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Introduction

Various cryptographic mechanisms are used to provide basic security services in modern information

and telecommunication systems, in particular, public-key (two-key) cryptosystems, in which a
problem of searching of secret key by public key connects to a solution of the well-known and hardest

mathematical problem (factoring, discrete logarithmization, etc.) [1-3]. However, with the
appearance of quantum computing based on the quantum mechanical principles, in particular,

superposition principle and quantum entanglement, a speed of solution of some mathematical

problems is significantly increasing [4]. Some quantum algorithms exist, for example, Shor's, Grover,
Deutsch–Jozsa, Simon’s algorithms, and another, an execution of which has far less time, than an

execution of any probabilistic classical algorithm [5-11]. Shor's algorithms allow to find all simple
multipliers of big numbers in a finite (and acceptable) time, or to solve a discrete logarithm problem.

Consequently, it allows to find a secret key of corresponding asymmetric cryptoalgorithm (RSA,
ECC, etc.) [10]. Thus, development and theoretical justification of new cryptoalgorithms, in which a

complexity of search of secret parameter by public key, remain high even take into account of possible

using of the quantum computing (i.e. for the post-quantum period), and is extremely important
scientific problem [12-14].

Amount possible candidates for the post-quantum cryptography, the algorithms, building of which
based on using of algebraic codes that are camouflaged on the common state code (random code,

complete code), occupy a special place [15-18]. These similar algorithms are called theoretical-code
schemes [19, 20], or crypto-codes transformations [21, 22] in Russian-languages literature. These

crypto-codes transformations remain steadfast even in a case of quantum computing use along with
a high speed of the crypto-transformations and a possibility to combine an error checking and

unauthorized familiarization protection [23]. Besides, todays different crypto-graphical primitives

(asymmetrical [15, 16, 18, 20] and symmetrical [17] encryption algorithms, pseudo-random
sequences and stream encryption generators [24-26], zero-knowledge proof (protocols) [27, 28],

electronic digital signature schemes [29, 30], identification [31, 32], etc.) based on algebraic codes
using, are already known. There is make this direction as universal tool, which allows to realize a

wide range of effective cryptographic information protection mechanisms based on unique
mathematical and program software. Nevertheless, computationally efficient attacks to separated

variants of theoretical-code schemes [19, 33 - 36] are known, basic scheme [15], which has been

proposed around 40 years ago, remains resistant to all well-known crypto-analysis methods.
Reliability and perceptivity of the crypto-code transformations, especially in the context of building

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