McEliece's public key cryptosystem based on non-binary algebraic codes

In this paper we carried out the construction of a public key cryptosystem based on algebraic geometry codes. Basically, we have developed the scheme proposed by McEliece. However, instead of using binary linear codes, we have worked with non-binary linear algebraic geometry codes on Hermitian curves. In the decryption process, we have used Sakata's algorithm, which plays an important role. An application is proposed for this system in order to be applied in a storage and retrieval systems for magnetic recording over nanoparticles.