Cryptanalysis of Schemes Based on Pseudoinverse Matrix  

作　　者：LIU Jinhui ZHANG Huanguo JIA Jianwei 

机构地区：[1]School of Computer, Wuhan University, Wuhan 430072,Hubei, China [2]Key Laboratory of Aerospace Information Security and Trusted Computing Ministry of Education, Wuhan 430072, Hubei, China

出　　处：《Wuhan University Journal of Natural Sciences》2016年第3期209-213,共5页武汉大学学报（自然科学英文版）

基　　金：Supported by the National Natural Science Foundation of China(61303212,61170080,61202386);the State Key Program of National Natural Science of China(61332019,U1135004);the Major Research Plan of the National Natural Science Foundation of China(91018008);Major State Basic Research Development Program of China(973 Program)(2014CB340600);the Natural Science Foundation of Hubei Province(2011CDB453,2014CFB440)

摘　　要：Advances in quantum computation threaten to break public key eryptosystems that are based on the difficulty of fac- torization or the difficulty of discrete logariths, although , no quantum algorithms have been found to be able to solve certain mathematical problems on non-commutative algebraic structures up to now. The proposed new quasi-inverse based cryptography scheme is vulnerable to a linear algebra attack based on the probable occurrence of weak keys in the generation process. In this paper, we illustrate that two of the quasi-inverse based cryptography are vulnerable to a structural attack and that it only requires polynomial time to obtain the equivalent keys for some given public keys. In addition, we conduct a detailed analysis on attack methods and provide some improved suggestions on these two schemes.Advances in quantum computation threaten to break public key eryptosystems that are based on the difficulty of fac- torization or the difficulty of discrete logariths, although , no quantum algorithms have been found to be able to solve certain mathematical problems on non-commutative algebraic structures up to now. The proposed new quasi-inverse based cryptography scheme is vulnerable to a linear algebra attack based on the probable occurrence of weak keys in the generation process. In this paper, we illustrate that two of the quasi-inverse based cryptography are vulnerable to a structural attack and that it only requires polynomial time to obtain the equivalent keys for some given public keys. In addition, we conduct a detailed analysis on attack methods and provide some improved suggestions on these two schemes.

关 键 词：CRYPTOGRAPHY post-quantum computational cryptography key exchange protocol CRYPTANALYSIS matrix decomposition 

分 类 号：TP305[自动化与计算机技术—计算机系统结构]