Научная электронная библиотека ULRICH'S Periodicals Directory

Сибирский государственный университет
науки и технологий имени академика М.Ф. Решетнева

Сибирский аэрокосмический журнал
ISSN 2712-8970 (Print) ISSN 2782-5760 (on-line)

Сведения об образовательной организации

UDK 512.624.2
POSSIBLE OPTIONS TO IMPROVE CRYPTOGRAPHIC RELIABILITY OF ALGORITHMS BASED ON NYBERG CONSTRUCTION
M. A. Dmitriev
Siberian Federal University 79, Svobodny Av., Krasnoyarsk, 660041, Russian Federation E-mail: makcmad@mail.ru
Nowadays one of the most used tools to protect data from unauthorized access is block symmetric-key cryptographic algorithms. The rapid growth of computer processing power and significant development of linear cryptanalysis actualize the task to continue increasing reliability of the existing algorithms, as well as developing new ones. An important component in determining the stability of a block symmetric-key cryptographic algorithm to the most common types of cryptanalysis is the quality of S-box substitution. This work was aimed at calculating and achieving all possible S-box substitutions, based on irreducible polynomials over the Galois field and their compositions. For this purpose a set of programs to obtain S-box substitutions which have different cryptographic characteristics with its help was developed. Calculation of the quantitative values of these characteristics was performed by presenting S-box substitutions in the form of sets of Boolean functions. Particular attention was paid to such characteristics as nonlinearity of Boolean functions, the maximum modulus of the correlation coefficients and the numbers of zeros of the correlation matrix of S-box substitutions, as those are the most important characteristics. These blocks substitutions can be the basis for further study of possible options to improve Rijndael algorithm’s cryptographic reliability.
Keywords: Rijndael algorithm, S-box, irreducible polynomial over the Galois field.
References

1. Mister S., Adams C. Practical S-box design. Proceedings, Workshop in selected areas of cryptography. SAC’96. 1996, P. 78–81.

2. Babenko L. K. Sovremennye algoritmy blochnogo shifrovaniya i metody ikh analiza [Current block encryption algorithms and methods of their analysis]. Moscow, Gelios ARV Publ., 2006, 376 p.

3. Mazurkov M. I. [Algebraic properties of cryptographic substitution tables of Rijndael and GOST 28147–89 cipher]. Trudy SIET. 2012, P. 149–151 (In Russ.).

4. Medvedeva T. E. [Evaluation of the reliability of GOST 28147–89 algorithm’s substitution tables]. Reshetnevskie chteniya [Reshetnev readings]. 2012, P. 666 (In Russ.).

5. Mazurkov M. I., Sokolov A. V. [Cryptographic properties of nonlinear transform of Rijndael cipher based on complete classes of irreducible polynomials], Pratsі Odes'kogo polіtekhnіchnogo unіversitetu. 2012, No. 2, P. 183–189 (In Russ.).

6. Lidl R., Niderrayter G. Konechnye polya [Finite fields]. Moscow, Mir Publ., 1988, 667 p.

7. Zhdanov O. N. Metodika vybora klyuchevoy informatsii dlya algoritma blochnogo shifrovaniya [Key information selection for the block cipher algorithm]. Moscow, INFRA-M Publ., 2013, P. 19–34.

8. Nyberg, K. Differentially uniform mappings for cryptography. Advances in cryptology. Proc. of EUROCRYPT’93. Lecture Notes in Compuer Springer- Verlag. Berlin, Heidelberg, New York, 1994, Vol. 765, P. 55–65.

9. Zhdanov O. N., Zolotarev V. V. Metody i sredstva kriptograficheskoy zashchity informatsii [Methods and means of cryptographic protection of information]. Krasnoyarsk, SibSAU Publ., 2008, 253 p.

10. Logachev O. A., Sal’nikov A. A., Yashchenko V. V. Bulevy funktsii v teorii kodirovaniya i kriptologii [Boolean functions in coding theory and cryptology]. Moscow, MTsNMO Publ., 2004, 470 p.

11. Vashkevich A. V., Zhdanov O. N. [Finding nonlinearity of a Boolean function by Walsh converting]. Reshetnevskie chteniya [Reshetnev readings]. Krasnoyarsk, 2012, P. 655–700 (In Russ.).

12. Nikitin D. A., D’yakonov K. V. [On the distribution of the values of the nonlinearity of Boolean functions]. Actual Problems of Information Technology Security: Materials of IV International scientific-practical conference [Actual problems of information technology security: materials of the IV International Scientific and Practical Conference]. Krasnoyarsk, SibSAU Publ., 2010, P. 15–22 (In Russ.).

13. Zhukov A. E. Nelineynost’ bulevykh funktsiy [Nonlinearity of Boolean functions]. Moscow, MGTU im. Baumana Publ., 2002, P 45–112.

14. Fuller J. Millan. W. Linear Redundancy in S-Boxes. Fast Software Encryption, 10th International Workshop. Sweden, Lund, 2003. Vol. 2887. P. 74–86.

15. Daemen J., Rijmen V. The Design of Rijndael. Springer-Verlag Berlin Heidelberg. Springer. 2002, P. 31–51.



Dmitriev Maksim Anatol’evich – postgraduate student, Siberian Federal University. E-mail: makcmad@mail.ru.