Tropical cryptography and implementation of matrix one-way function

In this article we re-announced about two versions of the matrix one-way function (However, one - one option is new ). With respect to the issue of relevance, we repeat, that the main advantage of the matrix one-way function is high speed operation. The first variant is the result of the natural development of cryptography and is associated with the use in the cryptography of new tropical arithmetic operations. The results their applications may be named as "Tropical Cryptography." But at the same time, regardless of the general algebraic values "Tropical Cryptography", it is the fact, that the construction of multiplicative groups, based on the our tropical operations, may be accepted as an integral part of the realization of the matrix one-way function. Therefore, its adoption and an implementation can be associated with its recognition. The second option , a new option - it is our long-term studies analyzing the results of our matrix one-way function and analysis related to tropical cryptography , and using them for a certain period of time (similar to those as ElGamal , in 1985, used the algorithm Diffi - Hellman for a certain period of time to implement his algorithm). Nevertheless , it should be noted that the tropical cryptography will not lead to a loss of speed of the matrix one-way function, as the tropical cryptography is applied for a certain time interval when the our matrix one- way function is used for key-exchanged via an open channel (Or other actions).