Tropical cryptography
In tropical analysis, tropical cryptography refers to the study of a class of cryptographic protocols built upon tropical algebras. In many cases, tropical cryptographic schemes have arisen from adapting classical 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, and the problem of solving systems of tropical polynomial equations has been shown to be NP-hard.Basic Definitions
The key mathematical object at the heart of tropical cryptography is the tropical semiring , or a generalization thereof. The operations are defined as follows for :
It is easily verified that with as the additive identity, these binary operations on form a semiring.
