Evaluation of cryptographic primitives security based on proximity to the Latin square

Abstract

At the heart of the creation of modern cryptographic systems is the use of cryptographic primitives. This has as its main goal of providing high security created cryptographic primitives and cryptosystem. For the development of cryptographic primitives used various mathematical transformations. To evaluate the security of cryptographic primitives are used very different approaches. The paper proposes a universal approach to the assessment of security of any cryptographic primitives. Cryptographic primitive - algorithms of reversible transformation of the block of the data of the fixed size with use of a set of key parameters of the fixed size is offered. It shown that substitution is a base cryptographic primitive through which it is possible to express all the others. At the heart of the offered approach lies the theorem of C. Shannon that defines perfect secrecy for secret-key systems and shows that they exist. For perfect security receive it is necessary, that the size of a key was not less than size of the converted data and the key was in regular intervals distributed. Matrix representation of similar system is a Latin square - rectangular table, in each line and each column all elements are various. For maximum security of cryptographic primitives defined optimal parameters of the substitutions table. For a number of cryptographic primitives obtained analytical and prognostic assessment of their security based on proximity to the Latin square.