# BLOCK SYMMETRIC CIPHER WITH RANDOM S-BOXES

## DOI:

https://doi.org/10.47839/ijc.18.1.1278## Keywords:

controlled enlarged S-blocks, dynamic cipher indicators, active S-blocks, random S-blocks, indicators of randomness, indicators of strength, pipeline processing.## Abstract

This paper describes a new 256-bit block symmetric substitution-permutation cipher, called managed substitution cipher. This is a cipher with single-layer permutated transformations in each cycle. The management of substituted transformations occur by including them in a chain so that the output value of the previous SL transform is fed to the input of the current fortified 32-bit substituted transformation (SL conversion) along with the current value of the input data block through the adder for modulo 2. This enables to activate almost all S-blocks of the second cycle and subsequent cycles and eventually improve the dynamic indicators of the arrival of the cipher to the state of random substitution. The results of the evaluation of randomness indicators and the possibility of using random S-blocks are given. It is shown that such construction of cycled function allows us to use random substitutions without any selection in a cipher without reducing its strength.## References

V.I. Dolgov, I.V. Lisitska, K.Ye. Lisitskyi, “The new concept of block symmetric ciphers design,” Telecommunications and Radio Engineering, vol. 76, issue 2, pp. 157-184, 2017.

J. Daemen, V. Rijmen, AES Proposal: Rijndael, USA, 1998. http://www.nist.gov/aes.

X. Lai, “On the design and security of block ciphers,” volume 1 of ETH Series in Information Processing, Hartung-Gorre Verlag, 1992.

X. Lai, J. Massey, “A proposal for a new block encryption standard,” in I. Damgard, editor, Advances in Cryptology - EUROCRYPT’90, vol. 473 of Lecture Notes in Computer Science, Springer-Verlag, 1991, pp. 389-404.

S. Landau, Polynomials in the Nation’s Service: Using Algebra to Design the Advanced Encryption Standard, February, 2004.

W. Meier, O. Staffelbach, “Nonlinearity criteria for cryptographic functions,” in Advances in Cryptology: Eurocrypt’89, W. Meier and O. Staffelbach eds., Lecture Notes I Computer Science, vol. 434, Springer-Verlag, Berlin, 1989, pp. 549-562.

J. Pieprzyk, J. Quisquater, J. Vandewalle, “Nonlinearity of exponent permutations,” Proceedings of the Advances in Cryptology: Eurocrypt’89, Springer-Verlag, Berlin, 1990, pp. 89-92.

J. Pieprzyk, On Bent Permutations, Technical Report CS91/11, Department of Computer Science, University of New South Wales; International Conference on Finite Fields, Coding Theory, and Advances in Communications and Computing, Las Vegas, 1991.

K. Nyberg, “Differentially uniform mappings for cryptography,” Proceedings of the Advances in Cryptology: Eurocrypt’93, T. Helleseth, ed., Springer-Verlag, Berlin, 1994, pp. 53-64.

J. Daemen, Cipher and Hash Function Design Strategies Based on Linear and Differential Cryptanalysis, Ph.D. thesis, Katholieke Universiteit, Leuven, Belgium, 1995.

V. Ridjmen, J. Daemen, B. Preneel, A. Bosselaers, E. De Win, “The cipher SHARK,” Proceedings of the Third International Workshop on Fast Software Encryption: D. Gollman, ed., Springer-Verlag, Berlin, 1996, pp. 99-112.

T. Jakobsen, L. Knudsen, “Attacks on block ciphers of low algebraic degree,” J. Cryptology, vol. 14, pp. 197-210, 2001.

J. Daemen, L. Knudsen, V. Ridjmen, “The block cipher square,” in Fast Software Encryption, E. Biham ed., Lecture Notes in Computer Science, vol. 1267, Springer-Verlag, Berlin, 1997.

P. Junod, S. Vaudenay, “FOX: a new family of block ciphers,” in H. Handschuh and A. Hasan, editors, Selected Areas in Cryptography: 11th International Workshop, SAC 2004, Waterloo, Canada, August 9-10, 2004, vol. 3357 of Lecture Notes in Computer Science, pp. 114-129. Springer-Verlag, 2004.

Open competition of symmetric block cryptographic algorithms of Ukraine [Online]. Available:http://www.dsszzi.gov.ua/dsszzi/control/uk/publish/article?art_id=49027&cat_id=38710 (in Ukrainian)

State standard of the Republic of Belarus. STB 34.101.31-2011. Information Technology. Information security Cryptographic encryption and integrity control algorithms. Publishing house of Gosstandart, Minsk, 2011, 35 p. (in Russian)

A New Encryption Standard of Ukraine: The Kalyna Block Cipher. [Online]. Available: https://eprint.iacr.org/2015/650.pdf

Information technology. Cryptographic protection of information. Block ciphers. GOST R 34.12 - 2015. Moscow, Standardinform, 2015, 21 p. (in Russian)

N. Ferguson, B. Schneier, Practical Cryptography, John Wiley & Sons, 2003, 432p.

A.J. Menezes, P.C. van Oorschot, S.A. Vanstone, Handbook of Applied Cryptography, CRC Press, 1997, 794 р.

I.D. Gorbenko, V.I. Dolgov, V.I. Rublinetskii, K.V. Korovkin, “Methods of information protection in communications systems and methods of their cryptoanalysis,” Telecommunications and Radio Engineering, vol. 52, issue 4, pp. 89-96, 1998.

I. Lisitskaya, T. Grinenko, S. Bezsonov, “Differential and linear properties analysis of the ciphers rijndael, serpent, threefish with 16-bit inputs and outputs,” Eastern European Journal of Enterprise Technologies, vol. 5, no. 4 (77), pp. 50-54, 2015.

О.О. Kuznetsov, Yu.І. Gorbenko, І.М. Bilozertsev, А.V. Аndrushkevych, О.P. Narizhnyi, “Algebraic immunity of non-linear blocks of symmetric ciphers,” Telecommunications and Radio Engineering, vol. 77, issue 4, pp. 309-325, 2018.

B. N. Tran, T. D. Nguyen and T. D. Tran, “A new S-box structure to increase complexity of algebraic expression for block cipher cryptosystems,” Proceedings of the 2009 International Conference on Computer Technology and Development, Kota Kinabalu, 2009, pp. 212-216.

A. Kuznetsov, R. Serhiienko, D. Prokopovych-Tkachenko, Y. Tarasenko, “Evaluation of algebraic immunity of modern block ciphers,” Proceedings of the 2018 IEEE 9th International Conference on Dependable Systems, Services and Technologies (DESSERT), Kyiv, Ukraine, 2018, pp. 288-293.

S. Sulaiman, Z. Muda, J. Juremi, “The new approach of Rijndael key schedule,” Proceedings of the 2012 International Conference on Cyber Security, Cyber Warfare and Digital Forensic (CyberSec), Kuala Lumpur, 2012, pp. 23-27.

A. Kuznetsov, I. Kolovanova, T. Kuznetsova, “Periodic characteristics of output feedback encryption mode,” Proceedings of the 2017 4th International Scientific-Practical Conference Problems of Infocommunications. Science and Technology (PIC S&T), Kharkov, 2017, pp. 193-198.

M. McLoone, J. V. McCanny, “High-performance FPGA implementation of DES using a novel method for implementing the key schedule,” IEE Proceedings - Circuits, Devices and Systems, vol. 150, no. 5, pp. 373-378, Oct. 2003.

A. Andrushkevych, Y. Gorbenko, O. Kuznetsov, R. Oliynykov, M. Rodinko, “Prospective lightweight block cipher for green IT engineering,” in: V. Kharchenko, Y. Kondratenko, J. Kacprzyk (eds) Green IT Engineering: Social, Business and Industrial Applications. Studies in Systems, Decision and Control, vol 171. Springer, Cham, pp. 95-112, 2019.

F. H. Nejad, S. Sabah, A. J. Jam, “Analysis of avalanche effect on advance encryption standard by using dynamic S-Box depends on rounds keys,” Proceedings of the 2014 International Conference on Computational Science and Technology (ICCST), Kota Kinabalu, 2014, pp. 1-5.

M. Rodinko, R. Oliynykov, “Open problems of proving security of ARX-based ciphers to differential cryptanalysis,” Proceedings of the 2017 4th International Scientific-Practical Conference Problems of Infocommunications. Science and Technology (PIC S&T), Kharkov, 2017, pp. 228-231.

H. Liu, C. Jin, “Lower bounds of differential and linear active S-boxes for 3D-like structure,” The Computer Journal, vol. 58, no. 4, pp. 904-921, April 2015.

C. U. Bhaskar, C. Rupa, “An advanced symmetric block cipher based on chaotic systems,” Proceedings of the 2017 Innovations in Power and Advanced Computing Technologies (i-PACT), Vellore, 2017, pp. 1-4.

M. Rodinko, R. Oliynykov, Y. Gorbenko, “Improvement of the high nonlinear S-boxes generation method,” Proceedings of the 2016 Third International Scientific-Practical Conference Problems of Infocommunications Science and Technology (PIC S&T), Kharkiv, 2016, pp. 63-66.

O. Kuznetsov, O. Potii, A. Perepelitsyn, D. Ivanenko, N. Poluyanenko, “Lightweight stream ciphers for green IT engineering,” in: V. Kharchenko, Y. Kondratenko, J. Kacprzyk (eds) Green IT Engineering: Social, Business and Industrial Applications. Studies in Systems, Decision and Control, vol 171, Springer, Cham, 2019, pp. 113-137.

D. D. Ismoyo, R. W. Wardhani, “Block cipher and stream cipher algorithm performance comparison in a personal VPN gateway,” Proceedings of the 2016 International Seminar on Application for Technology of Information and Communication (ISemantic), Semarang, 2016, pp. 207-210.

I. Gorbenko, O. Kuznetsov, Y. Gorbenko, A. Alekseychuk, V. Tymchenko, “Strumok keystream generator,” Proceedings of the 2018 IEEE 9th International Conference on Dependable Systems, Services and Technologies (DESSERT), Kyiv, Ukraine, 2018, pp. 294-299.

P. Jindal, B. Singh, “Analyzing the security-performance tradeoff in block ciphers,” Proceedings of the International Conference on Computing, Communication & Automation, Noida, 2015, pp. 326-331.

K. Lisickiy, V. Dolgov, I. Lisickaya, “Block cipher with improved dynamic indicators of the condition of a random substitution,” Proceedings of the 2017 4th International Scientific-Practical Conference Problems of Infocommunications. Science and Technology (PICS&T), Kharkov, 2017, pp. 391-395.

K. Lisickiy, V. Dolgov and I. Lisickaya, “Cipher with improved dynamic indicators of the condition of a random substitution,” Proceedings of the 2017 4th International Scientific-Practical Conference Problems of Infocommunications. Science and Technology (PIC S&T), Kharkov, 2017, pp. 396-399.

V. Dolgov, I. Ishchenko, “Proposals of using chameleon-signature in Ukrainian prototype of combined PKI,” Proceedings of the 2010 International Conference on Modern Problems of Radio Engineering, Telecommunications and Computer Science (TCSET), Lviv-Slavske, 2010, pp. 303-303.

V. Krasnobayev, A. Kuznetsov, S. Koshman, S. Moroz, “Improved method of determining the alternative set of numbers in residue number system,” in: O. Chertov, T. Mylovanov, Y. Kondratenko, J. Kacprzyk, V. Kreinovich, V. Stefanuk,” (eds) Recent Developments in Data Science and Intelligent Analysis of Information. ICDSIAI 2018. Advances in Intelligent Systems and Computing, vol. 836, Springer, Cham, 2019, pp. 319-328.

R. R. Bhat, V. Panchami, “A novel and robust symmetric block cipher for hand-held mobile devices,” Proceedings of the 2016 Online International Conference on Green Engineering and Technologies (IC-GET), Coimbatore, 2016, pp. 1-5.

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*International Journal of Computing*,

*18*(1), 89-100. https://doi.org/10.47839/ijc.18.1.1278

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