的一种加密机制,广泛应用于信息安全领域。为此,提出了基于Hermite插值的多项式的门限多秘密共享HITMSS(Hermite interpolation-based threshold multi-secret sharing)方案。利用椭圆曲线上的离散对数和双线性映射特性,实现了HITMSS方案的可验证性。HITMSS方案无需安全信道,并且参与者能够自行选择自己的份额,避免了分发者实施欺骗攻击的可能。同时,HITMSS方案能够动态地改变秘密数量,并且具有多重可用特性,降低了秘密分发的开销。与同类方案相比,提出的HITMSS方案复杂度低,安全性能高。

（ t, n） threshold secret sharing is a cryptographic mechanism to divide and disseminate information a- mong n participants, which is widely used in the field of information security. Therefore, Hermite interpolation- based threshold multi-secret sharing （HITMSS） scheme is proposed. Using the properties of discrete logarithm over elliptic curves and bilinear maps, a verifiable HITMSS scheme has been created in which there is no need for a secure channel and the participants can choose their own share. This feature avoids a possible of dealers cheating. The proposed method can change the number and value of the secrets as well as the threshold dynamicly. In addition, it has the multi-usability and reduces the cost of secret distribution. Compared with similar schemes, the proposed HITMSS scheme has low complexity and high security.