Abstract
The McEliece public-key cryptography (PKC) has fewer encryption/decryption operations compared to other PKC schemes such as RSA, ECC, and ElGamal. The use of Goppa codes in its implementation ensures the hardness of the decoding problem. Conversely, the original McEliece PKC has a low encryption rate and large key size. In this paper, a new variant of the McEliece cryptosystem is presented based on non-linear convolutional codes. Cascaded convolutional codes are used to be part of the public key with each stage of the cascade separated by a product cipher to increase the security level. Convolutional codes are used as an alternative to Goppa codes since the Viterbi decoding algorithm is suitable for high data-rate applications by providing maximum-likelihood solutions. The convolutional code used in the implementation increases both security and throughput due to its high error-correcting capacity. It is shown that the new variant has small key sizes with enhanced security-complexity trade-off. Cryptanalysis of the new version of the McEliece cryptosystem is performed using existing attacks of the classical cryptosystem to demonstrate the difficulties in breaking the new cryptosystem. Also, it is shown that security levels comparable to the original McEliece cryptosystem could be obtained by using smaller public key sizes of the new version if multiple stages of the generator matrix are employed. This aspect makes the new version of the McEliece cryptosystem attractive in mobile wireless networks since it could be ported onto a single Field Programmable Gate Array (FPGA).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
McEliece, R.J.: A public-key cryptosystem based on algebraic coding theory. In: DSN Progress Report, pp. 114–116 (1978)
Niederreiter, H.: Knapsack-type cryptosystems and algebraic coding theory. Probl. Contr. Inform. Theory 15, 159–166 (1986)
Gabidulin, E.M., Ourivski, A.V., Honary, B., Ammar, B.: Reducible rank codes and their applications to cryptography. IEEE Trans. Inf. Theory 49, 3289–3293 (2003)
Gaborit, P.: Shorter keys for code-based cryptography. In: Proceedings of WCC, pp. 81–90 (2005)
Sidelnikov, V.M.: A public-key cryptosystem based on binary Reed-Muller codes. Discrete Math. Appl. 4 (1994)
Baldi, M., Bianchi, M., Chiaraluce, F.: Security and complexity of the McEliece cryptosystem based on quasi-cyclic low-density parity-check codes. IET Inf. Secur. 7(3), 212–220 (2013)
Moufek, H., Guenda, K.: A new variant of the mceliece cryptosystem based on the smith form of convolutional codes. Cryptologia 42(3), 227–239 (2018)
Landais, G., Tillich, J.-P.: An efficient attack of a McEliece cryptosystem variant based on convolutional codes. In: Gaborit, P. (ed.) PQCrypto 2013. LNCS, vol. 7932, pp. 102–117. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38616-9_7
Trinca, D.: Sequential and parallel cascaded convolutional encryption with local propagation: toward future directions in symmetric cryptography. In: 3rd International Conference on Information Technology, USA, pp. 464–469 (2006)
Sone, M.E.: Efficient key management scheme to enhance security-throughput trade-off performance in wireless networks. In: Proceedings of the Science and Information Conference (SAI), London, UK, pp. 1249–1256 (2015)
Peterson, W.W., Weldon, E.J.: Error Correcting Codes, 2nd edn. MIT Press, Cambridge (1972)
Kumari, D., Saini, M.L.: Design and performance analysis of convolutional encoder and viterbi decoder for various generator polynomials. Int. J. Eng. Res. Appl. 6(5), 67–71 (2016)
Moufek, H., Guenda, K.: McEliece cryptosystem based on punctured convolutional codes and the pseudo-random generators. In: ACM Communications in Computer Algebra, vol. 49, No. 1 (2015)
Sone, M.: FPGA-based McEliece cryptosystem using non-linear convolutional codes. In: Proceeding of the 17th International Joint Conference on e-Business and Telecommunications (ICETE 2020) – SECRYPT, pp. 64–75 (2020)
Almeida, P., Napp, D., Pinto, R.: A new class of superregular matrices and MDP convolutional codes. Linear Algebra Appl. 439(7), 2145–2157 (2013)
Lathi, B.P.: Modern Digital and Analog Communication Systems, 3rd edn. Oxford University Press, Oxford (1998)
Loidreau, P., Sendrier, N.: Weak keys in the McEliece public-key cryptosystem. IEEE Trans. Inf. Theory 47(3), 1207–1211 (2001)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Appendix
Appendix
1.1 Transition Tables
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
Sone, M.E. (2021). Security and Complexity of a New Variant of the McEliece Cryptosystem Using Non-linear Convolutional Codes. In: Obaidat, M.S., Ben-Othman, J. (eds) E-Business and Telecommunications. ICETE 2020. Communications in Computer and Information Science, vol 1484. Springer, Cham. https://doi.org/10.1007/978-3-030-90428-9_2
Download citation
DOI: https://doi.org/10.1007/978-3-030-90428-9_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-90427-2
Online ISBN: 978-3-030-90428-9
eBook Packages: Computer ScienceComputer Science (R0)