We analyse some public keys cryptography in the classical algebra and tropical algebra. Currently one of the most secure system that is used is public key cryptography, which is based on discrete logarithm problem. The Dilfie-Helman public key and Stickel’s key ex-change protocol are the examples of the application of discrete logarithm problem in public key cryptography. This thesis will examine the possibilities of public key cryptography implemented within tropical mathematics. A tropical version of Stickel’s key exchange protocol was suggested by Grigoriev and Sphilrain We suggest some modifications of this scheme use commuting matrices in tropical algebra and discuss some possibilities of at- tacks on them. We also generalise Kotov and Ushakov’s attack and implement in our new protocols. In 2019, Grigoriev and Sphilrain [14] generated two new public key exchange protocols based on semidirect product. In this thesis we use some properties of CSR and ultimate periodicity in tropical algebra to construct an efficient attack on one of the protocols suggested in that paper