Abstract
In recent years, much research has been conducted on quantum computers – machine that exploit the phenomena of quantum mechanics to solve difficult or insoluble mathematical problems for conventional computers. If large-scale quantum computers are built, they will be able to break many of the public key cryptosystems currently in use. This would seriously compromise the confidentiality and integrity of digital communications on the internet. Post-quantum cryptography aims to develop secure cryptographic systems against both conventional as well as quantum computers for interacting with existing protocols and communication networks. In this paper we present a public key cryptosystem of McEliece based on the correcting codes, using two types of correcting codes; QC-MDPC and Goppa correcting codes. This latter seems very interesting considering its two characteristics, namely the power of correction and the efficient decoding algorithm which resistant to quantum attacks due to difficulty of decoding a linear code. On the other hand, QC-MDPC cryptosystem code is rapid and more secure than Goppa cryptosystem.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Chen, L., et al.: Report on post-quantum cryptography, vol. 12. US Department of Commerce, National Institute of Standards and Technology (2016)
Steiner, M., Tsudik, G., Waidner, M.: Diffie-Hellman key distribution extended to group communication, pp. 31–37 (1996)
Rivest, R.L., Shamir, A., Adleman, L.: A method for obtaining digital signatures and public-key cryptosystems, 26(1), 96–99 (1978)
Costello, C., Jao, D., Longa, P., Naehrig, M., Renes, J., Urbanik, D.: Efficient compression of SIDH public keys. In: Coron, J.-S., Nielsen, J.B. (eds.) EUROCRYPT 2017. LNCS, vol. 10210, pp. 679–706. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-56620-7_24
Overbeck, R., Sendrier, N.: Code-based cryptography. In: Bernstein, D.J., Buchmann, J., Dahmen, E. (eds.) Post-Quantum Cryptography, pp. 95–145. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-540-88702-7_4
Bos, J., et al.: CRYSTALS-kyber: a CCA-secure module-lattice-based KEM. In: 2018 IEEE European Symposium on Security and Privacy (EuroS&P), pp. 353–367. IEEE (2018)
McEliece, R.J.: A public-key cryptosystem based on algebraic. Coding Thv 4244, 114–116 (1978)
Monico, C., Rosenthal, J., Shokrollahi, A.: Using low density parity check codes in the McEliece cryptosystem. In: IEEE International Symposium on Information Theory (ISIT 2000) (2000)
Baldi, M., Chiaraluce, F.: Cryptanalysis of a new instance of McEliece cryptosystem based on QC-LDPC codes. In: 2007 IEEE International Symposium on Information Theory, pp. 2591–2595. IEEE (2007)
Baldi, M., Bodrato, M., Chiaraluce, F.: A new analysis of the McEliece cryptosystem based on QC-LDPC codes. In: Ostrovsky, R., De Prisco, R., Visconti, I. (eds.) SCN 2008. LNCS, vol. 5229, pp. 246–262. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85855-3_17
Misoczki, R., Tillich, J.P., Sendrier, N., Barreto, P.S.: MDPC-McEliece: new McEliece variants from moderate density parity-check codes. In: 2013 IEEE International Symposium on Information Theory, pp. 2069–2073. IEEE (2013)
Heyse, S., von Maurich, I., Güneysu, T.: Smaller keys for code-based cryptography: QC-MDPC McEliece implementations on embedded devices. In: Bertoni, G., Coron, J.-S. (eds.) CHES 2013. LNCS, vol. 8086, pp. 273–292. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40349-1_16
Von Maurich, I., Güneysu, T.: Lightweight code-based cryptography: QC-MDPC McEliece encryption on reconfigurable devices. In: 2014 Design, Automation & Test in Europe Conference & Exhibition (DATE), pp. 1–6. IEEE (2014)
Von Maurich, I., Oder, T., Güneysu, T.: Implementing QC-MDPC McEliece encryption. ACM Trans. Embed. Comput. Syst. (TECS) 14(3), 1–27 (2015)
Chaulet, J., Sendrier, N.: Worst case QC-MDPC decoder for McEliece cryptosystem. In: 2016 IEEE International Symposium on Information Theory (ISIT), pp. 1366–1370. IEEE (2016)
Janoska, A.: MDPC decoding algorithms and their impact on the McEliece cryptosystem, pp. 1085–1089 (2018)
Liva, G., Bartz, H.: Protograph-based quasi-cyclic MDPC codes for McEliece cryptosystems (2018)
Berlekamp, E., McEliece, R., Van Tilborg, H.: On the inherent intractability of certain coding problems (corresp.). IEEE Trans. Inf. Theory 24(3), 384–386 (1978)
Patterson, N.: The algebraic decoding of Goppa codes. IEEE Trans. Inf. Theory 21(2), 203–207 (1975)
Gallager, R.G.: Low-density parity-check codes, p. 8 (1962)
Maurich, I.V., Oder, T., Güneysu, T.: Implementing QC-MDPC McEliece encryption, 14(3), 1–27 (2015)
Chaulet, J., Sendrier, N.: Worst case QC-MDPC decoder for McEliece cryptosystem, pp. 1366–1370 (2016)
Tillich, J.-P.: The decoding failure probability of MDPC codes. In: 2018 IEEE International Symposium on Information Theory (ISIT), pp. 941–945. IEEE (2018)
Sendrier, N., Vasseur, V.: About low DFR for QC-MDPC decoding. In: Ding, J., Tillich, J.-P. (eds.) PQCrypto 2020. LNCS, vol. 12100, pp. 20–34. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-44223-1_2
Guo, Q., Johansson, T., Stankovski, P.: A key recovery attack on MDPC with CCA security using decoding errors. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016. LNCS, vol. 10031, pp. 789–815. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53887-6_29
Yamada, A., Eaton, E., Kalach, K., Lafrance, P., Parent, A.: QCMDPC KEM: a key encapsulation mechanism based on the QCMDPC McEliece encryption scheme. NIST Submission (2017)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
Azougaghe, Es., Farchane, A., Tazigh, I., Azougaghe, A. (2021). Comparative Study on the McEliece Public-Key Cryptosystem Based on Goppa and QC-MDPC Codes. In: Fakir, M., Baslam, M., El Ayachi, R. (eds) Business Intelligence. CBI 2021. Lecture Notes in Business Information Processing, vol 416. Springer, Cham. https://doi.org/10.1007/978-3-030-76508-8_25
Download citation
DOI: https://doi.org/10.1007/978-3-030-76508-8_25
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-76507-1
Online ISBN: 978-3-030-76508-8
eBook Packages: Computer ScienceComputer Science (R0)