新的安全分布式n个秘密乘积共享方案

由于Shamir的秘密共享方案并不具有乘法的同态性质, 因此针对安全分布式乘法计算中利用传统的Shamir线性多项式进行n个秘密乘积共享时需要不断调用两方秘密乘积子协议的缺点，首先用哥德尔数对保密数据进行编码，接着利用这种具有乘法同态的编码方法和一种加法同态承诺方案，实现了一种新的安全分布式一次性共享n个秘密乘积的方案，并证明了即使有恶意的参与者存在时，此方案仍为安全的。分析表明，本方案不但简单可行，而且相比传统方案效率明显提高。

New secure distributed secret sharing scheme of n product

Since Shamir’s secret sharing scheme does not have the property of the multiplicative homomorphism，an encoding method is utilized for privacy-preserving data to overcome the drawbacks in secure distributed multiplication calculation when using traditional Shamir’s polynomial to share the product of n secrets.Using this encoding method with multiplicative homomorphism and a commitment scheme supporting additive homomorphism，a new secure distributed secret sharing scheme of n product in one session is implemented and the proposed scheme is secure under the presence of malicious participants.The analysis shows that proposed scheme is not only more simple and feasible but also more efficient than previous schemes.