中文摘要：

为了避免单点失效引起安全隐患，通常采用门限技术来增强密码系统的可靠性。其中，如何构造有效的容错学习（ learing with error， LWE）求逆算法的门限方案被遗留为公开问题。提出了LWE求逆算法的门限方案T-LWE-Invert，该方案利用有限群上的秘密分享机制解决了陷门分享和LWE逆的计算问题。理论分析表明， T-LWE-Invert门限方案具有零知识可模拟性，并且与标准的LWE求逆算法具有相同的安全性。

英文摘要：

To solve security risks caused by single-point failures, it is usually preferred to apply secret sharing/threshold technique to strengthen the reliability of cryptosystems.How to construct efficient threshold scheme for LWE inversion be left as open problem.A threshold scheme for LWE inversion, called T-LWE-Invert was first proposed, and it solves trapdoor share and it computes the LWE inversion by secret sharing scheme for additive group.Theoretical analysis indi-cates that this scheme achieves zero-knowledge simulatablity, so it is as secure as original LWE inversion algorithm.