[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.
The key mathematical object at the heart of tropical cryptography is the tropical semiring
(also known as the min-plus algebra), or a generalization thereof.
as the additive identity, these binary operations on