Practical Cryptanalysis of a Public Key Cryptosystem Based on the Morphism of Polynomials Problem

作     者：Jaihui Chen Chik How Tan Xiaoyu Li 

作者机构：School of Computer Guangdong University of Technology Guangzhou 510006 China Temasek Laboratories NationalUniversity of Singapore Singapore 117411 Singapore the School of Computer Zhengzhou University of Aeronautics Zhengzhou 450046 China 

出 版 物：《Tsinghua Science and Technology》 (清华大学学报（自然科学版（英文版）)

年 卷 期：2018年第23卷第6期

页      面：671-679页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：cryptanalysis post-quantum cryptography multivariate public key cryptosystems morphism ofpolynomials problem 

摘      要：Multivariate Public Key Cryptography （MPKC） has intensively and rapidly developed during the past three decades. MPKC is a promising candidate for post-quantum cryptography. However, designing it is universally regarded as a difficult task to design a secure MPKC foundation scheme, such as an encryption scheme and key exchange scheme. In this work, we investigate the security of a new public key cryptosystem that is based on the Morphism of Polynomials （MP）. The public key cryptosystem proposed by Wang et al. （Wuhan University, China） comprises a key exchange scheme and encryption scheme. Its security can be provably reduced to the hardness of solving a new difficult problem, namely, the Decisional Multivariate Diffie Hellman （DMDH） problem. This problem Js a variant of the MP problem, which is difficult to solve by random systems. We present a proposition that reduces the DMDH problem to an easy example of the MP problem. Then, we propose an efficient algorithm for the Key Recover Attack （KRA） on the schemes of the public key cryptosystem. In practice, we are able to entirely break the cryptosystem＇s claimed parameter of 96 security levels in less than 17.252 s. Furthermore, we show that finding parameters that yield a secure and practical scheme is impossible.