DOI: https://doi.org/10.15587/1729-4061.2018.150903

Practical implementation of the Niederreiter modified crypto­code system on truncated elliptic codes

Serhii Yevseiev, Oleksii Tsyhanenko, Serhii Ivanchenko, Volodymyr Aleksiyev, Dmytrо Verheles, Sergey Volkov, Roman Korolev, Hryhorii Kots, Oleksandr Milov, Olexander Shmatko

Abstract


On the basis of the practical implementation of the classic Niederreiter scheme for non-binary codes, a pattern has been identified for practical implementation –fixing the admissible position vectors of the plaintext transformation based on equilibrium coding. The obtained set of position vectors of the error vector with a fixed set of masking matrices (the recipient's private key) allows us to obtain the algorithm for decoding the classical Niederreiter crypto-code scheme on non-binary codes. For this, a modification of the crypto-code system (CCS) is necessary. It is proposed to use the additional parameter of key data – the initialization vector (the set of invalid position vectors of the error vector). To counter the Sidelnikov attacks, it is proposed to use modified (shortened) algebraic-geometric (elliptic) codes (MEC). For this, it is necessary to use the second additional initialization vector (the set of positions for shortening the error vector). Based on the modification of the classical Niederreiter scheme on non-binary codes, applied algorithms for generating and decrypting a cryptogram in the Niederreiter modified crypto-code system based on modified (shortened) elliptic codes and software are proposed. To confirm the profitability of the proposed crypto-code system, the results of the comparative evaluation of energy consumption for the implementation of the classical Niederreiter scheme on elliptic codes and the implementation of the proposed system on modified elliptic codes are presented. The results confirm the possibility of practical implementation of the Niederreiter crypto-code system based on the proposed algorithms. At the same time, the required level of cryptographic strength of the crypto-code system, protection of the cryptosystem against the Sidelnikov attacks and an increase in the rate of cryptographic transformations by 3-5 times compared with the classical Niederreiter scheme are guaranteed

Keywords


Niederreiter modified crypto-code system; modified shortened elliptic codes; equilibrium coding

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References


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Yevseiev, S., Rzayev, Kh., Tsyhanenko, A. (2016). Analysis of the software implementation of the direct and inverse transform in non-binary equilibrium coding method. Ukrainian Scientific Journal of Information Security, 22 (2), 196–203.

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GOST Style Citations


Grishchuk R. V., Danik Yu. G. Osnovy kiberbezopasnosti: monografiya / Yu. G. Danik (Ed.). Zhitomir: ZHNAEU, 2016. 636 p.

Kiberprostranstvo i informacionnyy terrorizm. URL: http://vpoanalytics.com/2016/02/15/kiberprostranstvo-i-informacionnyj-terrorizm/

Security requirements for cryptographic modules. URL: https://csrc.nist.gov/publications/fips/fips140-2/fips1402.pdf

Zabezpechennia informatsiynoi bezpeky derzhavy: monohrafyia / Ivanchenko I. S., Khoroshko V. O., Khokhlachova Yu. Ye., Chyrkov D. V. Kyiv: PVP “Zadruha”, 2013. 170 p.

Bezpeka bankivskoi diyalnosti: monohrafiya / Kazakova N. F., Panfilov V. I., Skachek L. M., Skopa O. O., Khoroshko V. O. Kyiv: PVP “Zadruha”, 2013. 282 p.

Leonenko G. P., Yudin A. Yu. Problemy obespecheniya informacionnoy bezopasnosti sistem kriticheski vazhnoy informacionnoy infrastruktury Ukrainy // Information Technology and Security. 2013. Issue 1. P. 44–48.

Evseev S., Korol' O., Koc G. Analysis of the legal framework for the information security management system of the NSМEP // Eastern-European Journal of Enterprise Technologies. 2015. Vol. 5, Issue 3 (77). P. 48–59. doi: https://doi.org/10.15587/1729-4061.2015.51468

Yevseiev S., Tsyhanenko O. Development of asymmetrical crypto-coded construction of niderraiter on modified codes // Systemy obrobky informatsiyi. 2018. Issue 2 (153). P. 127–135. doi: https://doi.org/10.30748/soi.2018.153.16 

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Approaches to selection of combinatorial algorithm for optimization in network traffic control of safety-critical systems / Kuchuk G., Kharchenko V., Kovalenko A., Ruchkov E. // 2016 IEEE East-West Design & Test Symposium (EWDTS). 2016. doi: https://doi.org/10.1109/ewdts.2016.7807655 

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Achieving 128-bit Security Against Quantum Attacks in OpenVPN. URL: https://internetscriptieprijs.nl/wp-content/uploads/2017/04/1-Simon-de-Vries-UT.pdf

A Side-Channel Assisted Cryptanalytic Attack Against QcBits / Rossi M., Hamburg M., Hutter M., Marson M. E. // Lecture Notes in Computer Science. 2017. P. 3–23. doi: https://doi.org/10.1007/978-3-319-66787-4_1 

Enhanced public key security for the McEliece cryptosystem / Baldi M., Bianchi M., Chiaraluce F., Rosenthal J., Schipani D. 2014. URL: https://arxiv.org/pdf/1108.2462.pdf

Cho J. Y., Griesser H., Rafique D. A McEliece-Based Key Exchange Protocol for Optical Communication Systems // Lecture Notes in Electrical Engineering. 2017. P. 109–123. doi: https://doi.org/10.1007/978-3-319-59265-7_8 

Development of mceliece modified asymmetric crypto-code system on elliptic truncated codes / Yevseiev S., Rzayev K., Korol O., Imanova Z. // Eastern-European Journal of Enterprise Technologies. 2016. Vol. 4, Issue 9 (82). P. 18–26. doi: https://doi.org/10.15587/1729-4061.2016.75250 

Evseev S. P., Korol O. H. Teoretyko-metodolohichni zasady pobudovy hibrydnykh krypto-kodovykh konstruktsiy na zbytkovykh kodakh. Informacionnaya ekonomika: etapy razvitiya, metody upravleniya, modeli: monografiya. Kharkiv, VSHEM – HNEU im. S. Kuzneca, 2018. P. 233–280.

Sidel'nikov V. M. Kriptografiya i teoriya kodirovaniya // Materialy konferencii “Moskovskiy universitet i razvitie kriptografii v Rossii”. Moscow, 2002.

Dudykevych V. B., Kuznetsov O. O., Tomashevskyi B. P. Krypto-kodovyi zakhyst informatsiyi z nedviykovym rivnovahovym koduvanniam // Suchasnyi zakhyst informatsiyi. 2010. Issue 2. P. 14–23.

Dudykevych V. B., Kuznietsov O. O., Tomashevskyi B. P. Metod nedviikovoho rivnovahovoho koduvannia // Suchasnyi zakhyst informatsiyi. 2010. Issue 3. P. 57–68.

Zhang G., Cai S. Secure error-correcting (SEC) schemes for network coding through McEliece cryptosystem // Cluster Computing. 2017. doi: https://doi.org/10.1007/s10586-017-1294-5 

Morozov K., Roy P. S., Sakurai K. On unconditionally binding code-based commitment schemes // Proceedings of the 11th International Conference on Ubiquitous Information Management and Communication – IMCOM '17. 2017. doi: https://doi.org/10.1145/3022227.3022327 

Zhang G., Cai S. Universal secure error-correcting (SEC) schemes for network coding via McEliece cryptosystem based on QC-LDPC codes // Cluster Computing. 2017. doi: https://doi.org/10.1007/s10586-017-1354-x 

Moufek H., Guenda K. A New variant of the McEliece cryptosystem based on the Smith form of convolutional codes // Cryptologia. 2017. Vol. 42, Issue 3. P. 227–239. doi: https://doi.org/10.1080/01611194.2017.1362061 

Biswas B., Sendrier N. McEliece Cryptosystem Implementation: Theory and Practice // Lecture Notes in Computer Science. 2008. P. 47–62. doi: https://doi.org/10.1007/978-3-540-88403-3_4 

Yevseiev S., Rzayev Kh., Tsyhanenko A. Analysis of the software implementation of the direct and inverse transform in non-binary equilibrium coding method // Ukrainian Scientific Journal of Information Security. 2016. Vol. 22, Issue 2. P. 196–203.

Niederreiter H. Knapsack-Type Cryptosystems and Algebraic Coding Theory // Problems of Control and Information Theory. 1986. Vol. 15, Issue 2. P. 19–34.

A statistical test suite for random and pseudorandom number generators for cryptographic applications / Rukhin A., Sota J., Nechvatal J., Smid M., Barker E., Leigh S. et. al. // NIST Special Publication. 2000. doi: https://doi.org/10.6028/nist.sp.800-22 







Copyright (c) 2018 Serhii Yevseiev, Oleksii Tsyhanenko, Serhii Ivanchenko, Volodymyr Aleksiyev, Dmytrо Verheles, Sergey Volkov, Roman Korolev, Hryhorii Kots, Oleksandr Milov, Olexander Shmatko

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ISSN (print) 1729-3774, ISSN (on-line) 1729-4061