Skew differential Goppa codes and their application to Mceliece cryptosystem Gómez Torrecillas, José Lobillo Borrero, Francisco Javier Navarro Garulo, Gabriel Skew-differential Goppa code Decoding algorithm McEliece-type cryptosystem Research funded by grant (PID2019-110525GB-I00 / AEI / 10.13039/501100011033) and by the IMAG-Maria de Maeztu grant (CEX2020-001105-M / AEI / 10.13039/501100011033). A class of linear codes that extends classical Goppa codes to a non-commutative context is defined. An efficient decoding algorithm, based on the solution of a non-commutative key equation, is designed. We show how the parameters of these codes, when the alphabet is a finite field, may be adjusted to propose a McEliece-type cryptosystem. 2023-09-25T12:33:29Z 2023-09-25T12:33:29Z 2023-08-19 info:eu-repo/semantics/article Gómez-Torrecillas, J., Lobillo, F. . & Navarro, G. Skew differential Goppa codes and their application to Mceliece cryptosystem. Des. Codes Cryptogr. (2023). [https://doi.org/10.1007/s10623-023-01286-6] https://hdl.handle.net/10481/84648 10.1007/s10623-023-01286-6 eng http://creativecommons.org/licenses/by/4.0/ info:eu-repo/semantics/openAccess Atribución 4.0 Internacional Springer Nature