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计算机工程 ›› 2010, Vol. 36 ›› Issue (18): 155-157. doi: 10.3969/j.issn.1000-3428.2010.18.053

• 安全技术 • 上一篇    下一篇

MFE多变量公钥改进方案分析

田 礼1,2,鲍皖苏1   

  1. (1. 解放军信息工程大学电子技术学院,郑州 450004;2. 解放军78179部队,四川 都江堰 611830)
  • 出版日期:2010-09-20 发布日期:2010-09-30
  • 作者简介:田 礼(1983-),男,硕士研究生,主研方向:多变量公钥密码;鲍皖苏,教授、博士生导师
  • 基金资助:
    国家自然科学基金资助项目(10501053)

Analysis of Improved MFE Multivariate Public Key Scheme

TIAN Li1,2, BAO Wan-su1   

  1. (1. Electronic Technology Institute, PLA Information Engineering University, Zhengzhou 450004, China; 2. PLA 78179 Unit, Dujiangyan 611830, China)
  • Online:2010-09-20 Published:2010-09-30

摘要: 对改进的中等域方程(MFE)多变量公钥方案进行分析,指出其存在的缺陷,即中等域规模较小、中心映射的输入变量容易被分割。针对该缺陷,将明文空间划分为2个正交的子空间,当从其中一个子空间随机取值时,中心映射的部分输入变量值被确定,从而可得到足够多的线性方程。这样攻击者能够容易地由密文求出明文,从而攻破该方案。

关键词: 多变量公钥密码, 量子计算, 中等域方程, 二阶线性化方程

Abstract: This paper analyzes an improved Medium Field Equation(MFE) multivariate public key scheme, and finds some shortages of the design. Namely, the order of the medium field is very small, and input variables of the central map can be partitioned into two parts. Based on the above shortages, it can partition the space of plaintext into two disjointed subspaces. When it selects randomly an element in one subspace, a part of input variables of the central map are fixed, then it can get sufficient linear functions. The plaintext can be recovered from the ciphertext easily, hence the improved scheme is broken.

Key words: multivariate public key cryptography, quantum computation, Medium Field Equation(MFE), Second Order Linearization Equation(SOLE)

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