Abstract
AbstractA 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.
Funder
Agencia Estatal de Investigación
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computer Science Applications
Reference25 articles.
1. Albrecht M.R., Bernstein D.J., Chou T., Cid C., Gilcher J., Lange T., Maram V., von Maurich I., Misoczki R., Niederhagen R., Paterson K.G., Persichetti E., Peters C., Schwabe P., Sendrier N., Szefer J., Tjhai C.J., Tomlison M., Wang W.: Classic McEliece: conservative code-based cryptography. Tech. Report. NIST’s Post-Quantum Cryptography Standardization Project 10 (2020). https://classic.mceliece.org/.
2. Bartz H., Jerkovitz T., Puchinger S., Rosenkilde J.: Fast decoding of codes in the rank, subspace, and sum-rank metric. IEEE Trans. Inform. Theory 67, 5026–5050 (2021). https://doi.org/10.1109/TIT.2021.3067318.
3. Bueso J.L., Gómez-Torrecillas J., Verschoren A.: Algorithmic Methods in Non-commutative Algebra. Applications to Quantum groups. Springer, Dordrecht (2003) https://doi.org/10.1007/978-94-017-0285-0.
4. Delenclos J., Leroy A.: Noncommutative symmetric functions and w-polynomials. J. Algebra Appl. 06, 815–837 (2007). https://doi.org/10.1142/S021949880700251X.
5. Frandsen G.S.: On the density of normal bases in finite fields. Finite Fields Appl. 6, 23–38 (2000). https://doi.org/10.1006/ffta.1999.0263.