Keith Salvin presented a key exchange protocol using matrices in the general linear group, GL(r,Z_n), 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 Z_n.
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