Cryptanalysis of a GL(r,Zn)-Based Public Key System

Abdel Alim KAMAL  Amr YOUSSEF  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E95-A   No.4   pp.829-831
Publication Date: 2012/04/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E95.A.829
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Cryptography and Information Security
Keyword: 
general linear group,  cryptanalysis,  public key cryptography,  

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Summary: 
Keith Salvin presented a key exchange protocol using matrices in the general linear group, GL(r,Zn), where n is the product of two distinct large primes. The system is fully specified in the US patent number 7346162 issued in 2008. In the patent claims, it is argued that the best way to break this system is to factor n. Furthermore, for efficiency reasons, it is suggested to use r=2. In this letter, we show that this cryptosystem can be easily broken by solving a set of consistent homogeneous r2 linear equations in 2r unknowns over Zn.