Spline-wavelet bent robust codes

• Autorzy: Levina Alla , Ryaskin Gleb , Zikratov Igor

Identyfikatory

DOI

10.15439/2019F134

• Konferencja: Federated Conference on Computer Science and Information Systems (14 ; 01-04.09.2019 ; Leipzig, Germany)
• Języki publikacji: EN

Abstrakty

EN

This paper presents an application of spline-wavelet transformation and bent-functions for the construction of robust codes. To improve the non-linear properties of presented robust codes, bent-functions were used. Bent-functions ensure maximum non-linearity of functions, increasing the probability of detecting an error in the data channel. In the work different designs of codes based on wavelet transform and bent-functions are developed. The difference of constructions consists of using different grids for wavelet transformation and using different bent-functions. The developed robust codes have higher characteristics compared to existing. These codes can be used for ensuring the security of transmitted information.

Słowa kluczowe

EN

nonlinear code; probability; spline; wavelet transform

PL

kod nieliniowy; prawdopodobieństwo; transformacja falkowa

• Wydawca: Polskie Towarzystwo Informatyczne
• Czasopismo: Annals of Computer Science and Information Systems
• Rocznik: 2019
• Tom: Vol. 18
• Strony: 227--230
• Opis fizyczny: Bibliogr. 19 poz., wz., tab., wykr.

Twórcy

autor

Levina Alla

• University ITMO, ul. Lomonosova 9, Saint-Petersburg, Russia
• St. Petersburg Electrotechnical University "LETI", Professora Popova str., 5, Russia, Saint-Petersburg

autor

Ryaskin Gleb

• University ITMO, Saint-Petersburg, Russia

autor

Zikratov Igor

• The Bonch-Bruevich Saint-Petersburg State University of Telecommunications, Saint- Petersburg , Russia

Bibliografia

• 1. I. G. Burova and U. K. Demyanovich, Theory of Minimal Spline (SPSU, 2000).
• 2. G. Caire, R. L. Grossman and H. V. Poor, Wavelet transforms associated with finite cyclic groups, IEEE Trans. Inf. Theory 39(4) (1993) 1157–1166.
• 3. I. Daubechies, Ten Lectures on Wavelets, CBMS-NSF Conference Series in Applied Mathematics (SIAM, 1992).
• 4. U. K. Demyanovich, Calibration ratio for B-splines on nonuniform net, Mat. Model T 13(3) (2001)
• 5. U. K. Demyanovich, Minimal Splines and Wavelets (Vestnik SPSU, 2008)
• 6. F. Fekri, R. M. Mersereau and R. W. Schafer, Theory of wavelet transform over finite fields, IEEE International Conference on Acoustics, Speech, and Signal Processing 3 (1999) 1213–1216.
• 7. F. Fekri, S. W. McLaughlin, R. M. Mersereau and R. W. Schafer, Double circulant selfdual codes using finite-field wavelet transforms, Applied Algebra, Algebraic Algorithms and Error Correcting Codes Conference (Springer, 1999), pp. 355–364
• 8. Tokareva N., Bent Functions: Results and Applications to Cryptography, 2015.
• 9. A. Levina and S. Taranov, Spline-wavelet robust code under nonuniform codeword distribution, in 3rd Int. IEEE Computer, Communication, Control and Information Technology (IEEE, 2015).
• 10. A. B. Levina and S. V. Taranov, Algorithms of constructing linear and robust codes based on wavelet decomposition and its application, Cryptology, and Information Security (Springer, 2015), pp. 247–258.
• 11. A. B. Levina and S. V. Taranov, Second-order spline-wavelet robust code under nonuniform codeword distribution, Procedia Comput. Sci. 62 (2015) 297–302.
• 12. A. B. Levina and S. V. Taranov, Construction of linear and robust codes that is based on the scaling function coefficients of wavelet transforms, J. Appl. Ind. Math. 9(4) (2015) 540–546.
• 13. A. B. Levina and S. V. Taranov, New construction of algebraic manipulation detection codes based on wavelet transform, Proceedings of the 18th Conference of Open Innovations Association FRUCT - 2016, pp. 187-192
• 14. A. B. Levina and S. V. Taranov, Creation of codes based on wavelet transformation and its application in ADV612 chips, International Journal of Wavelets, Multiresolution and Information Processing - 2017, Vol. 15, No. 2, pp. 1750014
• 15. A. B. Levina and S. V. Taranov, AMD codes based on wavelet transform, 2017 Progress In Electromagnetics Research Symposium - Fall (PIERS-FALL) - 2017, pp. 2534-2539
• 16. Akdemir K.D., Wang Z., Karpovsky M. G., Sunar B., Design of Cryptographic Devices Resilient to Fault Injection Attacks Using Nonlinear Robust Codes // Fault Analysis in Cryptography, 2011.
• 17. Karpovsky M.G., Kulikowski K., Wang Z., Robust Error Detection in Communication and Computation Channels // Keynote paper, Int. Workshop on Spectral Techniques, 2007.
• 18. Carlet C. Boolean functions for cryptography and error correcting codes // Chapter of the monograph «Boolean Methods and Models», Cambridge Univ. Press (P. Hammer, Y. Crama eds.), 2007.
• 19. MacWilliams, F.J. and Sloane, N.J.A., The Theory of Error-Correcting Codes. Elsevier-North-Holland, Amsterdam, 1977.

Uwagi

1. Track 2: Computer Science & Systems

2. Technical Session: 6th International Conference on Cryptography and Security Systems

3. Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).