中文摘要：

多变量公钥密码体制被认为是后量子时代的一种安全的密码体制备选方案。针对原始中间域多变量公钥加密体制不能抵抗高阶线性方程攻击，外部干扰的思想被引入了中间域多变量公钥体制。在基于外部干扰的签名方案的基础上，重构了一种新的外部干扰，提出了一种优化的基于外部干扰的签名方案。优化方案保持了原签名方案结构简单、求逆容易的性质，在保证安全性的同时，使得公私钥空间大大缩小。

英文摘要：

Multivariate public key cryptosystem is believed to be an ahernative secure cryptography scheme in the post-quantum age. For the original medium-field multivariate public key encryption cryptosystem cannot resist high order linear equation attack, external perturbation is introduced to the medium-field multivariate public key scheme. Based on the signature scheme with external perturbation, a new external perturbation is redesigned and an optimized medium-field signature scheme with external perturbation is proposed. The optimized scheme can keep a simple structure and an easy inversion of the signature scheme, guarantee the security, and reduce the space for the public and secret key greatly.