=Paper=
{{Paper
|id=Vol-2923/paper4
|storemode=property
|title=Prospective Areas of Research in the Development of Post-Quantum Cryptography
|pdfUrl=https://ceur-ws.org/Vol-2923/paper4.pdf
|volume=Vol-2923
|authors=Vasyl Sheketa,Svitlana Chupakhina,Mariya Leshchenko,Larysa Tymchuk,Kostiantyn Chub
|dblpUrl=https://dblp.org/rec/conf/cpits/SheketaCLTC21
}}
==Prospective Areas of Research in the Development of Post-Quantum Cryptography==
https://ceur-ws.org/Vol-2923/paper4.pdf
Prospective Areas of Research in the Development of Post-
Quantum Cryptography
Vasyl Sheketaa, Svitlana Chupakhinab, Mariya Leshchenkoc, Larysa Tymchukd,
and Kostiantyn Chube
a
National Technical University of Oil and Gas, 15 Karpatska str., Ivano-Frankivsk, 76068, Ukraine
b
Vasyl Stefanyk Precarpathian National University, 57 Shevchenko str., Ivano-Frankivsk, 76000, Ukraine
c
Institute of Information Technologies and Learning, 9 M. Berlynskoho str., Kyiv, 04060, Ukraine
d
Center Ivan Chernyakhovsky National University of Defense, 28 Povitroflotskiy ave., Kyiv, 03049, Ukraine
e
Poltava V. G. Korolenko National Pedagogical University, 2 Ostrogradskogo str., Poltava, 36000, Ukraine
Abstract
Critical questions about the need to prepare both international and domestic information
infrastructure for the emergence of post-quantum mechanisms of cryptanalysis of critical
information on the corresponding computing systems are considered. This requires taking
into account the experience of the international community in developing and testing a series
of post-quantum standards in the field of cryptographic protection of key information. At the
same time, it is very important to take into account the following aspects that the Ukrainian
standardized system insists on the use of time-tested encryption mechanisms: when the long-
term studies of connectivity will not be detected in this mechanism. Except for the NTRU
scheme based on McAlice’s theory and other encoding schemes, post-quantum cryptography
has a history of up to 5 years. To some extent, NIST has been rushing to implement post-
quantum encryption technology (for example, a memorandum issued by the U.S. National
Security Agency in 2015 provided U.S. developers with encryption to protect important
information that has not yet been included in its products. Introduction of information
encryption technology. Algorithms based on elliptical curve operations avoid the
implementation of these algorithms to save resources with the proposed transition to post-
quantum algorithms), which forces us to carefully test new standards developed in the
procedures of the organization to avoid using standards for the generation of pseudo-random
numbers. Many researchers objected, but pointed to obvious loopholes, so the standard needs
to be revoked. Proceeding from this it is obvious that the moment of transition to post-
quantum cryptography will require fundamental reorganization of the whole basic
infrastructure of information protection, all methods of information protection using
asymmetric cryptographic algorithms, especially the infrastructure of an authentication
center. Taking into account the cost of these events, one should make a cautious decision
about the transition to post-quantum cryptography based on accurate forecasts of the
development of post-quantum computing system functions. Based on the above-mentioned
research, we can confidently say that the global IT community is actively preparing for
significant changes with the advent of the post-quantum era.
Keywords 1
Algorithms, cryptography, post-quantum computing system, encoding schemes, critical data,
software applications.
1. Introduction
In the era of rapid information development, active global research in the field of post-quantum
computing systems and computation is being carried out all over the world. Thus, the creation of a
supercomputing system that will use the post-quantum model in the processing of computational
Cybersecurity Providing in Information and Telecommunication Systems, January 28, 2021, Kyiv, Ukraine
EMAIL: vasylsheketa@gmail.com (A.1); cvitlana2706@gmail.com (B.2); darlyngpetra18@gmail.com (C.3); lucky.clio2017@gmail.com
(D.4); kchub2017@gmail.com (E.5)
ORCID: 0000-0002-1318-4895 (A.1); 0000-0002-3058-6650 (B.2); 0000-0003-4121-565X (C.3); 0000-0003-4678-2362 (D.4); 0000-0001-
6325-6466 (E.5)
©️ 2021 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
27
algorithms (post-quantum computing system), which in turn can create negative consequences for the
decryption of a number of cryptographic mechanisms of systems for the protection of important
information data. In the modern understanding of post-quantum computing technology, it is assumed
to create and manage complex post-quantum computing systems, which are created from a significant
volume of objects, at the level of separately created components such as individual atoms, ions,
photons, electrons, molecules, etc., which will be used for the protection of important data. This
scientific approach makes it possible to use such unusual phenomena as post-quantum superposition,
which is the ability of post-quantum computing systems to be in all possible known states at once.
And such post-quantum multi-coordination of objects is manifested by strong interrelationships
between different parameters of specially designed post-quantum computing systems. Therefore, the
modern period of information development of post-quantum technologies is often called the “second
quantum revolution.” In particular, on the created post-quantum computing system there will be an
opportunity to implement algorithms of factorization and discrete logarithmize in arbitrary groups
with polynomial complexity (Shore method), and the essence of his studies and the proposed
hypothesis (which made a lot of noise in the world), that it is the solution of the algorithmically
complex problem of number factorization is based on numerous modern algorithms and cryptography
systems. The algorithm found by Peter Shore in 1994 allows to solve this problem in polynomial time
(polynomial number of gates) and on polynomial number of qubits, while classical algorithms solve it
in super polynomial (sub-exponential) time. This means that once a post-quantum computer with a
sufficient number of qubits is created, all modern cryptography will be compromised. It will be
compromised immediately since any information hidden using this approach can be obtained by
anyone who has access to such a post-quantum computer [1, 3, 4, 5, 7].
The algorithm, discovered by Peter Shore in 1994, solves this problem in polynomial time (hence,
the number of valves is polynomial) and on polynomial qubits, while the classical algorithm solves it
in hyper polynomial time (sub-exponential). This means that once a post-quantum computing system
with sufficient qubits is created, all modern encryption technologies will be at risk. These cyber
defense systems will be tied up since any information hidden by these methods can be obtained by
any user who has the right to use this post-quantum computer [2, 6, 8, 10, 11].
The stability of the algorithm is based on the assumption of the complexity of solving the above
problems, including RSA (Rivest-Shamir-Adleman) Diffie-Hellman scheme, ECDSA (Elliptic Curve
Digital Signature Algorithm) the digital signature, and various standards. At the same time, the
currently known post-quantum algorithms for the analysis of hash functions and block cipher (the
F. Ambainis collision search method and the original M. Grover image search method) still have
exponential complexity, although their complexity is less than classical Fig. 1.
Grover diffusion operator
|0 n
H n H n 2|0n 0n |— In H n
Uw
|1 H
Figure 1: Grover Algorithm presentation
The meaning of the Grover algorithm is to “increase the target state amplitude” by reducing the
amplitude of all other classes. Geometrically speaking, the Grover algorithm consists of a precise
rotation of the current state vector of a post-quantum computer in the direction of the target state
(movement along the shortest path ensures optimality of the Grover algorithm) [9, 12, 15, 16].
Each iteration step gives a rotation of 2α, where the angle between Iõ and Ixtar is defined as π/2 – α.
Further prolongation of iterative calculations of operator G will give a continuation of circumvention
of the circle in the real plane generated by these vectors.
The stability of the algorithm processing is based in the proposed cases on the assumption of the
complexity of solving the above problems, including RSA, Diffie-Hellman scheme, digital signature
28
ECDSA, and various other approaches and standards. At the same time, since the currently known
post-quantum algorithms for the analysis of hash functions and block cipher (the Amboina’s collision
search method and the original Grover image search method) still have a significant exponential
complexity, although their complexity is less than the classical approaches [13, 17, 18].
At the same time, experts assess differently the prospects of creating a working sample of post-
quantum computing systems with capabilities sufficient to solve practical problems of cryptanalysis.
The estimated time for the creation of such a post-quantum computer is from 7 to 25 years. Some
especially pessimistic scientists believe that physical obstacles to the creation of post-quantum
computing systems cannot be overcome, where the main feature of the functioning of post-quantum
computing systems is based on the number of qubit-base blocks in it [14, 20, 21, 24].
The main feature of the post-quantum computing system functions is the number of qubit-base
blocks. Thus, the condition of the cryptanalysis task is set as the initial state of the qubit system, from
which the post-quantum computing system is built, to perform a number of transformations defined
by the post-quantum algorithm. As a result of the final measurement of the qubit system state, an
optimal solution to the cryptanalysis problem can be found. However, in this case, in the process of
calculating and accurately measuring the state of qubits, it is necessary to overcome the physical
degradation of qubits, so there are great engineering and physical difficulties [22, 27, 28, 30].
For a successful solution of the cryptographic analysis task, it is necessary to perform factorization
of number N, which is the secret key of the RSA cryptographic system, using the Shore method it is
necessary to use approximately 4/3logN cubits and a polynomial number of computational operations.
At present, the cryptographic protection standards used in business models, which regulate the
application of RSA software and data protection system, recommend the use of a numerical sequence
with a length of at least 2048 bits, so to perform a successful cryptographic analysis of such a
sequence will require a post-quantum computing system with a power of more than 2736 cubits [19,
23, 26].
2. Prospective Development of Crypto Mechanisms on Post-Quantum
Computing Systems
At the moment there are several commercial prototypes of post-quantum computing systems,
including those developed by such companies as IBM and D-Wave. These post-quantum computing
systems are designed to solve global optimization problems and are not suitable for detailed sequence
cryptanalysis. At the same time, it should be noted that at the beginning of this year one of the firms
(IBM) which is actively engaged in the development of post-quantum computing systems presented to
the IT community a “personal” 20-cubit post-quantum computer. It was mounted in a case with a total
volume of about 9m3. D-Wave post-quantum computing systems, which are used, including by
Google and NASA, have, according to the manufacturer, a productive capacity of up to 1,152 cubic
meters. These post-quantum computing systems are grouped into several clusters, but the nature of
their internal topological relationships allows us to assert with some certainty that they have
significant limitations that these devices are built for post-quantum computing models [25, 28, 29].
The areas of synthesis of cryptographic computational schemes resistant to cryptanalysis using
both classical approaches and post-quantum computing have received the general name “post-
quantum cryptography.” The first international conference dedicated to the problems of PQCrypto
cryptanalysis was held in 2006 and has since become an annual conference.
In today’s realities, research conducted by the international cryptographic community in the field
of improvement and synthesis of post-quantum cryptographic algorithms has intensified thanks to the
efforts of the National Institute of Standards and Technology (NIST), which organized a forum for
submitting proposals for standardization and discussion of post-quantum cryptographic computational
schemes. (It should also be noted that this event is not a contest of ideas, as it does not involve the
nomination and awarding of the winner, but only the identification of a set of optimal synthesis
solutions for further practical research with the prospect of standardization.
During this forum, more than 179 descriptions of cryptographic mechanisms were offered, which
were developed by different teams of authors from different countries, including Ukraine. These
proposals were the basis for symposia, where the analysis of these cryptographic mechanisms was
29
summarized. Thus, the cryptographic mechanisms submitted for analysis and discussion have the
following implementation: encryption, digital signature, key encapsulation, and shared key
generation. And taking into account the experience of NIST’s previous studies on the creation of
block cipher (AES) and hash functions (SHA-3), a set of research works on cryptanalysis of the
proposed mechanisms and creation of new standards and proposals based on them may take from 4 to
7 years.
Thus, among the developments of complex cybersecurity systems, NIST systems are used by
thousands of commercial and non-profit organizations around the world to minimize cybersecurity
risks for critical infrastructure. Where there were formalized requirements for computing system
endurance, both formal (strictly proved based on the assumption of the complexity of solutions to a
certain task) and practical.
2.1. Asymmetric Encryption Systems for Infrastructure Critical Data
For asymmetric encryption systems with infrastructure critical data (listed from minor
requirements to strong ones):
Resistance of cryptanalysis to the threat of text cipher definition against cyberattack based on
selected open text (Indistinguishability Against Chosen Plaintext Attack, IND-CPA).
Cryptanalysis resistance to the threat of ciphertext determination against cyberattack and based
on selected ciphertext (Indistinguishability Against Chosen Plaintext Attack, IND-CCA).
Cryptanalysis resistance to the threat of ciphertext determination against cyberattack based on
(non-adaptive) selected plaintext (Indistinguishability Against (non-adaptive) Chosen Plaintext
Attack, IND-CPA1).
Resistance of cryptanalysis to the threat of text cipher determination against cyberattack based
on (incorrectly) selected ciphertext (Indistinguishability Against (non-adaptive) Chosen
Plaintext Attack, IND-CCA1).
Resistance of cryptanalysis to the threat of distinguishing text ciphers from an attack based on
adaptively chosen plaintext (Indistinguishability Against Adaptive Chosen Plaintext Attack,
IND-CPA2).
Cryptanalysis vulnerability to text cipher differentiation against an adaptively matched
plaintext attack (Indistinguishability Against Adaptive Chosen Plaintext Attack, IND-CCA2).
2.2. Features of using Electronic Signature Mechanisms
To select effective electronic signature schemes, developers of computer systems for processing
critical information should pay special attention to the following levels of cybersecurity in order from
weak to strongest:
Strong resistance of cryptographic protection to active attacks based on selected messages
SUF-CMA (Strong Enforceability under Chosen Message Attacks).
Strongest of cryptographic protection against active based on existential forgery using selected
messages EUF-CMA (Eventually Enforceability under Chosen Message Attacks).
2.3. Practical Resistance of Cryptographic Signature Crypto-Mechanisms to
Cryptanalysis
Determining the practical resistance of crypto-mechanisms of digital signature to the specified
conditions from the company NIST one of the developers of the world crypto standards provides five
different levels of resistance Table 1.
30
Table 1.
Five levels of crypto mechanism resistance
Level Practical crypto mechanism
I Equivalent to finding a 128-bit block cipher key
II Equivalent search for 256-bit hash function collisions
III Equivalent to finding a 256-bit block cipher key
IV Equivalent search for 384-bit hash function collisions
V Equivalent to finding a 384-bit block cipher key
Thus, for each proposal, it was necessary to provide formal and practical proof of the firmness of
cryptographic mechanisms of digital signatures against cryptanalysis, as well as to propose certain
sets of parameters for different levels of cryptographic firmness of the proposed schemes.
To solve this rather complicated and at the same time practical task, 69 proposals were submitted,
27 of which were unacceptable because their crypto-mechanisms were weak to cryptanalysis.
At the same time, the practical analysis of cryptographic mechanisms of the submitted proposals
did not do without curiosities, for example, the proposal submitted by D. Berstein with the co-authors,
namely, for the organization of the fifth cryptographic level of critical data protection, they proposed
to use RSA cryptographic mechanism with the exponential size of keys larger than 1 Gbyte.
Let’s give an example of the basic synthesis of solutions for cryptographic protection of critical
data, which apply to compete to NIST groups of developers of crypto-mechanisms:
Using integer lattice theory for crypto-mechanisms.
Using error correction codes for crypto-mechanisms.
Using for crypto-mechanisms multi-members from many variables.
Use of cryptographic hash functions for crypto-mechanisms.
Use of curves on super-singular elliptical curves for crypto-mechanisms; use of hash functions
for crypto-mechanisms.
Highly specialized tasks for crypto-mechanisms (Search Problem or Braid Group operation,
A. Keli octonion algebra, P. Chebyshev polynomials, etc.).
Ring learning with errors (RLWE) is a computational problem-solving solution underlying new
cryptographic algorithms such as NewHope to prevent quantum computing systems from performing
cryptanalysis and provide a foundation for strong homomorphic encryption. Thus, cryptographic
mechanisms with public keys are based on the construction of mathematical tasks. If there is a
sufficiently large quantum computing system, it can successfully solve some of these crypto analysis
problems, which are now used in cryptography, so that crypto researchers will protect critical
information and need to look for persistent problems. The use of homomorphic encryption is a form
of encryption that provides mathematical computations with encrypted critical text, for example, we
can use arithmetic operations with certain values stored in an encrypted data warehouse.
RLWE is more appropriate to be called ring error training, it’s just a big Learning With Errors
(LWE) problem, which specializes in multi-member rings over end fields. Because of the complexity
of solving RLWE problems even on quantum computers, RLWE-based encryption technology may
become the basis of public-key cryptography in the future, as well as problems of integer factorization
and discrete logarithm have become public secrets since the early 1980s. The basis of key
cryptography is the same. An important feature of cryptography with cyclic error learning is that the
RLWE solution can be used to solve the Problem of Shortest Vectors (SVP) of NP-hard lattice.
Crypto-mechanisms based on lattice theory (see an example of the corresponding mechanisms for
generating a common key in Fig. 1) is based on a number of complex problems, including the NP
problem of searching for the shortest vector (SVP) and searching for the nearest vector (SNP); the
problem of error learning (LWE; RLWE) and the problem of searching for the smallest integer
solution of the system of linear algebraic equations (SIS).
Example 1 of a generalized crypto mechanism Ring learning with errors (RLWE)
𝑅𝑞 = 𝑍𝑞 [𝑋]/(𝑋 𝑛 + 1)
𝜉 is error distribution (usually Gaussian)
sequence crypto secret key 𝑠 ∈ 𝑅𝑞
31
public-key cryptographic sequence 𝑎𝑠 + 𝑒, 𝑎 ∈𝑅 𝑅𝑞 , 𝑒 errors
Diffie-Hellman cryptographic algorithm: 𝑎𝑠 + 𝑒, 𝑏ś + á the common key of the
𝑣 = 𝑎𝑠ś + é𝑠 ≈ 𝑏𝑠ś + 𝑒ś; 𝑠, ś, 𝑒, é − is small relative to some norm
Among the developers of crypto-mechanisms for digital signatures, which were preliminary
analyzed and positively evaluated by NIST, according to their initial requirements, which were based
on lattice theory: Compact LWE; CRYSTALS-KYBER; Ding Key Exchange; EMBLEM and
R.EMBLEM; FrodoKEM; HILA5; KINDI; LAS; LIMA; Lizard; LOTUS; NewHORE; qTESLA.
For example, since the late 1970s, the problem of coding theory has been considered in
cryptography. Although the McAlice scheme has been cracked by cryptographers in many individual
cases, it may remain stable as long as the Goppa code is used.
Example 2 of the R. McEliece cryptography mechanism
G is generating a double linear (n, k) matrix—code that corrects k errors
𝑆 ∈𝑅 𝐺𝐿(𝑘, 2) is random matrix
𝑃 is supplied 𝑛 × 𝑛 matrix
𝐺՜ = 𝑆𝐺𝑃; (𝐺՜, 𝑡) is a public key, (𝑆, 𝐺, 𝑃) is a secret key
Encoded: 𝑐 = 𝐸(𝑚) = 𝑚𝐺՜ + 𝑒, 𝑒 is random weight vector t
Decryption: 𝑐՜ = 𝑐 ∗ 𝑃−1 ; 𝑚՜ is code decoding result 𝐺; 𝑚 = 𝑚՜ ∗ 𝑆 −1
Participants who accepted NIST’s proposal include the development and analysis of crypto
mechanics, which are based on coding theory: BIG QUAKE, BIKE, Classic McEliece, Edon-K,
HQC, LAKE, LEDApkc, Lepton, LOCKER, McNie, NTS-KEM, QC-MDPC KEM, Ramstake,
RLCE-KEM, RQC, RaCoSS, RankSign.
Since the mid-1980s, from the point of view of synthetic cryptography, the following idea has
been studied: the use of NP-complete tasks for solving polynomial systems. (Example 3). At the same
time, various practical and effective methods to solve this problem have been developed (method XL,
F4, F5, etc.), and many encryption schemes based on this task have been successful.
Example 3. Pure crypto mechanism scheme
In the final field K is chosen easily reversible square display 𝐹: 𝐾 𝑛 → 𝐾 𝑛 , 𝑚 ≥ 𝑛, and
reversible linear display (linear endomorphism) 𝑆: 𝐾 𝑚 → 𝐾 𝑚 , 𝑇: 𝐾 𝑛 → 𝐾 𝑛 ;
sequence crypto secret key—presentation of 𝑆, 𝐹, 𝑇;
public-key cryptographic sequence—presentation of 𝑃 = 𝑆 • 𝐹 • 𝑇;
Encoded: 𝑚 ∈ 𝐾 𝑛 , 𝑐 = 𝐸(𝑚) = 𝑃(𝑚);
Decryption: 𝑥 = 𝑆 −1 (𝑐), 𝑦 =; 𝐹 −1 (𝑥), 𝑦 = 𝐶 −1 (𝑦).
Competing groups of developers, which are based on this paradigm of the question on the
development and improvement of existing crypto mechanisms with NIST, are as follows: CFPKM,
Giophantus, DualModeMS, GeMSS, Gui, HiMQ-3, LUOV, MQDSS, Rainbow, SRTPI, DME.
And the hash-based signature scheme, developed back in the late 1970s for the one-time signature
of Lamport and Winternitz, makes it suitable for the construction of multiple signature schemes based
on the tree structure of a special type of hash value. In this way, the companies SPHINCS+ and
GravitySPHINCS which used this idea in one form or another are direct competitors of NIST.
3. Practical Use of Crypto Mechanisms for Critical Data
It should be noted that the NIST experts have not voiced an unambiguous preference for
cryptographic mechanisms when choosing a basic integrated solution, but only excluded the most
peculiar vulnerable solutions (which accounted for the majority of cyber-attacks).
The next step is to fix and improve the cryptographic plan, which has entered the second phase,
and the deadline for this process is late 2020. Also important is the validity of the proposed NIST
competition plan. It should be noted that all cryptographic schemes, without exception, have the size
of parameters, key length and, as a rule, the length of an encrypted text message (signature, shared
key) is greater than that of a traditional cryptographic computer scheme with the same security level
as the traditional calculator as RSA, ECDH, ECDSA. In practice, it usually requires significantly
more computing resources, such as the performance of the cryptographic system, the use of processor
time, and available memory.
32
Consequently, the transition to inverse post-quantum cryptography will require a significant
increase in computing resources dedicated to the cryptographic conversion of critical data streams to
reliably support the functions of a secure network for processing critical information [31, 32].
The International Organization for Standardization/International Electrotechnical Commission also
covers the field of post-quantum standardization of cryptography. Therefore, the professional
technical committee responsible for the standardization of information protection mechanisms has
started to create a configuration file that will reflect the main direction of the post-quantum
cryptographic scheme after its creation.
Thus, summing up our review it is possible to assert with certainty that today only a small number
of proposed crypto mechanisms from the following groups working in this direction deserve the close
attention of developers of software systems with the maintenance of critical information.
For public-key encryption and key encapsulation: BIKE, Classic McEliece, CRYSTALS-KYBER,
FrodoKEM, HQC, LAC, LEDAcrypt (derivative scheme from LEDAkem/LEDApkc), NewHope,
NTRU (from NTRUEncrypt/NEMTRU-HRSS-KYBER NTRU Prime, NTS-KEM, ROLLO
(derivative scheme from LAKE/LOCKER/Ouroboros-R), Round5 (derivative scheme from
Hila5/Round2), RQC, SABER, SIKE, Three Bears.
For digital signature schemes: CRYSTALS-DILITHIUM, FALCON, GeMSS, LUOV, MQDSS,
Picnic, qTESLA, Rainbow, SPHINCS+.
4. Conclusions
It is also necessary to prepare the domestic information infrastructure for the emergence of post-
quantum cryptanalysis and corresponding computing systems. Of course, it is necessary to take into
account the experience of the international community for developing and testing a series of post-
quantum standards in the field of cryptographic protection of key information. However, the
following aspects should be taken into account.
Usually, the Ukrainian standardized system insists on using time-tested encryption mechanisms:
no loopholes will be detected in this mechanism during long-term research. Except for the NTRU
scheme based on McAlice’s theory and other encoding schemes, post-quantum cryptography has a
history of up to 5 years.
To some extent, NIST has been hasty in taking steps to implement post-quantum encryption
technology (for example, a memorandum issued by the U.S. National Security Agency in 2015
provided U.S. developers with encryption to protect important information that has not yet been
included in its products. Introduction of encrypted information. Algorithms based on elliptical curve
operations, avoid the implementation of these algorithms to save resources for the proposed transition
to post-quantum algorithms), forcing us to carefully test new standards developed in the procedures of
the organization to avoid using standards for the generation of pseudo-random numbers. The
repetition of the scandalous Dual_EC_DRBG history has been standardized. Many researchers
objected, but pointed to obvious loopholes, so the standard needs to be revoked.
Proceeding from this it is obvious that the moment of transition to post-quantum cryptography will
require fundamental reorganization of the entire basic infrastructure of information security, all
methods of information protection using asymmetric cryptographic algorithms, especially the
infrastructure of the authentication center. Taking into account the cost of these events, we should
make a cautious decision on the transition to post-quantum cryptography based on accurate forecasts
of the development of post-quantum computing system functions.
The moment of transition to post-quantum cryptography will require fundamental reorganization
of all basic infrastructure of information security, all methods of information protection using
asymmetric cryptographic algorithms, especially the infrastructure of the authentication center.
Taking into account the cost of these events, it is necessary to make a cautious decision on the
transition to post-quantum cryptography using accurate data of forecasts of the development of post-
quantum computing system functions.
Based on the above scientific research, we can confidently say that the international IT community
is actively preparing for significant changes with the advent of the post-quantum era.
33
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