DOI: https://doi.org/10.15588/1607-3274-2019-4-17

AVALANCHE CHARACTERISTICS OF CRYPTOGRAPHIC FUNCTIONS OF TERNARY LOGIC

A. V. Sokolov, O. N. Zhdanov

Abstract


Context. The development and aplication of cryptographic algorithms based on many-valued logic functions makes it important
to research their cryptographic properties and develop effective criteria for the cryptographic quality of their components. The
development of efficient methods for the synthesis of high-quality cryptographic primitives based on the functions of many-valued
logic is also an important task. The object of this research is the process of improving the efficiency of cryptographic algorithms
based on many-valued logic functions.
Objective. The purpose of this paper is to generalize the error propagation criterion and the strict avalanche criterion for the case
of functions of three-valued logic.
Method. The emergence of cryptography based on many-valued logic functions led to the understanding that today’s dominant
cryptographic algorithms based on binary algebraic constructions are only a special case of more general trends. Numerous researches show that the use of cryptographic constructions based on many-valued logic functions leads to the creation of cryptoalgorithms that more fully implement the principles of diffusion and confusion. One of the most important cases of many-valued logic functions are 3-functions, which are also used in quantum cryptography. This article is another step towards developing cryptographic constructions based on many-valued logic functions.
Results. The definition of the propagation criterion was extended to the case of functions of three-valued logic. On the basis of
the propagation criterion for the functions of three-valued logic, the definition of a strict avalanche criterion was introduced, which
describes the stability of cryptographic constructions against differential cryptanalysis attacks. We experimentally determined the
number of 3-functions of length N=9, satisfying the strict avalanche criterion. A method based on three constructive rules is proposed, which allows to synthesize a complete set of 864 S-boxes of length N=9 satisfying strict avalanche criterion. This set of Sboxes is basic for the application of Kim’s construction, which allows to recurrently increase the length of the S-box to the required
value. The paper shows that using Kim’s construction to increase the length preserves the S-box satisfying to a strict avalanche criterion, while allowing to obtain S-boxes with satisfactory non-linearity value as well as small output and input vectors correlation.
Conclusions. The most important criterion of cryptographic quality, which shows the stability of the cryptographic algorithm to
attacks of differential cryptanalysis is the propagation criterion that was generalized to the case of 3-functions. The existence of 3-
functions of length N=9 satisfying the strict avalanche criterion is shown, and their full set is found. On the basis of the proposed
constructive method, a complete set of S-boxes of length N=9 that satisfy the strict avalanche criterion was synthesized. It is shown that the Kim scheme can be applied to recurrently increase the length of S-boxes based on many-valued logic functions. As an actual direction for the continuation of the research, the development of regular and constructive methods for th

Keywords


Cryptography, differential properties, ternary logic, Boolean function.

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