In tropical analysis, tropical cryptography refers to the study of a class of cryptographic protocols built upon tropical algebras.[1] In many cases, tropical cryptographic schemes have arisen from adapting classical (non-tropical) schemes to instead rely on tropical algebras. The case for the use of tropical algebras in cryptography rests on at least two key features of tropical mathematics: in the tropical world, there is no classical multiplication (a computationally expensive operation), and the problem of solving systems of tropical polynomial equations has been shown to be NP-hard.
(R\cup\{infty\}, ⊕ , ⊗ )
x,y\inR\cup\{infty\}
x ⊕ y=min\{x,y\}
x ⊗ y=x+y
It is easily verified that with
infty
R\cup\{infty\}