Open Access
Research Article
New McEliece cryptosystem based on non-permutation equivalent polar codes
*Belkacem ImineCorresponding authorimine.belkacem@gmail.combelkacem.imine@univ-usto.dzLaboratory of Coding and Security of Information (LACOSI)Faculty of Electrical Engineering(USTO) 1505 Oran M’Naouer 31000University of Science and Technology of OranAlgeriaView full profile → , Naima Hadj-Saidnaima.hadjsaid@univ-usto.dzFaculty of Computer Science1505 Oran M’Naouer 31000University of Science and Technology of Oran (USTO)AlgeriaView full profile → , Adda Ali-Pachaadda.alipacha@univ-usto.dzLaboratory of Coding and Security of Information (LACOSI)Faculty of Electrical Engineering(USTO) 1505 Oran M’Naouer 31000University of Science and Technology of OranAlgeriaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 30 Sep 2020
- Accepted:
- 28 Feb 2021
- Published Online:
- 02 Aug 2021
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-1312
- Pages:
- 103–114
Abstract
In this paper, we propose a new McEliece public-key cryptosystem based on polar codes with non-permutation equivalent. Due to the fact that polar code is a decreasing monomial code, any permutation of columns of its generator matrix can be found. Thus, any McEliece cryptosystem based on only the permutation equivalent of the standard polar code seems to be insecure against some structural attacks. In contrast, our proposed scheme is able to resist against these attacks and achieves good security level against the generic decoding attacks.
Keywords
Subject Classifications
94A6011T7114G50
References
- Arikan, E.: Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Symmetric Binary-Input Memoryless Channels. IEEE Transactions on Information Theory. 55, 7, 3051–3073 (2009). https://doi.org/10.1109/TIT.2009.2021379. [Crossref], [Web of Science ®], [Google Scholar]
- Baldi, M. et al.: Quasi-Cyclic Low-Density Parity-Check Codes in the McEliece Cryptosystem. In: 2007 IEEE International Conference on Communications. pp. 951–956 (2007). https://doi.org/10.1109/ICC.2007.161. [Crossref], [Google Scholar]
- 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 (2007). https://doi.org/10.1109/ISIT.2007.4557609. [Crossref], [Google Scholar]
- Bardet, M., et al.: Cryptanalysis of the McEliece Public Key Cryptosystem Based on Polar Codes. In: Takagi, T. (ed.) Post-Quantum Cryptography. pp. 118–143 Springer International Publishing, Cham (2016). https://doi.org/10.1007/978-3-319-29360-8_9. [Crossref], [Google Scholar]
- Berlekamp, E. et al.: On the inherent intractability of certain coding problems (Corresp.). IEEE Transactions on Information Theory. 24, 3, 384–386 (1978). https://doi.org/10.1109/TIT.1978.1055873. [Crossref], [Web of Science ®], [Google Scholar]
- Canteaut, A., Chabaud, F.: A new algorithm for finding minimum-weight words in a linear code: application to McEliece’s cryptosystem and to narrow-sense BCH codes of length 511. IEEE Transactions on Information Theory. 44, 1, 367–378 (1998). https://doi.org/10.1109/18.651067. [Crossref], [Web of Science ®], [Google Scholar]
- Diffie, W., Hellman, M.: New directions in cryptography. IEEE Transactions on Information Theory. 22, 6, 644–654 (1976). https://doi.org/10.1109/TIT.1976.1055638. [Crossref], [Web of Science ®], [Google Scholar]
- Dumer, I.: On minimum distance decoding of linear codes. In: Proc. 5th Joint Soviet-Swedish Int. Workshop Inform. Theory. pp. 50–52 (1991). [Google Scholar]
- Faure, C., Minder, L.: Cryptanalysis of the McEliece cryptosystem over hyperelliptic codes. In Proceedings of the 11th international workshop on Algebraic and Combinatorial Coding Theory, ACCT. pp. 99–107 (2008). [Google Scholar]
- Hooshmand, R. et al.: PKC-PC: A variant of the McEliece public-key cryptosystem based on polar codes. IET Communications. 14, 12, 1883–1893 (2020). https://doi.org/10.1049/iet-com.2019.0689. [Crossref], [Web of Science ®], [Google Scholar]
- Hooshmand, R. et al.: Reducing the key length of mceliece cryptosystem using polar codes. In: 2014 11th International ISC Conference on Information Security and Cryptology. pp. 104–108 (2014). https://doi.org/10.1109/ISCISC.2014.6994031. [Crossref], [Google Scholar]
- Janwa, H., Moreno, O.: McEliece Public Key Cryptosystems Using Algebraic-Geometric Codes. Designs, Codes and Cryptography. 8, 3, 293–307 (1996). https://doi.org/10.1023/A:1027351723034. [Crossref], [Google Scholar]
- Kakelli Anil Kumar, Addepalli V. N. Krishna & K. Shahu Chatrapati (2017) New secure routing protocol with elliptic curve cryptography for military heterogeneous wireless sensor networks, Journal of Information and Optimization Sciences, 38:2, 341-365, DOI: 10.1080/02522667.2016.1220092 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]
- Lee, P.J., Brickell, E.F.: An Observation on the Security of McEliece’s Public-Key Cryptosystem. In: Barstow, D., et al. (eds.) Advances in Cryptology — EUROCRYPT ‘88. pp. 275–280 Springer, Berlin, Heidelberg (1988). https://doi.org/10.1007/3-540-45961-8_25. [Crossref], [Google Scholar]
- Leon, J.S.: A probabilistic algorithm for computing minimum weights of large error-correcting codes. IEEE Transactions on Information Theory. 34, 5, 1354–1359 (1988). https://doi.org/10.1109/18.21270.
Views: 197Downloads: 64Citations: 0
