Development of crypto-code constructs based on LDPC codes

Authors

DOI:

https://doi.org/10.15587/1729-4061.2022.254545

Keywords:

crypto-code constructs, low-density parity-check codes, security concept

Abstract

The results of developing post-quantum algorithms of McEliece and Niederreiter crypto-code constructs based on LDPC (Low-Density Parity-Check) codes are presented. With the rapid growth of computing capabilities of mobile technologies and the creation of wireless mesh and sensor networks, Internet of Things technologies, and smart technologies on their basis, information security is becoming an urgent problem. At the same time, there is a need to consider security in two circuits, internal (directly within the network infrastructure) and external (cloud technologies). In such conditions, it is necessary to integrate threats to both the internal and external security circuits. This allows you to take into account not only the hybridity and synergy of modern targeted threats, but also the level of significance (degree of secrecy) of information flows and information circulating in both the internal and external security circuits. The concept of building security based on two circuits is proposed. To ensure the security of wireless mobile channels, it is proposed to use McEliece and Niederreiter crypto-code constructs based on LDPC codes, which allows integration into the credibility technology of IEEE 802.15.4, IEEE 802.16 standards. This approach provides the required level of security services (confidentiality, integrity, authenticity) in a full-scale quantum computer. Practical security technologies based on the proposed crypto-code constructs, online IP telephony and the Smart Home system based on the use of an internal server are considered

Author Biographies

Serhii Pohasii, National Technical University “Kharkiv Polytechnic Institute”

PhD, Associate Professor

Department of Cyber Security

Serhii Yevseiev, National Technical University “Kharkiv Polytechnic Institute”

Doctor of Technical Sciences, Professor, Head of Department

Department of Cyber Security

Oleksandr Zhuchenko, Ukrainian State University of Railway Transport

PhD, Associate Professor

Department of Transport Communications

Oleksandr Milov, National Technical University “Kharkiv Polytechnic Institute”

Doctor of Technical Sciences, Professor

Department of Cyber Security

Volodymyr Lysechko, Ukrainian State University of Railway Transport

PhD, Associate Professor

Department of Transport Communications

Oleksandr Kovalenko, Central Ukrainian National Technical University

Doctor of Technical Sciences, Associate Professor

Department of Cybersecurity and Software

Maryna Kostiak, Lviv Polytechnic National University

PhD, Senior Lecturer

Department of Information Security

Andrii Volkov, Ivan Kozhedub Kharkiv National Air Force University

Department of Tactics of Air Defense Force of Land Force

Aleksandr Lezik, Ivan Kozhedub Kharkiv National Air Force University

PhD, Associate Professor

Department of Tactics of Air Defense Force of Land Force

Vitalii Susukailo, Lviv Polytechnic National University

Postgraduate Student

Department of Information Security

References

  1. Branco, P. de M. (2017). A new LDPC-based McEliece cryptosystem. Tecnico Lisboa, 79. Available at: https://fenix.tecnico.ulisboa.pt/downloadFile/1970719973967111/Thesis.pdf
  2. Engelbert, D., Overbeck, R., Schmidt, A. (2007). A Summary of McEliece-Type Cryptosystems and their Security. Journal of Mathematical Cryptology, 1 (2). doi: https://doi.org/10.1515/jmc.2007.009
  3. Misoczki, R., Tillich, J.-P., Sendrier, N., Barreto, P. S. L. M. (2012). MDPC-McEliece: New McEliece Variants from Moderate Density Parity-Check Codes. Available at: https://eprint.iacr.org/2012/409.pdf
  4. Baldi, M., Bodrato, M., Chiaraluce, F. (2008). A New Analysis of the McEliece Cryptosystem Based on QC-LDPC Codes. Security and Cryptography for Networks, 246–262. doi: https://doi.org/10.1007/978-3-540-85855-3_17
  5. Chang, K. (2012). I.B.M. Researchers Inch Toward Quantum Computer. The New York Times. Available at: http://www.nytimes.com/2012/02/28/technology/ibm-inch-closer-on-quantum-computer.html?_r=1&hpw
  6. Eisenbarth, T., Güneysu, T., Heyse, S., Paar, C. (2009). MicroEliece: McEliece for Embedded Devices. Cryptographic Hardware and Embedded Systems - CHES 2009, 49–64. doi: https://doi.org/10.1007/978-3-642-04138-9_4
  7. Ghosh, S., Delvaux, J., Uhsadel, L., Verbauwhede, I. (2012). A Speed Area Optimized Embedded Co-processor for McEliece Cryptosystem. 2012 IEEE 23rd International Conference on Application-Specific Systems, Architectures and Processors. doi: https://doi.org/10.1109/asap.2012.16
  8. Heyse, S. (2011). Implementation of McEliece Based on Quasi-dyadic Goppa Codes for Embedded Devices. Lecture Notes in Computer Science, 143–162. doi: https://doi.org/10.1007/978-3-642-25405-5_10
  9. Persichetti, E. (2012). Compact McEliece keys based on quasi-dyadic Srivastava codes. Journal of Mathematical Cryptology, 6 (2). doi: https://doi.org/10.1515/jmc-2011-0099
  10. Minder, L. (2007). Cryptography Based on Error Correcting Codes. Lausanne. doi: https://doi.org/10.5075/epfl-thesis-3846
  11. Overbeck, R., Sendrier, N. (2009). Code-based cryptography. Post-Quantum Cryptography, 95–145. doi: https://doi.org/10.1007/978-3-540-88702-7_4
  12. Bernstein, D. J., Lange, T., Peters, C. (2008). Attacking and Defending the McEliece Cryptosystem. Lecture Notes in Computer Science, 31–46. doi: https://doi.org/10.1007/978-3-540-88403-3_3
  13. Cayrel, P.-L., Hoffmann, G., Persichetti, E. (2012). Efficient Implementation of a CCA2-Secure Variant of McEliece Using Generalized Srivastava Codes. Lecture Notes in Computer Science, 138–155. doi: https://doi.org/10.1007/978-3-642-30057-8_9
  14. Misoczki, R., Barreto, P. S. L. M. (2009). Compact McEliece Keys from Goppa Codes. Lecture Notes in Computer Science, 376–392. doi: https://doi.org/10.1007/978-3-642-05445-7_24
  15. Faugère, J.-C., Otmani, A., Perret, L., Tillich, J.-P. (2010). Algebraic Cryptanalysis of McEliece Variants with Compact Keys. Lecture Notes in Computer Science, 279–298. doi: https://doi.org/10.1007/978-3-642-13190-5_14
  16. Berger, T. P., Cayrel, P.-L., Gaborit, P., Otmani, A. (2009). Reducing Key Length of the McEliece Cryptosystem. Lecture Notes in Computer Science, 77–97. doi: https://doi.org/10.1007/978-3-642-02384-2_6
  17. Baldi, M., Chiaraluce, F. (2007). Cryptanalysis of a new instance of McEliece cryptosystem based on QC-LDPC Codes. 2007 IEEE International Symposium on Information Theory. doi: https://doi.org/10.1109/isit.2007.4557609
  18. Baldi, M., Chiaraluce, F., Garello, R. (2006). On the Usage of Quasi-Cyclic Low-Density Parity-Check Codes in the McEliece Cryptosystem. 2006 First International Conference on Communications and Electronics. doi: https://doi.org/10.1109/cce.2006.350824
  19. Baldi, M., Chiaraluce, F., Garello, R., Mininni, F. (2007). Quasi-Cyclic Low-Density Parity-Check Codes in the McEliece Cryptosystem. 2007 IEEE International Conference on Communications. doi: https://doi.org/10.1109/icc.2007.161
  20. Monico, C., Rosenthal, J., Shokrollahi, A. (2000). Using low density parity check codes in the McEliece cryptosystem. 2000 IEEE International Symposium on Information Theory (Cat. No.00CH37060). doi: https://doi.org/10.1109/isit.2000.866513
  21. Otmani, A., Tillich, J.-P., Dallot, L. (2010). Cryptanalysis of Two McEliece Cryptosystems Based on Quasi-Cyclic Codes. Mathematics in Computer Science, 3 (2), 129–140. doi: https://doi.org/10.1007/s11786-009-0015-8
  22. Misoczki, R., Tillich, J.-P., Sendrier, N., Barreto, P. S. L. M. (2013). MDPC-McEliece: New McEliece variants from Moderate Density Parity-Check codes. 2013 IEEE International Symposium on Information Theory. doi: https://doi.org/10.1109/isit.2013.6620590
  23. Bernstein, D. J., Buchmann, J., Dahmen, E. (Eds.) (2009). Post-Quantum Cryptography. Springer, 246. doi: https://doi.org/10.1007/978-3-540-88702-7
  24. Courtois, N. T., Finiasz, M., Sendrier, N. (2001). How to Achieve a McEliece-Based Digital Signature Scheme. Lecture Notes in Computer Science, 157–174. doi: https://doi.org/10.1007/3-540-45682-1_10
  25. Faugere, J.-C., Gauthier-Umana, V., Otmani, A., Perret, L., Tillich, J.-P. (2011). A distinguisher for high rate McEliece cryptosystems. 2011 IEEE Information Theory Workshop. doi: https://doi.org/10.1109/itw.2011.6089437
  26. Gaborit, P. (2005). Shorter keys for code based cryptography. In International Workshop on Coding and Cryptography – WCC’2005, 81–91.
  27. Heyse, S., von Maurich, I., Güneysu, T. (2013). Smaller Keys for Code-Based Cryptography: QC-MDPC McEliece Implementations on Embedded Devices. Lecture Notes in Computer Science, 273–292. doi: https://doi.org/10.1007/978-3-642-40349-1_16
  28. Baldi, M., Bianchi, M., Chiaraluce, F. (2013). Security and complexity of the McEliece cryptosystem based on quasi‐cyclic low‐density parity‐check codes. IET Information Security, 7 (3), 212–220. doi: https://doi.org/10.1049/iet-ifs.2012.0127
  29. Yevseiev, S., Tsyhanenko, O., Ivanchenko, S., Aleksiyev, V., Verheles, D., Volkov, S. et. al. (2018). Practical implementation of the Niederreiter modified crypto­code system on truncated elliptic codes. Eastern-European Journal of Enterprise Technologies, 6 (4 (96)), 24–31. doi: https://doi.org/10.15587/1729-4061.2018.150903
  30. Yevseiev, S., Hryhorii, K., Liekariev, Y. (2016). Developing of multi-factor authentication method based on niederreiter-mceliece modified crypto-code system. Eastern-European Journal of Enterprise Technologies, 6 (4 (84)), 11–23. doi: https://doi.org/10.15587/1729-4061.2016.86175
  31. Yevseiev, S., Ponomarenko, V., Laptiev, O., Milov, O., Korol, O., Milevskyi, S. et. al.; Yevseiev, S., Ponomarenko, V., Laptiev, O., Milov, O. (Eds.) (2021). Synergy of building cybersecurity systems. Kharkiv: РС ТЕСHNOLOGY СЕNTЕR, 188. doi: https://doi.org/10.15587/978-617-7319-31-2
  32. Yevseiev, S., Korol, O., Kots, H. (2017). Construction of hybrid security systems based on the crypto-code structures and flawed codes. Eastern-European Journal of Enterprise Technologies, 4 (9 (88)), 4–21. doi: https://doi.org/10.15587/1729-4061.2017.108461
  33. Sidel'nikov, V. M. (2002). Kriptografiya i teoriya kodirovaniya. Materialy konferentsii: Moskovskiy universitet i razvitie kriptografii v Rossii. Moscow: MGU.
  34. Ranjitha, C. R., Thomas, J., Chithra, K. R. (2016). A brief study on LDPC codes. International Journal of Engineering Research and General Science, 4 (2), 612–618. Available at: http://pnrsolution.org/Datacenter/Vol4/Issue2/85.pdf
  35. Broul´ım, J. (2018). LDPC codes - new methodologies. University of West Bohemia, 127. Available at: https://cds.cern.ch/record/2730008/files/CERN-THESIS-2018-479.pdf
  36. Zhu, H., Pu, L., Xu, H., Zhang, B. (2018). Construction of Quasi-Cyclic LDPC Codes Based on Fundamental Theorem of Arithmetic. Wireless Communications and Mobile Computing, 2018, 1–9. doi: https://doi.org/10.1155/2018/5264724
  37. Singh, H. (2020). Code based Cryptography: Classic McEliece. arxiv.org. doi: https://doi.org/10.48550/arXiv.1907.12754
  38. Chen, P.-J., Chou, T., Deshpande, S., Lahr, N., Niederhagen, R., Szefer, J., Wang, W. (2022). Complete and Improved FPGA Implementation of Classic McEliece. Cryptology ePrint Archive: Report 2022/412. URL: https://eprint.iacr.org/2022/412
  39. Liva, G., Song, S., Lan, L., Zhang, Y., Lin, S., Ryan, W. E. (2017). Design of LDPC Codes: A Survey and New Results. Journal of Communications Software and Systems, 2 (3), 191. doi: https://doi.org/10.24138/jcomss.v2i3.283
  40. Richardson, T. J., Urbanke, R. L. (2001). Efficient encoding of low-density parity-check codes. IEEE Transactions on Information Theory, 47 (2), 638–656. doi: https://doi.org/10.1109/18.910579
  41. Chandrasetty, V. A., Aziz, S. M. (2011). FPGA Implementation of a LDPC Decoder using a Reduced Complexity Message Passing Algorithm. Journal of Networks, 6 (1). doi: https://doi.org/10.4304/jnw.6.1.36-45
  42. Wang, Y. (2008). Generalized constructions, decoding and implementation of LDPC codes. University of Hawaii at Manoa. Available at: https://scholarspace.manoa.hawaii.edu/bitstream/10125/20577/Ph.D._AC1.H3_5085_r.pdf
  43. Sarvaghad-Moghaddam, M., Ullah, W., Jayakody, D. N. K., Affes, S. (2020). A New Construction of High Performance LDPC Matrices for Mobile Networks. Sensors, 20 (8), 2300. doi: https://doi.org/10.3390/s20082300
  44. Hübner, C., Merz, H., Hansemann, T. (2009). Gebäudeautomation. Kommunikationssysteme mit EIB/KNX, LON und BACnet. Hanser. doi: https://doi.org/10.3139/9783446422636
  45. CKA001473B8668. KNX Technical Manual. Busch-Presence detector KNX / Busch-Watchdog Sky KNX (2017). Busch-Jaeger Elektro GmbH, 198. Available at: https://library.e.abb.com/public/ddedcbf7ab704705affb179ca91e0fa2/2CKA001473B8668_Prasenzmelder_6131_03_ABB_EN.pdf
  46. Technical documentation on KNX devices (2006). ABB.
  47. KNX Handbook Version 1.1 Revision 1 (2004). Konnex Association.
  48. ABB i-bus KNX KNX Security Panel GM/A 8.1 Product Manual. Busch-Watchdog Sky KNX (2016). Busch-Jaeger Elektro GmbH, 648.
  49. ABB GPG Building Automation Webinar ABB i-bus® KNX Basics and Products (2016). ABB, 86. Available at: https://library.e.abb.com/public/d26bd890d3ef476fbc3a59a2fdca6116/Webinar%20ABB%20i-bus%20KNX%20-%20KNX%20Basics%20and%20Products.pdf
  50. Manual for KNX Planning (2017). Siemens Switzerland Ltd, 100.
  51. Security Technology KNX-Intrusion Alarm System L240 Installation, Commissioning, Operation (2010). Busch-Watchdog Sky KNX. Busch-Jaeger Elektro GmbH, 116.
  52. Kottapalli, N. (2011). Diameter and LTE Evolved Packet System. Corporate Headquarters, 10. Available at: http://go.radisys.com/rs/radisys/images/paper-lte-diameter-eps.pdf
  53. Ventura, H. (2002). Diameter - Next generation’s AAA protocol. Institutionen för Systemteknik, 66. Available at: https://www.diva-portal.org/smash/get/diva2:18347/FULLTEXT01.pdf
  54. Vinay Kumar, S. B., Harihar, M. N. (2012). Diameter-Based Protocol in the IP Multimedia Subsystem. International Journal of Soft Computing and Engineering (IJSCE), 1 (6), 266–269. Available at: https://www.ijsce.org/portfolio-item/F0320121611/
  55. Qanbari, S., Mahdizadeh, S., Rahimzadeh, R., Behinaein, N., Dustdar, S. (2016). Diameter of Things (DoT): A Protocol for Real-Time Telemetry of IoT Applications. Lecture Notes in Computer Science, 207–222. doi: https://doi.org/10.1007/978-3-319-43177-2_14
  56. Tschofenig, H. (2019). Diameter: new generation AAA protocol – design, practice, and applications. John Wiley & Sons, Inc. doi: https://doi.org/10.1002/9781118875889
  57. Ugrozy bezopasnosti yadra paketnoy seti 4G (2017). Available at: https://www.ptsecurity.com/ru-ru/research/analytics/epc-2017/
  58. Uyazvimosti protokola Diameter v setyakh 4G (2018). Available at: https://www.ptsecurity.com/ru-ru/research/analytics/diameter-2018/
  59. Yevseiev, S., Melenti, Y., Voitko, O., Hrebeniuk, V., Korchenko, A., Mykus, S. et. al. (2021). Development of a concept for building a critical infrastructure facilities security system. Eastern-European Journal of Enterprise Technologies, 3 (9 (111)), 63–83. doi: https://doi.org/10.15587/1729-4061.2021.233533
  60. Yevseiev, S., Pohasii, S., Khvostenko, V. (2021). Development of a protocol for a closed mobile internet channel based on post-quantum algorithms. Information Processing Systems, 3 (166), 35–40. doi: https://doi.org/10.30748/soi.2021.166.03

Downloads

Published

2022-04-30

How to Cite

Pohasii, S., Yevseiev, S., Zhuchenko, O., Milov, O., Lysechko, V., Kovalenko, O., Kostiak, M., Volkov, A., Lezik, A., & Susukailo, V. (2022). Development of crypto-code constructs based on LDPC codes . Eastern-European Journal of Enterprise Technologies, 2(9 (116), 44–59. https://doi.org/10.15587/1729-4061.2022.254545

Issue

Vol. 2 No. 9 (116) (2022): Information and controlling system

Section

Information and controlling system

License

Copyright (c) 2022 Serhii Pohasii, Serhii Yevseiev, Oleksandr Zhuchenko, Oleksandr Milov, Volodymyr Lysechko, Oleksandr Kovalenko, Maryna Kostiak, Andrii Volkov, Aleksandr Lezik, Vitalii Susukailo

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.

A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.