Prerequisites for Developing a Methodology for Estimating and Increasing Cryptographic Strength based on Many-Valued Logic Functions

Abstract

One of the most important components of modern information security systems is the cryptographic subsystem, which solves the problem of ensuring the integrity, confidentiality, and authentication of transmitted and stored information. In this case, the main component of the cryptographic subsystem is the block symmetric cipher (BSC) used for cryptographic transformation of large amounts of data. These components are so often used in information processing and transmission systems that the blocks corresponding to them are now implemented in processors in the form of separate hardware modules [1]. We also note the fact that in many countries the described cryptographic constructions are standardized and are used to protect the information in the specialized information systems which are critical for national security. In particular, in Ukraine, the Kalyna crypto algorithm which is described by the DSTU 7624:2014 standard [2], is used to protect the information in military and civilian systems for processing and storing information. These circumstances make the task of estimation and improving the cryptographic quality of these algorithms especially urgent. The fundamental principles on which any modern cryptographic algorithm is built are the principles of diffusion and confusion proposed by C. Shannon [3]. However, like Shannon's theorem, the principles of diffusion and confusion give only the idea of the quality of cryptographic constructions and the cryptographic algorithms built on their basis. Nonetheless, they provide neither specific methods for estimation of the quality of cryptographic primitives and cryptographic algorithms, nor methods for constructing cryptographic primitives and algorithms that would best implement the principles of diffusion and confusion. Since the formulation of the principles of diffusion and confusion by C. Shannon, many attempts have been made to create a comprehensive theory for estimating the quality of cryptographic algorithms and primitives based on them, which would be focused on the estimation of the ability of cryptographic algorithms components and their superpositions to resist possible attacks using modern cryptanalysis methods. Nevertheless, the further development of cryptanalysis methods, in particular, the emergence of cryptanalytic attacks based on many-valued logic functions [4], as well as the active development of quantum cryptanalysis methods [5], determines the need for further improvement of methods for estimation of the cryptographic quality of existing structures, and the development of new cryptographic constructions, and cryptographic algorithms that meet the developed cryptographic quality criteria. The purpose of this paper is to research the prerequisites for creating a methodology for estimation and increasing the cryptographic strength based on the mathematical apparatus of many-valued logic functions.