Implementación de la criptografía de la curva elíptica en el lenguaje Haskell

Abstract

Elliptic curve cryptography is a currently important topic in the security of communications, it has several implementations in different imperative programming languages, however it lacks of applications in declarative languages and particularly in functional paradigms such as Haskell, This would allow an easier implementation and maintenance, that is why the current research implemented the cryptography of the elliptic curve in the form of a library in the Haskell language, particularly in the ECDH (Elliptic Curve Diffie-Hellman) and EIGamal algorithms, through the implementation of algorithms of number theory and abstract algebra for the arithmetic of finite fields and elliptic curves. The methodology used was based on a qualitative approach at explanatory level, focused on a specialized bibliographic review. Particularly, documents concerning the practical implementation of the theory and the use of the Haskell language were studied. A library that implements both methods of elliptic curve cryptography with important functions and methods of number theory, finite field arithmetic, elliptic curves and the encrypted ECDH and ElGamal, in a public repository on GitHub, as well as a complete documentation. It is concluded that this type of language is suitable for this type of applications and facilitates their maintenance.