椭圆曲线上的信息论安全的可验证秘密共享方案

Information-theoretic secure verifiable secret sharing scheme on elliptic curve group

基于椭圆曲线上的双线性对技术,构造一种可验证秘密共享方案。该方案的信息率为2/3,与Pederson的方案(Crypto91)及相关方案相比,本方案在相同的安全级别下有较高的信息率,从而提高了秘密共享协议的效率。同时,理论上证明该方案是信息论安全的。最后,将上述方案推广到无可信中心的情况,设计了无可信中心的秘密共享方案。经分析表明,所提方案具有更高的安全性和有效性,能更好地满足应用需求。

Based on the bilinear pair on elliptic curves, a verifiable secret sharing （VSS） and distributed verifiable secret sharing were constructed. The information rate of the scheme is 2/3. Compared with Pederson＇s scheme （Crypto91） and the related schemes, the scheme is more efficient under the same security level. At the same time, the security of the scheme was proved theoretically. The result reveals that the scheme is information-theoretic security. Finally, the VSS has been extensions to the case without a dealer （or without a trusted center）. A distributive verifiable secret sharing based on bilinear pair was proposed. Analysis shows that these schemes are more secure and effective than others, and it can be more applicable in special situation.