Categories
  Encyclosphere.org ENCYCLOREADER
  supported by EncyclosphereKSF

Tropical cryptography

From HandWiki - Reading time: 1 min

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.

Basic Definitions

The key mathematical object at the heart of tropical cryptography is the tropical semiring (R{},,) (also known as the min-plus algebra), or a generalization thereof. The operations are defined as follows for x,yR{}:

xy=min{x,y}
xy=x+y

It is easily verified that with as the additive identity, these binary operations on R{} form a semiring.

References

  1. Grigoriev, Dima; Shpilrain, Vladimir (2014). "Tropical Cryptography". Communications in Algebra 42 (6): 2624–2632. doi:10.1080/00927872.2013.766827. ISSN 0092-7872. 




Licensed under CC BY-SA 3.0 | Source: https://handwiki.org/wiki/Tropical_cryptography
22 views | Status: cached on September 15 2024 04:05:06
↧ Download this article as ZWI file
Encyclosphere.org EncycloReader is supported by the EncyclosphereKSF