Fault-tolerant backup storage system for confidential data in distributed servers

TELKOMNIKA Telecommunication Computing Electronics and Control
Vol. 21, No. 5, October 2023, pp. 1030~1038
ISSN: 1693-6930, DOI: 10.12928/TELKOMNIKA.v21i5.25305  1030
Journal homepage: http://telkomnika.uad.ac.id
Fault-tolerant backup storage system for confidential data in
distributed servers
Olzhas Tasmagambetov, Yerzhan Seitkulov, Ruslan Ospanov, Banu Yergaliyeva
Department of Information Security, L. N. Gumilyov Eurasian National University, Astana, Kazakhstan
Article Info ABSTRACT
Article history:
Received May 08, 2023
Revised Jun 05, 2023
Accepted Jun 06, 2023
This article addresses the critical issue of securing backup storage for
confidential data, a key concern in safeguarding the operations of critical
information systems dealing with extensive amounts of sensitive
information. The study proposes a novel cryptographic fault-tolerant backup
storage system for confidential data, leveraging cryptographic algorithms
and protocols. These protocols enable message encryption, ensuring
decryption is only possible after a specified time period. The proposed
system combines various distributed key generation protocols, proactive
secret sharing protocols, asymmetric encryption algorithms, and digital
signature algorithms. By employing such cryptographic protocols,
it becomes feasible to develop and implement a robust, fault-tolerant service
for backing up confidential data.
Keywords:
Backup storage
Cryptographic algorithms
Elliptic curve cryptography
Information security
System fault tolerance This is an open access article under the CC BY-SA license.
Corresponding Author:
Yerzhan Seitkulov
Department of Information Security, L. N. Gumilyov Eurasian National University
Astana, Kazakhstan
Email: yerzhan.seitkulov@gmail.com
1. INTRODUCTION
This study focuses on addressing the security concerns associated with backing up confidential data.
It is an essential issue in maintaining the security of critical information systems that handle substantial
volumes of sensitive information. Specifically, the practical methods and protocols developed in this work
aim to facilitate the creation of a model for a fault-tolerant information storage service operating within
specified time constraints. Requirements for methods of ensuring the availability and fault tolerance of
information resources, hardware for processing and storing data are established for providing information
security during maintenance of informatization objects [1]-[4]. At the same time, for this, the owners ensure
the availability of a backup server room, data servers, data storage systems and data transmission channels.
Depending on the class of data criticality and computing resources, deployment of a mirror-loaded hot “clone”
of servers in a backup server room, an unloaded cold backup and storage of spare sets of server equipment and
data storage systems, as well as copies of the information resources themselves, should be provided. In addition,
redundancy of the life support systems of servers and the server room (guaranteed power supply (UPS, diesel
generator sets)) and grounding, air conditioning and ventilation systems, gas fire extinguishing and access
control independent of the fire safety systems of the building, as well as raised floors (to counteract flooding) is
provided. Also, for critical data of a fault tolerance class with a utilization rate of at least 98.7 percent
approaches to decomposition, their isolation, compatibility are used. In approaches to decomposition, computing
resources are distributed between virtual machines. In approaches to their isolation, the crash of one of them does
not affect the others. In approaches to compatibility, the software can run on standardized operating platforms.
The above is associated with the requirements to exclude a single point of failure at the logical and physical
levels of server hardware, software, separation of computing resources at the hardware and software levels.

TELKOMNIKA Telecommun Comput El Control 
Fault-tolerant backup storage system for confidential data in distributed servers (Olzhas Tasmagambetov)
1031
Fault tolerance in accordance with uniform requirements is also implemented by organizational measures by
developing procedures for recovering from failures and failures of servers and software, ensuring the safety
of virtual machine images, and storing spare parts in close proximity to server rooms. To achieve reliability
indicators of placement inside server rooms in critical informatization objects, methods of equipment location
are used to reduce the risks of threats. At the same time, one of the aspects of the fault-tolerant use of
information resources is the backup storage of a complete copy of archived data.
The daily operational activities of an employee using personal computers and information systems
in state bodies are associated with the creation of various kinds of information necessary for decision-making
and the provision of public services. The specified data and documents in electronic digital form may be with
different levels of relevance to the solution of various kinds of tasks, but may be necessary in the future for
the employee. Therefore, in the information and analytical activities of a civil servant, various kinds of
“drafts”, “document templates”, saved responses to requests, extracts from legal acts that are not subject to
accounting or do not meet the selection criteria for inclusion in the centralized information resources of the
unit or archives. It should be noted that some part of the electronic information stored on computers contains
personal data of citizens or other confidential information. In this regard, it can be assumed that such
documents in each subdivision of the state body are stored on computer equipment, the circulation of which
cannot be controlled, are of interest to intruders, and the loss of which can cause certain damage and paralyze
the activities of the state body. In this light, the most secure model is the storage and processing of
confidential data using a decentralized architecture in which concentration, processing and storage, as well as
guaranteed destruction, are carried out according to certain protocols [5]-[7].
In this paper, we consider a model of functioning of a fault-tolerant backup storage system of protected
information during a specific period using encryption techniques within a secure cryptographic framework
named as elliptic curve time-lapse cryptography (ECTLC). The procedure relies on time-lapse cryptography
(TLC) [8], [9], which establishes a cryptographic protocol for encrypting client data in a manner that ensures
decryption cannot occur before a specific designated time, regardless of whether the sender desires it. TLC
incorporates the Pedersen’s distributed key generation (DKG) protocol, the Feldman’s threshold verifiable
secret sharing (VSS) protocol, and the ElGamal encryption. The agreed-upon parameters of the ElGamal
encryption algorithm, including a prime number 𝑝 that generates a prime order element 𝑔, are utilized by TLC.
These parameters can be found, for example, in request for comments (RFC) 3526 and RFC 5114. ECTLC
employs analogous algorithms found in elliptic curve cryptography. More precisely, it employs a DKG
protocol that is dependent on the discrete logarithm problem on elliptic curves, the Pedersen’s threshold VSS
protocol, and the ElGamal encryption that is specifically tailored for elliptic curves (ECs). In this paper we
propose new cryptographic fault-tolerant backup storage system of confidential data based on above
mentioned cryptographic algorithms and protocols. It is different from Yergaliyeva et al. [10] where
Shamir’s secret sharing technology and Diffie-Hellman protocol on an elliptic curve were used. Furthermore,
there exists the potential to incorporate novel and enhanced algorithms into the protocol, which can offer
increased efficiency and expanded functionality. Specifically, to guarantee data encryption over an extended
duration, the proactive secret sharing protocol, as outlined in Sun et al. [11], can be employed.
2. METHOD
Now we consider the model of functioning of a fault-tolerant backup storage system of protected
information during a specific period. The parties included in the suggested model consist of:
a) The portal (𝑃𝑟) responsible for receiving applications from clients to store confidential information.
b) The client (𝐶𝑙) is a party who utilizes the portal as a user.
c) The service (𝑆𝑟) – it consists of 𝑛 distributed servers that are geographically separated from one
another, error-free and secretly performing calculations provided by the protocol, securely storing all
their secret data, having a secure method of backing up data for disaster recovery. The assumption is
made that the servers do not engage in collusion, meaning they do not share or transfer confidential data
among themselves. All servers can privately and secretly exchange information with each other,
forming a network. A threshold value 𝑡 is assumed such that at most 𝑡 − 1 servers can break the
protocol and at least 𝑡 servers are reliable. The condition 𝑛 ≥ 2𝑡 − 1 (𝑡 ≤ (𝑛 + 1) 2
⁄ ) must be satisfied,
for example, if 𝑛 = 3, then 𝑡 ≤ 2.
The model provides using the agreed parameters of the used elliptic curve: elliptic curve modulus-prime
number 𝑝, EC equation, coefficients 𝑎 and 𝑏 of this equation from field 𝐹𝑝, EC point 𝐺 of prime order 𝑝.
These settings can be found, for example, at the website of the SafeCurves project [12]. SafeCurves is a project
that aims to provide elliptic-curve cryptography (ECC) security, not just elliptic curve discrete logarithm
problem (ECDLP) security. It provides criteria for choosing curves that keep simple implementations safe.
Efficiency is an important factor in curve selection and most standards prioritize efficiency. However,

 ISSN: 1693-6930
TELKOMNIKA Telecommun Comput El Control, Vol. 21, No. 5, October 2023: 1030-1038
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SafeCurves does not prioritize efficiency unless it interacts with security concerns. The SafeCurves website
provides security ratings for various specific curves, some of which have been proposed for deployment or
are currently in use. In the model under consideration, the M-511 elliptic curve can be used with the
following parameters [12].
− The elliptic curve modulus, the prime number
𝑞 = 2511
− 1 =
67039039649712985497870124991029230637396829102961966888617807218608
8201503677348840093714908345171384501592909324302542687694140597328497321682450
3041861.
− The elliptic curve equation
𝑦2
= 𝑥3
+ 530438𝑥2
+ 𝑥𝑚𝑜𝑑𝑞
− The equation coefficients 𝑎 and 𝑏 from the finite field
− 𝐹𝑞: 𝑎 = 530438, 𝑏 = 1
− The base point of prime order 𝑁 on the elliptic curve
𝐺 = (𝑥𝐺, 𝑦𝐺) = (5,
17360859007097926424827522860389970695051812781717659187866778424758212450543074
5177116625808811349787373477), 𝑁 = 2508
1072475475963574762404453151406812184207075662743483302896554080882767
50620 = 83798799562141231872337656238786538296746036378702458610772259023261025
18796074108048767793830555087621410592584974489349870525087756261624609307379422
99.
The M-511 curve satisfies requirements to basic parameters, ECDLP safety requirements and ECC
safety requirements in addition to ECDLP safety. Curve M-511 has a sufficient security level of 2252.3
, and
therefore provides resistance to various attacks [12]. Overview of the model (protocol):
− Step 1: the client performs a typical login procedure on the portal.
− Step 2: the client submits a data encryption request (for a specific message, 𝑚) to 𝑃𝑟.
− Step 3: 𝑃𝑟 forwards the 𝐶𝑙’s request to 𝑆𝑟, including the 𝐶𝑙’s unique ID, the moment of time 𝑇𝐼𝐷 when
the request was dispatched, and the designated moment of time 𝑇𝐼𝐷 + 𝛿𝐼𝐷 by which the 𝐶𝑙’s data should
remain encrypted and inaccessible for decryption. These steps are illustrated in Figure 1.
Figure 1. Steps 1-3
− Step 4: each service server 𝑃𝑖 receives a request.
− Step 5: each server 𝑃𝑖 chooses random values 𝑎𝑖0, 𝑎𝑖1, …, 𝑎𝑖𝑘, 𝑏𝑖0, 𝑏𝑖1, …, 𝑏𝑖𝑘, where 𝑘 = 𝑡 − 1, from
the field 𝐹𝑝 (i.e., 0 ≤ 𝑎𝑖𝑟 < 𝑝, 0 ≤ 𝑏𝑖𝑟 < 𝑝). 𝑎𝑖0 is a part of the private key.
− Step 6: then each server 𝑃𝑖 calculates 𝑠𝑖𝑗 = 𝑎𝑖0 + 𝑎𝑖1𝑗 + 𝑎𝑖2𝑗2
+ ⋯ + 𝑎𝑖𝑘𝑗𝑘(𝑚𝑜𝑑𝑞) and
𝑠′𝑖𝑗 = 𝑏𝑖0 + 𝑏𝑖1𝑗 + 𝑏𝑖2𝑗2
+ ⋯ + 𝑏𝑖𝑘𝑗𝑘(𝑚𝑜𝑑𝑞), where 𝑗 ≠ 𝑖 is a number of the server 𝑃𝑗, 1 ≤ 𝑗 ≤ 𝑛.
− Step 7: then each server 𝑃𝑖 calculates 𝐶𝑖𝑟 = 𝑎𝑖𝑟𝐺 + 𝑏𝑖𝑟𝐺′, 0 ≤ 𝑟 ≤ 𝑘 (here the operations of adding the
points of an elliptic curve and multiplying a point by a number are applied).
− Step 8: then each server 𝑃𝑖 sends 𝑠𝑖𝑗 and 𝑠′𝑖𝑗 to the servers 𝑃𝑗 over private communication channels
between 𝑃𝑖 and 𝑃𝑗, and publicly publishes 𝐶𝑖𝑟 (0 ≤ 𝑟 ≤ 𝑘) with its digital signature 𝑆𝐼𝐺𝑁𝑖.
− Step 9: each server 𝑃𝑖, having received 𝑠𝑗𝑖 and 𝑠′𝑗𝑖 from the servers 𝑃𝑗, 1 ≤ 𝑗 ≤ 𝑛, 𝑗 ≠ 𝑖, checks for
equality 𝑠𝑗𝑖𝐺 + 𝑠′𝑗𝑖𝐺′
= ∑ 𝑖𝑟
𝐶𝑗𝑟
𝑘
𝑟=0 (∗).
If equality (∗) does not hold for values 𝑠𝑗𝑖 and 𝑠′𝑗𝑖 received from the server 𝑃𝑗, then the server 𝑃𝑖 complains
against 𝑃𝑗. If the server 𝑃𝑖 receives a complaint against himself, he publishes 𝑠𝑖𝑗 and 𝑠′𝑖𝑗 with his digital
signature 𝑆𝐼𝐺𝑁𝑖, satisfying the equality (∗).

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− Step 10: each server 𝑃𝑖 marks as disqualified each server that received more than 𝑘 complaints or
responded to a complaint with values that do not satisfy the equality (∗).
− Step 11: each server 𝑃𝑖 creates a set 𝑄 of all non-disqualified servers. Each server 𝑃𝑖 from the set 𝑄
calculates 𝐴𝑖0 = 𝑎𝑖0𝐺 and publishes 𝐴𝑖0 with its digital signature 𝑆𝐼𝐺𝑁𝑖.
− Step 12: each server 𝑃𝑖 from the set 𝑄 receives 𝐴𝑗0 and calculates the public key 𝑃𝑘𝑖 = ∑ 𝐴𝑗0
𝑗∈𝑄 .
− Step 13: each server 𝑃𝑖 forms the key structure (𝐾𝑆) 𝐾𝐼𝐷 = (𝐼𝐷, 𝑇𝐼𝐷, 𝛿𝐼𝐷, 𝑃𝐾𝐼𝐷 = 𝑃𝑘𝑖) with its digital
signature 𝑆𝐼𝐺𝑁𝑖.
− Step 14: each server 𝑃𝑖 sends the generated 𝐾𝑆 to 𝑃𝑟.
− Step 15: 𝑃𝑟 transmits the received 𝐾𝑆 to 𝐶𝑙. These two steps are illustrated in Figure 2.
Figure 2. Steps 14-15
− Step 16: the client verifies 𝐷𝑆𝑠 𝑆𝐼𝐺𝑁𝑖(𝐾𝐼𝐷) against the published 𝐾𝑆𝑠 𝐾𝐼𝐷, ensuring that they match
and meet the minimum requirements for 𝑡 participants, and also verifies the identity associated with the
key structures.
− Step 17: 𝐶𝑙 generates a symmetric key 𝑠 to encrypt the message 𝑚.
− Step 18: 𝐶𝑙 encrypts the message 𝑚 with the key 𝑠.
− Step 19: 𝐶𝑙 encrypts the symmetric key 𝑠 as follows. The key 𝑠 is placed at the point of the elliptic curve:
a point 𝑀 = (𝑥, 𝑦) is chosen such that the part of the vector 𝑥 is fixed and corresponds to the key 𝑠, and
the vector 𝑦 satisfies the elliptic curve equation for the selected 𝑥, i.e., 𝑦 is the square root modulo 𝑝
(Shanks’ algorithm). A random number 𝑟, 0 < 𝑟 < 𝑞 is chosen. 𝐶1 = 𝑟𝐺: 𝑟𝐺 = 𝐺 + 𝐺 + ⋯ + 𝐺 is
calculated (𝑟 times) (+ is addition operation on an 𝐸𝐶). 𝐶2 = 𝑀 + 𝑟𝑃𝑘 is calculated, where 𝑃𝑘 is the
public key (elliptic curve point). A pair (𝐶1, 𝐶2) is a ciphertext.
− Step 20: the client sends an encrypted message 𝑚 and an encrypted symmetric key 𝑠 to the portal. This
step is illustrated in Figure 3.
Figure 3. Step 20
− Step 21: 𝑃𝑟 securely stores the encrypted data and encrypted key, linking them to the 𝐶𝑙’s ID and other
parameters including the specified time mentioned in the request.
− Step 22: once the designated time specified in the request is reached, or at any point thereafter, 𝑃𝑟 sends
a request to 𝑆𝑟 to obtain a private key, providing the 𝐶𝑙’s ID, public key, and time parameters. This step
is illustrated in Figure 4.

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Figure 4. Step 22
− Step 23: every server receives a request and distributes its private key among the other servers.
− Step 24: each server obtains the private keys from the other servers, computes the combined private
key, associates it with the corresponding public key, securely stores it in its database, and transmits the
private key to 𝑃𝑟.
− Step 25: 𝑃𝑟 receives the private key and decrypts the symmetric key using this key as follows. 𝐷𝑘𝐶1 is
calculated where 𝐷𝑘 is private key. −𝐷𝑘𝐶1 is calculated (inverse element for 𝐷𝑘𝐶1). (−𝐷𝑘𝐶1) + 𝐶2 = 𝑀
is calculated.
− Step 26: the portal decrypts the client’s data.
Note: as a component of 𝑆𝑟, it is possible to utilize a small network of managers who operate as a
cohesive management team for overseeing 𝑆𝑟. The primary duty of this team is to generate a schedule of
public keys and corresponding private keys produced by 𝑆𝑟. They also manage an internal bulletin board
exclusively for 𝑆𝑟’s members and maintain an open bulletin board accessible to 𝑆𝑟’s users. Every manager
will keep their individual duplicates of these boards.
The servers and users of the service will examine the messages posted on each copy of the bulletin
board and determine the correct values based on the majority of entries. Each server in the service
accompanies every message with a digital signature. The activities of all participants in the protocol are
synchronized using a public and trusted clock, such as the ones provided by National Institute of Standards
and Technology (NIST). The service has the capability to generate key structures periodically. For example,
it can generate keys with a lifespan of one week every day, or keys with a duration of 4 hours for every interval
of 20 minutes. Such a schedule is posted on the open bulletin board by the managers. Furthermore, 𝑆𝑟 has the
capability to accept user requests for generating new keys with designated durations. The managers receive
these requests and publicly announce them on the open bulletin board. The servers then generate keys in
accordance with the protocol, sign them, and publish the signed 𝐾𝑆s on the open bulletin board. Additionally,
𝑆𝑟 welcomes user requests for generating new keys with specific lifespans. The managers handle these requests
and post them on the open bulletin board. The servers adhere to the protocol to generate keys, sign them, and
make the signed 𝐾𝑆s available on the open bulletin board.
3. RESULTS AND DISCUSSION
The main findings of the study can be summarized as follows. The present study focuses new
cryptographic fault-tolerant backup storage system of confidential data based on TLC, specifically the variant
known as ECTLC. TLC refers to a method of encrypting data or information so that it can only be accessed
or decrypted after a certain amount of time has passed. The time-lapse aspect is used as a security feature to
ensure that the data remains protected until the specified time has elapsed. This technology is used in various
applications, such as secure file storage or information sharing, where it is important to restrict access to
sensitive information until a specified period has passed. The security of information systems created using
time-lapse cryptography refers to the measures taken to protect sensitive and confidential information stored
within these systems from unauthorized access, tampering, and theft. This can include techniques such as
encryption, access control, and secure data storage practices. The goal of these security measures is to
maintain the confidentiality, integrity, and availability of the information stored within the system and
prevent any malicious attacks from compromising it [13]-[16]. The level of security in a time-lapse
cryptography system depends on various factors, such as the complexity of the cryptographic algorithms
used, the robustness of the underlying infrastructure, and the implementation of secure software development
practices [17]-[19].

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ECTLC is a modification of TLC that is based on elliptic curves. The security of ECTLC is based
on the hardness of the discrete logarithm problem (DLP) over elliptic curves. As long as this problem
remains hard, the encrypted information will be secure against unauthorized access. However, it is crucial to
emphasize that the security of ECTLC is only as strong as the weakest link in the system, and various factors
such as implementation errors, side-channel attacks, or weaknesses in the underlying cryptographic
primitives can affect the overall security of the system. It is important to properly implement and deploy
ECTLC in order to ensure its security. This includes proper selection of cryptographic parameters, secure
implementation of cryptographic primitives, and proper handling of keys and encrypted information.
Additionally, it is important to regularly assess the security of this protocol in light of new developments in
cryptography and computer science to ensure that it continues to provide a high level of security [20]-[22].
The DKG protocol based on the DLP on EC, used in ECTLC, is a cryptographic algorithm for
generating shared secret keys between multiple parties in a secure and efficient manner. The security of such
a protocol relies on the computational hardness of the DLP over EC. In these protocols, each participant
generates a public-private key pair, and the public keys are combined to generate a shared secret key.
The security of the shared secret key relies on the intractability of the DLP over EC. As long as this problem
remains hard, the shared secret key will be secure against unauthorized access.
Pedersen verifiable threshold secret sharing protocol, used in ECTLC, is a cryptographic protocol
for securely sharing a secret among multiple parties in such a way that a threshold of parties must cooperate
to reconstruct the secret. The security of the Pedersen’s threshold VSS protocol relies on the hardness of the
DLP and the computational indistinguishability of the commitment scheme used. In this protocol, a dealer
distributes shares of the secret to each participant, and any threshold number of participants can cooperate to
reconstruct the secret. The protocol also includes a verifiable reconstruction process, in which any participant
can verify the correctness of the reconstructed secret, ensuring that the secret has not been tampered with or
reconstructed incorrectly. The security of the protocol is considered to be strong as long as the underlying
cryptographic assumptions hold.
The ElGamal encryption algorithm on elliptic curves, used in TLC, is a public-key encryption
algorithm that is based on the mathematical problem of computing discrete logarithms over elliptic curves.
The security of ElGamal encryption on elliptic curves is based on the computational hardness of the DLP
over elliptic curves. In the ElGamal encryption algorithm, a sender encrypts a message using the recipient’s
public key, and the recipient can then decrypt the message using their private key. The security of the
encrypted message relies on the intractability of the DLP over elliptic curves, making it computationally
infeasible for an attacker to compute the private key from the public key [23]-[25].
In this model, the client performs a standard login to the portal. This step is a standard login process
that is generally considered secure, provided the portal has implemented secure authentication mechanism.
It is important to ensure that the authentication mechanisms used by the portal are strong enough to prevent
unauthorized access to the system. This may include methods such as multi-factor authentication, strong
password policies, and encryption of sensitive user data. Additionally, within the model, 𝐶𝑙 submits a request
to 𝑃𝑟 to encrypt specific information, denoted as message 𝑚. The security of this step depends on the
encryption algorithm used, as well as the secure transmission of the message to the portal. If the encryption
algorithm used is strong and the transmission of the message is secure (eg., using SSL/TLS), then this step can
be considered secure. In this step, 𝑃𝑟 forwards the 𝐶𝑙’s request to 𝑆𝑟, including essential details such as 𝐶𝑙’s
unique ID, the timestamp of the request, and the designated timeframe during which 𝐶𝑙’s data must remain
encrypted and inaccessible for decryption. The security of this step depends on the security of the transfer of the
request from the portal to the service, as well as the secure storage of metadata by the portal and the service. It is
important to secure the transmission of the request and the secure storage of the metadata.
In addition, the use of a unique customer ID and decryption time limits can help prevent unauthorized access
to customer data. In general, the security of the steps in the considered model depends on various factors,
such as the security of the authentication mechanisms, the strength of the encryption algorithm used, and the
secure transmission and storage of data. It is important to ensure that all these factors are carefully considered
and implemented to ensure the security of the system.
In comparison with other studies, the present study contributes by specifically focusing on the
application of TLC and its variant, ECTLC, based on elliptic curves. While other studies may have explored
different cryptographic methods or variants, this study delves into the security aspects, underlying protocols,
and algorithms specific to ECTLC. The findings of this study have significant implications for the field of
cryptography and information security. TLC, especially ECTLC, offers an additional layer of security by
leveraging the time factor for data access. The use of elliptic curves and the reliance on the hardness of the
DLP provide strong security guarantees, but proper implementation and deployment are crucial for
maintaining the overall security of the system. The DKG protocol and the Pedersen’s threshold VSS protocol
provide secure ways of generating shared secret keys and sharing secrets among multiple parties. These
protocols offer robust security as long as the underlying cryptographic assumptions hold, ensuring that

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sensitive information remains protected and tamper-proof. The ElGamal encryption algorithm on elliptic
curves provides secure communication through public-key encryption. The intractability of the DLP over
ECs ensures the confidentiality of the encrypted messages, protecting them from unauthorized access.
The strengths of this study lie in its focus on time-lapse cryptography, specifically ECTLC, and its detailed
exploration of the underlying protocols and algorithms. The study provides a comprehensive understanding
of the security aspects of ECTLC, including the distributed key generation protocol, the Pedersen’s threshold
VSS protocol, and the ElGamal encryption algorithm.
It is important to note that, as with any cryptographic protocol, the security of these algorithms is only
as strong as the weakest link in the system, and various factors such as implementation errors, side-channel
attacks, or weaknesses in the underlying cryptographic primitives can affect the overall security of the system.
It is important to properly implement and deploy such protocols in order to ensure its security. This includes
proper selection of cryptographic parameters, secure implementation of cryptographic primitives, and proper
handling of keys and encrypted messages. Additionally, it is important to regularly assess the security of this
algorithm in light of new developments in cryptography and computer science to ensure that it continues to
provide a high level of security.
In conclusion, TLC, particularly the variant ECTLC, offers an innovative approach to securing data
and information. The use of elliptic curves and the reliance on the hardness of the DLP provide a strong
foundation for security. However, proper implementation, secure software development practices, and regular
security assessments are essential to maintain the overall security of the system. Recommendations for future
research include conducting empirical studies to evaluate the real-world effectiveness and performance of
ECTLC, including its resistance to potential attacks. Furthermore, staying updated with new developments in
cryptography and computer science is crucial to ensure that ECTLC continues to provide a high level of
security. Additionally, exploring potential applications and use cases for TLC and ECTLC in various domains
can help further understand their practical implications and benefits.
4. CONCLUSION
In this paper, a model of functioning of a fault-tolerant backup data storage system for a given time
is considered. The model is based on the cryptographic encryption protocol for a given time ECTLC.
The protocol effectively combines the DKG protocol that relies on the discrete logarithm on ECs, the
Pedersen’s threshold VSS protocol, an ElGamal encryption on ECs, and an electronic DS. The protocol
permits the usage of predefined parameters, which include the prime number modulus (𝑝) of the EC, the
equation and coefficients (𝑎 and 𝑏) of the EC from the field (𝐹𝑝), and a point (𝐺) on the EC with a prime
order (𝑞) specifically for the ElGamal encryption on EC. A fault-tolerant backup storage system for
confidential data in distributed servers based on ECTLC is a specialized solution designed to provide both
data protection and fault tolerance while incorporating cryptographic techniques that take into account the
passage of time. This type of system utilizes distributed storage architecture, where data is replicated across
multiple servers or nodes. The redundancy ensures that even if one or more servers fail, the confidential data
remains accessible and intact. The distributed nature of the system also enhances fault tolerance and
resilience to hardware failures. By combining fault tolerance mechanisms with ECTLC, the system ensures
the protection and availability of confidential data stored in distributed servers. It addresses potential
hardware failures and provides secure transmission of sensitive information over extended periods, all while
maintaining the confidentiality and integrity of the data.
It is worth noting that further research and evaluation are necessary to assess the efficiency, security,
and effectiveness of the fault-tolerant backup storage system based on time-lapse cryptography. Ongoing
studies can help refine the protocols, algorithms, and parameters used and ensure that the system remains
resistant to known attacks and meets the evolving security requirements for safeguarding confidential data in
distributed environments. Hence, it will be essential to conduct a study in the future to evaluate and choose
the most efficient algorithms and parameters mentioned earlier for the developed protocol. The ECTLC
protocol, which is derived from TLC, presents a solution for transmitting confidential messages to future
recipients. However, instead of the distributed key generation, verifiable thresholding, and encryption
algorithms used in TLC, algorithms based on elliptic curve cryptography are used, which suggests greater
efficiency. At the same time, it is assumed that these changes do not affect the resistance to known attacks.
ACKNOWLEDGEMENTS
This work is supported by the SC of the MSHE of the Republic of Kazakhstan, grant No. AP14869013.

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 ISSN: 1693-6930
1038
BIOGRAPHIES OF AUTHORS
Olzhas Tasmagambetov He is a doctoral student on the specialty “Information
Security”, Gumilyov ENU, Astana, Kazakhstan. He is a specialist in the field of cybersecurity,
has publications in domestic journals. He has extensive practical experience in law
enforcement. In addition, he works at the Institute of Information Security and Cryptology as a
leading researcher. He can be contacted at email: 5999452@mail.ru.
Yerzhan Seitkulov Ph.D, Professor at the Department of Information Security,
the Gumilyov ENU, Astana, Kazakhstan. Research interests - cryptography, coding theory,
cloud computing, voice information protection, supercomputer technologies, distributed
computing. He is also the head of a number of scientific and technical projects and programs
through line ministries. Over the past 10 years, he has led 8 scientific projects in the field of
information security. He can be contacted at email: yerzhan.seitkulov@gmail.com.
Ruslan Ospanov He is a doctoral student on the specialty “Information Security”,
L.N. Gumilyov Eurasian National University, Astana, Kazakhstan. His research interests are
cryptology, blockchain technology, big data, coding theory, the Internet of things. He is the
author of the development of a new hash function, and he also developed new methods for
generating optimal s-boxes used in symmetric cryptographic algorithms. He can be contacted
at email: ospanovrm@gmail.com.
Banu Yergaliyeva She is a doctoral student on the specialty “Information
Security”, L.N. Gumilyov Eurasian National University, Astana, Kazakhstan. She is a leading
researcher at the Scientific Institute of Information Security and Cryptology. Research interests -
applied cryptography, cloud technologies, Internet of things, secure processing in the cloud,
secure storage of big data in the cloud. She can be contacted at email:
banu.yergaliyeva@gmail.com.

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