Open AccessKey recovery on several matrix public‐key encryption schemes
Author(s) -
Wang Houzhen,
Zhang Huanguo,
Tang Shaohua
Publication year - 2016
Publication title -
iet information security
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.308
H-Index - 34
eISSN - 1751-8717
pISSN - 1751-8709
DOI - 10.1049/iet-ifs.2015.0183
Subject(s) - public key cryptography , key (lock) , exponentiation , mathematics , encryption , matrix (chemical analysis) , finite field , scheme (mathematics) , key encapsulation , theoretical computer science , computer science , algebra over a field , key exchange , discrete mathematics , computer security , pure mathematics , mathematical analysis , materials science , composite material
Eight years ago, Pei et al . described a matrix public‐key encryption scheme based on the matrix factorisation over a finite field. Recently, Gu and Zheng also proposed a similar scheme based on the non‐abelian factorisation assumption. The security of these schemes is essentially based on a two‐side matrices exponentiation (TSME) problem. In this study, the authors show that the TSME problem is susceptible to a very efficient linearisation equations attack. Regardless of the public key parameters, the authors can easily find an equivalent key only in polynomial time (2 n 5 (log n +1)) from the public key alone, and thus it is very practical and can be implemented within less than 1/20 of a second on the recommended system parameters of the schemes.