Cryptanalysis of Tropical Encryption Scheme Based on Double Key Exchange

A tropical encryption scheme is analyzed in this paper, which uses double key exchange protocol (KEP). The key exchange protocol is divided into two stages: The first stage of the key exchange uses matrix power function in a tropical semiring; the obtained shared key at the first phase of the key exchange serves as an input for the second phase. This paper proves that the common secret key of the first key exchange phase can be obtained by solving linear equations, and when the order of the matrix is 50, the time to solve the shared key is less than 1 second. Finally, the common secret key of the second phase can be obtained through KU attack and common secret key of the first key exchange. So the protocol isn’t secure.