Cryptoanalysis of a public key exchange based on circulant matrix over digital semiring

We present a cryptanalysis of a key exchange protocol based on the digital semiring. For this purpose, we find the maximal solution of a linear system over such semiring, and use the properties of circulant matrix to demonstrate that the protocol is vulnerable. Specifically, we provide an efficient attack that recovers the shared secret key from publicly exchanged information for any instance of the digital semiring in polynomial time.