15 research outputs found
Dynamics of heart rate variability in rats with streptozotocin-induced diabetes
Background: Diabetes mellitus (DM) has a negative impact on all organs. This is due to insufficiency of blood supply and the disruption of the trophic function of the nervous system. One of the most serious complication of DM is diabetic foot caused be vascular and neurological reasons. Correction of vascular disorders is effectively treated by modern therapeutic approaches, but the damage of nervous system has been studied insufficiently. Aims: To investigate the dynamics of damage to the vegetative nervous system on the laboratory model of DM. Materials and methods: DM in rats was induced by injection of streptozotocin at a dose of 65 mg/kg in citrate buffer (DM group). The control group of rats received a citrate buffer equivalent (CB group). Rats with DM were given a maintenance therapy with insulin in a dose of 2 units/kg/day. On 42 days of experience, a round wound with a diameter of 2 cm on the back of the animals was observed. Before the DM simulation, then on the 42, 50, 58 and 66 days of its development, an electrocardiogram (ECG) was recorded in the rats at a frequency of 2 kHz digitising in a state of calm wakefulness and after cold exposure. For 5 minutes ECG fragments, heart rate and heart rate variability (HRV) in the temporal domain were calculated, characterising: 1) the total heart rate variability (tHRV) according to SDRR, SDHR, KVRR and KVHR; 2) the effect of the parasympathetic department of the autonomic nervous system (aANS) for RMSSD and pNN3; 3) the contribution of the sympathetic department of the ANS (sANS) by SDAvgRR, SDAvgHR. The spectral parameters were estimated in the frequency domain: the total power of the spectrum is TR (range: 0–2.5 Hz), the powers in the low and high frequency ranges are LF (range: 0.2–0.8 Hz) and HF (range: 0.8–2.5 Hz) LF/HF. Weekly, the tail withdrawal time was measured in a temperature pain test (55°C). Results: During the development of diabetes, the level of glucose in the blood increased 4–7 times compared with the normal level. The reaction time of the pain test in rats with DM increased by 20%–30% at the end of the experiment. At 42 days, the development of bradycardia (267 beats/min) was observed in rats with DM. The indicators of tHRV decreased by a factor of 2 due to a decrease in the contribution of sANS. The reaction to CP in the SD group differs from the norm by the severity of the individual components of the HRV structure, which indicates functional denervation of the heart and the development of diabetic neuropathy. Conclusions: As the diabetes progressed, signs of neuropathy were observed. The overall HRV parameters decreased, the ratio of the contributions of sANS and pANS to the regulation of heart rate changed, and the temperature sensitivity decreased
SYNERGY OF BUILDING CYBERSECURITY SYSTEMS
The development of the modern world community is closely related to advances in computing resources and cyberspace. The formation and expansion of the range of services is based on the achievements of mankind in the field of high technologies. However, the rapid growth of computing resources, the emergence of a full-scale quantum computer tightens the requirements for security systems not only for information and communication systems, but also for cyber-physical systems and technologies.
The methodological foundations of building security systems for critical infrastructure facilities based on modeling the processes of behavior of antagonistic agents in security systems are discussed in the first chapter.
The concept of information security in social networks, based on mathematical models of data protection, taking into account the influence of specific parameters of the social network, the effects on the network are proposed in second chapter.
The nonlinear relationships of the parameters of the defense system, attacks, social networks, as well as the influence of individual characteristics of users and the nature of the relationships between them, takes into account.
In the third section, practical aspects of the methodology for constructing post-quantum algorithms for asymmetric McEliece and Niederreiter cryptosystems on algebraic codes (elliptic and modified elliptic codes), their mathematical models and practical algorithms are considered. Hybrid crypto-code constructions of McEliece and Niederreiter on defective codes are proposed. They can significantly reduce the energy costs for implementation, while ensuring the required level of cryptographic strength of the system as a whole. The concept of security of corporate information and educational systems based on the construction of an adaptive information security system is proposed.
ISBN 978-617-7319-31-2 (on-line)ISBN 978-617-7319-32-9 (print)
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How to Cite: Yevseiev, S., Ponomarenko, V., Laptiev, O., Milov, O., Korol, O., Milevskyi, S. et. al.; Yevseiev, S., Ponomarenko, V., Laptiev, O., Milov, O. (Eds.) (2021). Synergy of building cybersecurity systems. Kharkiv: Π Π‘ Π’ΠΠ‘HNOLOGY Π‘ΠNTΠR, 188. doi: http://doi.org/10.15587/978-617-7319-31-2
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Indexing:
Π ΠΎΠ·Π²ΠΈΡΠΎΠΊ ΡΡΡΠ°ΡΠ½ΠΎΡ ΡΠ²ΡΡΠΎΠ²ΠΎΡ ΡΠΏΡΠ»ΡΠ½ΠΎΡΠΈ ΡΡΡΠ½ΠΎ ΠΏΠΎΠ²βΡΠ·Π°Π½ΠΈΠΉ Π· Π΄ΠΎΡΡΠ³Π½Π΅Π½Π½ΡΠΌΠΈ Π² ΠΎΠ±Π»Π°ΡΡΡ ΠΎΠ±ΡΠΈΡΠ»ΡΠ²Π°Π»ΡΠ½ΠΈΡ
ΡΠ΅ΡΡΡΡΡΠ² Ρ ΠΊΡΠ±Π΅ΡΠΏΡΠΎΡΡΠΎΡΡ. Π€ΠΎΡΠΌΡΠ²Π°Π½Π½Ρ ΡΠ° ΡΠΎΠ·ΡΠΈΡΠ΅Π½Π½Ρ Π°ΡΠΎΡΡΠΈΠΌΠ΅Π½ΡΡ ΠΏΠΎΡΠ»ΡΠ³ Π±Π°Π·ΡΡΡΡΡΡ Π½Π° Π΄ΠΎΡΡΠ³Π½Π΅Π½Π½ΡΡ
Π»ΡΠ΄ΡΡΠ²Π° Ρ Π³Π°Π»ΡΠ·Ρ Π²ΠΈΡΠΎΠΊΠΈΡ
ΡΠ΅Ρ
Π½ΠΎΠ»ΠΎΠ³ΡΠΉ. ΠΠ΄Π½Π°ΠΊ ΡΡΡΡΠΌΠΊΠ΅ Π·ΡΠΎΡΡΠ°Π½Π½Ρ ΠΎΠ±ΡΠΈΡΠ»ΡΠ²Π°Π»ΡΠ½ΠΈΡ
ΡΠ΅ΡΡΡΡΡΠ², ΠΏΠΎΡΠ²Π° ΠΏΠΎΠ²Π½ΠΎΠΌΠ°ΡΡΡΠ°Π±Π½ΠΎΠ³ΠΎ ΠΊΠ²Π°Π½ΡΠΎΠ²ΠΎΠ³ΠΎ ΠΊΠΎΠΌΠΏβΡΡΠ΅ΡΠ° ΠΏΠΎΡΠΈΠ»ΡΡ Π²ΠΈΠΌΠΎΠ³ΠΈ Π΄ΠΎ ΡΠΈΡΡΠ΅ΠΌ Π±Π΅Π·ΠΏΠ΅ΠΊΠΈ Π½Π΅ ΡΡΠ»ΡΠΊΠΈ ΡΠ½ΡΠΎΡΠΌΠ°ΡΡΠΉΠ½ΠΎ-ΠΊΠΎΠΌΡΠ½ΡΠΊΠ°ΡΡΠΉΠ½ΠΈΡ
, Π°Π»Π΅ Ρ Π΄ΠΎ ΠΊΡΠ±Π΅ΡΡΡΠ·ΠΈΡΠ½ΠΈΡ
ΡΠΈΡΡΠ΅ΠΌ Ρ ΡΠ΅Ρ
Π½ΠΎΠ»ΠΎΠ³ΡΠΉ.
Π£ ΠΏΠ΅ΡΡΠΎΠΌΡ ΡΠΎΠ·Π΄ΡΠ»Ρ ΠΎΠ±Π³ΠΎΠ²ΠΎΡΡΡΡΡΡΡ ΠΌΠ΅ΡΠΎΠ΄ΠΎΠ»ΠΎΠ³ΡΡΠ½Ρ ΠΎΡΠ½ΠΎΠ²ΠΈ ΠΏΠΎΠ±ΡΠ΄ΠΎΠ²ΠΈ ΡΠΈΡΡΠ΅ΠΌ Π±Π΅Π·ΠΏΠ΅ΠΊΠΈ Π΄Π»Ρ ΠΎΠ±'ΡΠΊΡΡΠ² ΠΊΡΠΈΡΠΈΡΠ½ΠΎΡ ΡΠ½ΡΡΠ°ΡΡΡΡΠΊΡΡΡΠΈ Π½Π° ΠΎΡΠ½ΠΎΠ²Ρ ΠΌΠΎΠ΄Π΅Π»ΡΠ²Π°Π½Π½Ρ ΠΏΡΠΎΡΠ΅ΡΡΠ² ΠΏΠΎΠ²Π΅Π΄ΡΠ½ΠΊΠΈ Π°Π½ΡΠ°Π³ΠΎΠ½ΡΡΡΠΈΡΠ½ΠΈΡ
Π°Π³Π΅Π½ΡΡΠ² Ρ ΡΠΈΡΡΠ΅ΠΌ Π±Π΅Π·ΠΏΠ΅ΠΊΠΈ.
Π£ Π΄ΡΡΠ³ΠΎΠΌΡ ΡΠΎΠ·Π΄ΡΠ»Ρ ΠΏΡΠΎΠΏΠΎΠ½ΡΡΡΡΡΡ ΠΊΠΎΠ½ΡΠ΅ΠΏΡΡΡ ΡΠ½ΡΠΎΡΠΌΠ°ΡΡΠΉΠ½ΠΎΡ Π±Π΅Π·ΠΏΠ΅ΠΊΠΈ Π² ΡΠΎΡΡΠ°Π»ΡΠ½ΠΈΡ
ΠΌΠ΅ΡΠ΅ΠΆΠ°Ρ
, ΡΠΊΠ° Π·Π°ΡΠ½ΠΎΠ²Π°Π½Π° Π½Π° ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ½ΠΈΡ
ΠΌΠΎΠ΄Π΅Π»ΡΡ
Π·Π°Ρ
ΠΈΡΡΡ Π΄Π°Π½ΠΈΡ
, Π· ΡΡΠ°Ρ
ΡΠ²Π°Π½Π½ΡΠΌ Π²ΠΏΠ»ΠΈΠ²Ρ ΠΊΠΎΠ½ΠΊΡΠ΅ΡΠ½ΠΈΡ
ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΡΠ² ΡΠΎΡΡΠ°Π»ΡΠ½ΠΎΡ ΠΌΠ΅ΡΠ΅ΠΆΡ ΡΠ° Π½Π°ΡΠ»ΡΠ΄ΠΊΡΠ² Π΄Π»Ρ Π½Π΅Ρ.
ΠΡΠ°Ρ
ΠΎΠ²ΡΡΡΡΡΡ Π½Π΅Π»ΡΠ½ΡΠΉΠ½Ρ Π²Π·Π°ΡΠΌΠΎΠ·Π²'ΡΠ·ΠΊΠΈ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΡΠ² ΡΠΈΡΡΠ΅ΠΌΠΈ Π·Π°Ρ
ΠΈΡΡΡ, Π°ΡΠ°ΠΊ, ΡΠΎΡΡΠ°Π»ΡΠ½ΠΈΡ
ΠΌΠ΅ΡΠ΅ΠΆ, Π° ΡΠ°ΠΊΠΎΠΆ Π²ΠΏΠ»ΠΈΠ² ΡΠ½Π΄ΠΈΠ²ΡΠ΄ΡΠ°Π»ΡΠ½ΠΈΡ
Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊ ΠΊΠΎΡΠΈΡΡΡΠ²Π°ΡΡΠ² Ρ Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΡ Π²Π·Π°ΡΠΌΠΎΠ²ΡΠ΄Π½ΠΎΡΠΈΠ½ ΠΌΡΠΆ Π½ΠΈΠΌΠΈ.
Π£ ΡΡΠ΅ΡΡΠΎΠΌΡ ΡΠΎΠ·Π΄ΡΠ»Ρ ΡΠΎΠ·Π³Π»ΡΠ΄Π°ΡΡΡΡΡ ΠΏΡΠ°ΠΊΡΠΈΡΠ½Ρ Π°ΡΠΏΠ΅ΠΊΡΠΈ ΠΌΠ΅ΡΠΎΠ΄ΠΎΠ»ΠΎΠ³ΡΡ ΠΏΠΎΠ±ΡΠ΄ΠΎΠ²ΠΈ ΠΏΠΎΡΡΠΊΠ²Π°Π½ΡΠΎΠ²ΠΈΡ
Π°Π»Π³ΠΎΡΠΈΡΠΌΡΠ² Π΄Π»Ρ Π°ΡΠΈΠΌΠ΅ΡΡΠΈΡΠ½ΠΈΡ
ΠΊΡΠΈΠΏΡΠΎΡΠΈΡΡΠ΅ΠΌ ΠΠ°ΠΊ-ΠΠ»ΡΡΠ° ΡΠ° ΠΡΠ΄Π΅ΡΡΠ΅ΠΉΡΠ΅ΡΠ° Π½Π° Π°Π»Π³Π΅Π±ΡΠ°ΡΡΠ½ΠΈΡ
ΠΊΠΎΠ΄Π°Ρ
(Π΅Π»ΡΠΏΡΠΈΡΠ½ΠΈΡ
ΡΠ° ΠΌΠΎΠ΄ΠΈΡΡΠΊΠΎΠ²Π°Π½ΠΈΡ
Π΅Π»ΡΠΏΡΠΈΡΠ½ΠΈΡ
ΠΊΠΎΠ΄Π°Ρ
), ΡΡ
ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ½Ρ ΠΌΠΎΠ΄Π΅Π»Ρ ΡΠ° ΠΏΡΠ°ΠΊΡΠΈΡΠ½Ρ Π°Π»Π³ΠΎΡΠΈΡΠΌΠΈ. ΠΠ°ΠΏΡΠΎΠΏΠΎΠ½ΠΎΠ²Π°Π½ΠΎ Π³ΡΠ±ΡΠΈΠ΄Π½Ρ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΡΡ ΠΊΡΠΈΠΏΡΠΎΠΊΠΎΠ΄Ρ ΠΠ°ΠΊ-ΠΠ»ΡΡΠ° ΡΠ° ΠΡΠ΄Π΅ΡΡΠ΅ΠΉΡΠ΅ΡΠ° Π½Π° Π΄Π΅ΡΠ΅ΠΊΡΠ½ΠΈΡ
ΠΊΠΎΠ΄Π°Ρ
. ΠΠΎΠ½ΠΈ Π΄ΠΎΠ·Π²ΠΎΠ»ΡΡΡΡ ΡΡΡΠΎΡΠ½ΠΎ Π·Π½ΠΈΠ·ΠΈΡΠΈ Π΅Π½Π΅ΡΠ³Π΅ΡΠΈΡΠ½Ρ Π²ΠΈΡΡΠ°ΡΠΈ Π½Π° ΡΠ΅Π°Π»ΡΠ·Π°ΡΡΡ, Π·Π°Π±Π΅Π·ΠΏΠ΅ΡΡΡΡΠΈ ΠΏΡΠΈ ΡΡΠΎΠΌΡ Π½Π΅ΠΎΠ±Ρ
ΡΠ΄Π½ΠΈΠΉ ΡΡΠ²Π΅Π½Ρ ΠΊΡΠΈΠΏΡΠΎΠ³ΡΠ°ΡΡΡΠ½ΠΎΡ ΡΡΡΠΉΠΊΠΎΡΡΡ ΡΠΈΡΡΠ΅ΠΌΠΈ Π² ΡΡΠ»ΠΎΠΌΡ. ΠΠ°ΠΏΡΠΎΠΏΠΎΠ½ΠΎΠ²Π°Π½ΠΎ ΠΊΠΎΠ½ΡΠ΅ΠΏΡΡΡ Π±Π΅Π·ΠΏΠ΅ΠΊΠΈ ΠΊΠΎΡΠΏΠΎΡΠ°ΡΠΈΠ²Π½ΠΈΡ
ΡΠ½ΡΠΎΡΠΌΠ°ΡΡΠΉΠ½ΠΈΡ
ΡΠ° ΠΎΡΠ²ΡΡΠ½ΡΡ
ΡΠΈΡΡΠ΅ΠΌ, ΡΠΊΡ Π·Π°ΡΠ½ΠΎΠ²Π°Π½Ρ Π½Π° ΠΏΠΎΠ±ΡΠ΄ΠΎΠ²Ρ Π°Π΄Π°ΠΏΡΠΈΠ²Π½ΠΎΡ ΡΠΈΡΡΠ΅ΠΌΠΈ Π·Π°Ρ
ΠΈΡΡΡ ΡΠ½ΡΠΎΡΠΌΠ°ΡΡΡ.
ISBN 978-617-7319-31-2 (on-line)ISBN 978-617-7319-32-9 (print)
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Π―ΠΊ ΡΠΈΡΡΠ²Π°ΡΠΈ: Yevseiev, S., Ponomarenko, V., Laptiev, O., Milov, O., Korol, O., Milevskyi, S. et. al.; Yevseiev, S., Ponomarenko, V., Laptiev, O., Milov, O. (Eds.) (2021). Synergy of building cybersecurity systems. Kharkiv: Π Π‘ Π’ΠΠ‘HNOLOGY Π‘ΠNTΠR, 188. doi: http://doi.org/10.15587/978-617-7319-31-2
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ΠΠ½Π΄Π΅ΠΊΡΠ°ΡΡΡ:
 
Electrical activity in rat retina in a streptozotocin-induced diabetes model
Objectives: Diabetic retinopathy remains the major cause of blindness among the working-age population of developed countries. Considering this, experimental models of diabetes involving laboratory animals are important for assessing clinically significant methods to determine early pathologic alterations of the retina. The early detection of diabetic retinopathy in combination with a search for new pathogenetic targets will enable focusing on new strategies to limit the development of critical changes in the retina and to prolong retinal functioning during the development of diabetes mellitus.
Aim: This study aimed to define parameters of electroretinography test that identifies changes due to retinal impairment in diabetes.
Methods: Experimental diabetes was induced in Wistar rats by intraperitoneally injecting streptozocin (65 mg/kg; group DM). The control group (CB) received intraperitoneal injections of the vehicle, i.e. citric buffer. On each consecutive day of the experiment, all rats received insulin detemir (2 u/kg). Ophthalmoscopy and electroretinography were conducted before initiating the experiment and after 50, 58 and 66 days of injectin sptreptozocin.
Results: Amid 2u\kg insulin injection the glucose level in venous blood in DM group amounted to 30-40 mM. The ophthalmoscopy showed that the optic nerve disk paled by the 50th day, with its line erasing. During electroretinography, wave amplitude in oscillatory potential test tended to decrease. -wave latency of photopic system increased with -wave latency of photopic system and - and -waves latency of scotopic system not altering. In addition, the amplitude of rhythmic stimulation of 8 and 12 Hz decreased.
Conclusion: The most apparent parameters of electroretinography for modelling streptozocin-induced diabetes are wave amplitude during the oscillatory potential test, photopic B-wave latency and the amplitude of rhythmic stimulation. These results suggest that in diabetes, ischaemic injury is an important cause of early dysfunction of inner retinal layers
The Relationship between Executive Functions and Dance Classes in Preschool Age Children
The development of executive functions is of the utmost importance for academic success at school and the social adaptation of children. Dance class attendance is one of the factors promoting the development of these functions in children. This study was aimed to explore the relationship between extra dance class attendance and executive functions in preschool age children. The executive function level was assessed using NEPSY-II subtests “Sentences Repetition”, “Memory for Designs”, “Inhibition”, “Statue”, and “Dimensional Change Card Sort”. The data on extra dance classes were collected by means of a questionnaire for parents. In the study, 86 typically developing 5–6-year-old children participated. No statistically significant differences in executive functions’ levels were discovered in children taking only extra dance classes for at least 6 months and children taking no extra classes. The obtained data plays an important role for the design of further investigations of the topic
The Relationship between Executive Functions and Dance Classes in Preschool Age Children
The development of executive functions is of the utmost importance for academic success at school and the social adaptation of children. Dance class attendance is one of the factors promoting the development of these functions in children. This study was aimed to explore the relationship between extra dance class attendance and executive functions in preschool age children. The executive function level was assessed using NEPSY-II subtests βSentences Repetitionβ, βMemory for Designsβ, βInhibitionβ, βStatueβ, and βDimensional Change Card Sortβ. The data on extra dance classes were collected by means of a questionnaire for parents. In the study, 86 typically developing 5β6-year-old children participated. No statistically significant differences in executive functionsβ levels were discovered in children taking only extra dance classes for at least 6 months and children taking no extra classes. The obtained data plays an important role for the design of further investigations of the topic
Paper for the 2005 PAA Annual meeting
Mortality crisis in Russia was discussed many times in the scientific literature. However little attention was paid to the problems of the quality of mortality statistics in Russia, which is rapidly deteriorating. During the first half of 1990s mortality from such cause as "injuries undetermined whether accidentally or purposely inflicted" grew with particularly rapid pace. In this study we tested a hypothesis that mortality from violent causes of death (particularly in middle-aged men from marginal social groups) is concealed using death codes from the class "Symptoms, signs and ill-defined conditions" (ICD-9). Reported mortality from this group of causes increased 6-fold for males and 9-fold for females in 1989-2002. This hypothesis of concealing criminal cases of violent deaths under the mask of ill-defined conditions was confirmed using case study of death certificates from the Kirov region of Russia. It is likely that mortality from violent causes in Russia is significantly underestimated by the official statistics
Neurohumoral mechanisms of keratinocytes regulation in diabetes mellitus
The extent of damage to the nervous, vascular and microcirculatory systems in diabetic patients determine the regulation ofΒ physiological events that lead to the formation of chronic wounds, reduction of patient quality of life and increase of the financial value of medical care. Successful physiological repair is impossible without the successive phases of inflammation, proliferation and wound healing. Keratinocytes are the major cellular barrier components of the epidermis. These cells play an important role in physiological repair, as suggested by recent research, with many cells able to secrete steroid hormones de novo. Damage to the integrity of the skin leads to keratinocyte activation, triggering a cascade of reactions that contribute to changes in epidermal cell phenotype and lead to their proliferation and migration, analogous to changes in cellular adhesion and configuration of the cytoskeleton. An open question remains as to how the keratinocyte cell cycle, which is altered under conditions of hyperglycemia, and neurotransmitter metabolism during different stages of physiological repair are regulated. Understanding these processes will provide a scientific basis for the development of new targets for pharmacotherapies
Π ΠΎΠ·ΡΠΎΠ±ΠΊΠ° Π³ΡΠ±ΡΠΈΠ΄Π½ΠΎΡ ΠΊΡΠΈΠΏΡΠΎ-ΠΊΠΎΠ΄ΠΎΠ²ΠΎΡ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΡΡ Π½ΡΠ΄Π΅ΡΡΠ°ΠΉΡΠ΅ΡΠ° Π½Π° Π·Π±ΠΈΡΠΊΠΎΠ²ΠΈΡ ΠΊΠΎΠ΄Π°Ρ
The use of the Niederreiter modified crypto-code structure (MCCS) with additional initialization vectors (with many invalid positional vectors of the error vector and multiple positions of shortening the error vector) requires an increase in the speed of cryptographic transformation of the system as a whole. For this purpose, it is proposed to use flawed codes. Flawed codes allow you to increase the speed of code transformations by reducing the power of the field while damaging the plaintext and reducing the amount of data transferred by damaging the ciphertext. This approach allows the construction of hybrid crypto-code structures based on the synthesis of Niederreiter modified crypto-code structures on modified (shortened or extended) codes on elliptic curves with damaging procedures. A significant difference from classical hybrid (complex) cryptosystems is the use of asymmetric cryptosystems to ensure data security with fast crypto-transformation procedures (generation and decoding of a codogram). The paper discusses methods for constructing flawed codes and approaches for using the Niederreiter hybrid crypto-code structure on modified elliptic codes. Practical algorithms are proposed for using the MV2 damage mechanism in the Niederreiter crypto-code structure on modified elliptic codes, which makes it possible to implement a hybrid crypto-code structure. The results of a comparative assessment of energy consumption for the formation of an information package with various methods of damage, which determined the choice of damage method in practical algorithms. The conducted studies confirm the competitive efficiency of the proposed cryptosystem in Internet technologies and mobile networks, ensuring practical implementation on modern platforms and the necessary cryptographic strength under post-quantum cryptographyΠΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅ ΠΌΠΎΠ΄ΠΈΡΠΈΡΠΈΡΠΎΠ²Π°Π½Π½ΠΎΠΉ ΠΊΡΠΈΠΏΡΠΎ-ΠΊΠΎΠ΄ΠΎΠ²ΠΎΠΉ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠΈ (ΠΠΠΠ) ΠΠΈΠ΄Π΅ΡΡΠ°ΠΉΡΠ΅ΡΠ° Ρ Π΄ΠΎΠΏΠΎΠ»Π½ΠΈΡΠ΅Π»ΡΠ½ΡΠΌΠΈ Π²Π΅ΠΊΡΠΎΡΠ°ΠΌΠΈ ΠΈΠ½ΠΈΡΠΈΠ°Π»ΠΈΠ·Π°ΡΠΈΠΈ (Ρ ΠΌΠ½ΠΎΠΆΠ΅ΡΡΠ²ΠΎΠΌ Π½Π΅Π΄ΠΎΠΏΡΡΡΠΈΠΌΡΡ
ΠΏΠΎΠ·ΠΈΡΠΈΠΎΠ½Π½ΡΡ
Π²Π΅ΠΊΡΠΎΡΠΎΠ² Π²Π΅ΠΊΡΠΎΡΠ° ΠΎΡΠΈΠ±ΠΎΠΊ ΠΈ ΠΌΠ½ΠΎΠΆΠ΅ΡΡΠ²ΠΎΠΌ ΠΏΠΎΠ·ΠΈΡΠΈΠΉ ΡΠΊΠΎΡΠΎΡΠ΅Π½ΠΈΡ Π²Π΅ΠΊΡΠΎΡΠ° ΠΎΡΠΈΠ±ΠΊΠΈ) ΡΡΠ΅Π±ΡΠ΅Ρ ΡΠ²Π΅Π»ΠΈΡΠ΅Π½ΠΈΡ Π±ΡΡΡΡΠΎΠ΄Π΅ΠΉΡΡΠ²ΠΈΡ ΠΊΡΠΈΠΏΡΠΎΠΏΡΠ΅ΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°Π½ΠΈΡ ΡΠΈΡΡΠ΅ΠΌΡ Π² ΡΠ΅Π»ΠΎΠΌ. ΠΠ»Ρ ΡΡΠΎΠ³ΠΎ ΠΏΡΠ΅Π΄Π»Π°Π³Π°Π΅ΡΡΡ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°ΡΡ ΡΡΠ΅ΡΠ±Π½ΡΠ΅ ΠΊΠΎΠ΄Ρ. Π£ΡΠ΅ΡΠ±Π½ΡΠ΅ ΠΊΠΎΠ΄Ρ ΠΏΠΎΠ·Π²ΠΎΠ»ΡΡΡ ΡΠ²Π΅Π»ΠΈΡΠΈΡΡ ΡΠΊΠΎΡΠΎΡΡΡ ΠΊΠΎΠ΄ΠΎΠ²ΡΡ
ΠΏΡΠ΅ΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°Π½ΠΈΠΉ Π·Π° ΡΡΠ΅Ρ ΡΠΌΠ΅Π½ΡΡΠ΅Π½ΠΈΡ ΠΌΠΎΡΠ½ΠΎΡΡΠΈ ΠΏΠΎΠ»Ρ ΠΏΡΠΈ Π½Π°Π½Π΅ΡΠ΅Π½ΠΈΠΈ ΡΡΠ΅ΡΠ±Π° ΠΎΡΠΊΡΡΡΡ ΡΠ΅ΠΊΡΡΡ ΠΈ ΡΠΌΠ΅Π½ΡΡΠΈΡΡ ΠΎΠ±ΡΠ΅ΠΌ ΠΏΠ΅ΡΠ΅Π΄Π°Π²Π°Π΅ΠΌΡΡ
Π΄Π°Π½Π½ΡΡ
Π·Π° ΡΡΠ΅Ρ Π½Π°Π½Π΅ΡΠ΅Π½ΠΈΡ ΡΡΠ΅ΡΠ±Π° ΡΠΈΡΡΡΠ΅ΠΊΡΡΡ. Π’Π°ΠΊΠΎΠΉ ΠΏΠΎΠ΄Ρ
ΠΎΠ΄ ΠΏΠΎΠ·Π²ΠΎΠ»ΡΠ΅Ρ ΡΡΡΠΎΠΈΡΡ Π³ΠΈΠ±ΡΠΈΠ΄Π½ΡΠ΅ ΠΊΡΠΈΠΏΡΠΎ-ΠΊΠΎΠ΄ΠΎΠ²ΡΠ΅ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠΈ Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ ΡΠΈΠ½ΡΠ΅Π·Π° ΠΌΠΎΠ΄ΠΈΡΠΈΡΠΈΡΠΎΠ²Π°Π½Π½ΡΡ
ΠΊΡΠΈΠΏΡΠΎΠΊΠΎΠ΄ΠΎΠ²ΡΡ
ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠΉ ΠΠΈΠ΄Π΅ΡΡΠ°ΠΉΡΠ΅ΡΠ° Π½Π° ΠΌΠΎΠ΄ΠΈΡΠΈΡΠΈΡΠΎΠ²Π°Π½Π½ΡΡ
(ΡΠΊΠΎΡΠΎΡΠ΅Π½Π½ΡΡ
ΠΈΠ»ΠΈ ΡΠ΄Π»ΠΈΠ½Π΅Π½Π½ΡΡ
) ΠΊΠΎΠ΄Π°Ρ
Π½Π° ΡΠ»Π»ΠΈΠΏΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΊΡΠΈΠ²ΡΡ
Ρ ΠΏΡΠΎΡΠ΅Π΄ΡΡΠ°ΠΌΠΈ Π½Π°Π½Π΅ΡΠ΅Π½ΠΈΡ ΡΡΠ΅ΡΠ±Π°. Π‘ΡΡΠ΅ΡΡΠ²Π΅Π½Π½ΡΠΌ ΠΎΡΠ»ΠΈΡΠΈΠ΅ΠΌ ΠΎΡ ΠΊΠ»Π°ΡΡΠΈΡΠ΅ΡΠΊΠΈΡ
Π³ΠΈΠ±ΡΠΈΠ΄Π½ΡΡ
(ΠΊΠΎΠΌΠΏΠ»Π΅ΠΊΡΠ½ΡΡ
) ΠΊΡΠΈΠΏΡΠΎΡΠΈΡΡΠ΅ΠΌ ΡΠ²Π»ΡΠ΅ΡΡΡ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅ Π½Π΅ΡΠΈΠΌΠΌΠ΅ΡΡΠΈΡΠ½ΠΎΠΉ ΠΊΡΠΈΠΏΡΠΎΡΠΈΡΡΠ΅ΠΌΡ Π΄Π»Ρ ΠΎΠ±Π΅ΡΠΏΠ΅ΡΠ΅Π½ΠΈΡ Π±Π΅Π·ΠΎΠΏΠ°ΡΠ½ΠΎΡΡΠΈ Π΄Π°Π½Π½ΡΡ
Ρ Π±ΡΡΡΡΡΠΌΠΈ ΠΏΡΠΎΡΠ΅Π΄ΡΡΠ°ΠΌΠΈ ΠΊΡΠΈΠΏΡΠΎΠΏΡΠ΅ΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°Π½ΠΈΡ (ΡΠΎΡΠΌΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ ΠΈ ΡΠ°ΡΠΊΠΎΠ΄ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΊΠΎΠ΄ΠΎΠ³ΡΠ°ΠΌΠΌΡ). Π ΡΠ°Π±ΠΎΡΠ΅ ΡΠ°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°ΡΡΡΡ ΡΠΏΠΎΡΠΎΠ±Ρ ΠΏΠΎΡΡΡΠΎΠ΅Π½ΠΈΡ ΡΡΠ΅ΡΠ±Π½ΡΡ
ΠΊΠΎΠ΄ΠΎΠ² ΠΈ ΠΏΠΎΠ΄Ρ
ΠΎΠ΄Ρ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΡ Π² Π³ΠΈΠ±ΡΠΈΠ΄Π½ΠΎΠΉ ΠΊΡΠΈΠΏΡΠΎ-ΠΊΠΎΠ΄ΠΎΠ²ΠΎΠΉ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠΈ ΠΠΈΠ΄Π΅ΡΡΠ°ΠΉΡΠ΅ΡΠ° Π½Π° ΠΌΠΎΠ΄ΠΈΡΠΈΡΠΈΡΠΎΠ²Π°Π½Π½ΡΡ
ΡΠ»Π»ΠΈΠΏΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΊΠΎΠ΄Π°Ρ
. ΠΡΠ΅Π΄Π»Π°Π³Π°ΡΡΡΡ ΠΏΡΠ°ΠΊΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ Π°Π»Π³ΠΎΡΠΈΡΠΌΡ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΡ ΠΌΠ΅Ρ
Π°Π½ΠΈΠ·ΠΌΠ° Π½Π°Π½Π΅ΡΠ΅Π½ΠΈΡ ΡΡΠ΅ΡΠ±Π° MV2 Π² ΠΊΡΠΈΠΏΡΠΎ-ΠΊΠΎΠ΄ΠΎΠ²ΠΎΠΉ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠΈ ΠΠΈΠ΄Π΅ΡΡΠ°ΠΉΡΠ΅ΡΠ° Π½Π° ΠΌΠΎΠ΄ΠΈΡΠΈΡΠΈΡΠΎΠ²Π°Π½Π½ΡΡ
ΡΠ»Π»ΠΈΠΏΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΊΠΎΠ΄Π°Ρ
, ΡΡΠΎ ΠΏΠΎΠ·Π²ΠΎΠ»ΡΠ΅Ρ ΡΠ΅Π°Π»ΠΈΠ·ΠΎΠ²Π°ΡΡ Π³ΠΈΠ±ΡΠΈΠ΄Π½ΡΡ ΠΊΡΠΈΠΏΡΠΎ-ΠΊΠΎΠ΄ΠΎΠ²ΡΡ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΡ. ΠΡΠΈΠ²Π΅Π΄Π΅Π½Ρ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ ΡΡΠ°Π²Π½ΠΈΡΠ΅Π»ΡΠ½ΠΎΠΉ ΠΎΡΠ΅Π½ΠΊΠΈ ΡΠ½Π΅ΡΠ³ΠΎΠ·Π°ΡΡΠ°Ρ Π½Π° ΡΠΎΡΠΌΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΎΠ½Π½ΠΎΠΉ ΠΏΠΎΡΡΠ»ΠΊΠΈ ΠΏΡΠΈ ΡΠ°Π·Π»ΠΈΡΠ½ΡΡ
ΡΠΏΠΎΡΠΎΠ±Π°Ρ
Π½Π°Π½Π΅ΡΠ΅Π½ΠΈΡ ΡΡΠ΅ΡΠ±Π°, ΡΡΠΎ ΠΎΠΏΡΠ΅Π΄Π΅Π»ΠΈΠ»ΠΎ Π²ΡΠ±ΠΎΡ ΡΠΏΠΎΡΠΎΠ±Π° Π½Π°Π½Π΅ΡΠ΅Π½ΠΈΡ ΡΡΠ΅ΡΠ±Π° Π² ΠΏΡΠ°ΠΊΡΠΈΡΠ΅ΡΠΊΠΈΡ
Π°Π»Π³ΠΎΡΠΈΡΠΌΠ°Ρ
. ΠΡΠΎΠ²Π΅Π΄Π΅Π½Π½ΡΠ΅ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ ΠΏΠΎΠ΄ΡΠ²Π΅ΡΠΆΠ΄Π°ΡΡ ΠΊΠΎΠ½ΠΊΡΡΠ΅Π½ΡΡΡ ΡΡΡΠ΅ΠΊΡΠΈΠ²Π½ΠΎΡΡΡ ΠΏΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½Π½ΠΎΠΉ ΠΊΡΠΈΠΏΡΠΎΡΠΈΡΡΠ΅ΠΌΡ Π² ΠΠ½ΡΠ΅ΡΠ½Π΅Ρ-ΡΠ΅Ρ
Π½ΠΎΠ»ΠΎΠ³ΠΈΡΡ
ΠΈ ΠΌΠΎΠ±ΠΈΠ»ΡΠ½ΡΡ
ΡΠ΅ΡΡΡ
, ΠΎΠ±Π΅ΡΠΏΠ΅ΡΠ΅Π½ΠΈΡ ΠΏΡΠ°ΠΊΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΡΠ΅Π°Π»ΠΈΠ·Π°ΡΠΈΠΈ Π½Π° ΡΠΎΠ²ΡΠ΅ΠΌΠ΅Π½Π½ΡΡ
ΠΏΠ»Π°ΡΡΠΎΡΠΌΠ°Ρ
ΠΈ Π½Π΅ΠΎΠ±Ρ
ΠΎΠ΄ΠΈΠΌΠΎΠΉ ΠΊΡΠΈΠΏΡΠΎΡΡΠΎΠΉΠΊΠΎΡΡΠΈ Π² ΡΡΠ»ΠΎΠ²ΠΈΡΡ
ΠΏΠΎΡΡΠΊΠ²Π°Π½ΡΠΎΠ²ΠΎΠΉ ΠΊΡΠΈΠΏΡΠΎΠ³ΡΠ°ΡΠΈΠΈΠΠΈΠΊΠΎΡΠΈΡΡΠ°Π½Π½Ρ ΠΌΠΎΠ΄ΠΈΡΡΠΊΠΎΠ²Π°Π½ΠΎΡ ΠΊΡΠΈΠΏΡΠΎ-ΠΊΠΎΠ΄ΠΎΠ²ΠΎΡ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΡΡ (ΠΠΠΠ) ΠΡΠ΄Π΅ΡΡΠ°ΠΉΡΠ΅ΡΠ° Π· Π΄ΠΎΠ΄Π°ΡΠΊΠΎΠ²ΠΈΠΌΠΈ Π²Π΅ΠΊΡΠΎΡΠ°ΠΌΠΈ ΡΠ½ΡΡΡΠ°Π»ΡΠ·Π°ΡΡΡ (Π· ΠΌΠ½ΠΎΠΆΠΈΠ½ΠΎΡ Π½Π΅ΠΏΡΠΈΠΏΡΡΡΠΈΠΌΠΈΡ
ΠΏΠΎΠ·ΠΈΡΡΠΉΠ½ΠΈΡ
Π²Π΅ΠΊΡΠΎΡΡΠ² Π²Π΅ΠΊΡΠΎΡΠ° ΠΏΠΎΠΌΠΈΠ»ΠΎΠΊ Ρ ΠΌΠ½ΠΎΠΆΠΈΠ½ΠΎΡ ΠΏΠΎΠ·ΠΈΡΡΠΉ ΡΠΊΠΎΡΠΎΡΠ΅Π½Π½Ρ Π²Π΅ΠΊΡΠΎΡΠ° ΠΏΠΎΠΌΠΈΠ»ΠΊΠΈ) Π²ΠΈΠΌΠ°Π³Π°Ρ Π·Π±ΡΠ»ΡΡΠ΅Π½Π½Ρ ΡΠ²ΠΈΠ΄ΠΊΠΎΠ΄ΡΡ ΠΊΡΠΈΠΏΡΠΎΠΏΠ΅ΡΠ΅ΡΠ²ΠΎΡΠ΅Π½Ρ ΡΠΈΡΡΠ΅ΠΌΠΈ Π²ΡΡΠ»ΠΎΠΌΡ. ΠΠ»Ρ ΡΡΠΎΠ³ΠΎ ΠΏΡΠΎΠΏΠΎΠ½ΡΡΡΡΡΡ Π²ΠΈΠΊΠΎΡΠΈΡΡΠΎΠ²ΡΠ²Π°ΡΠΈ Π·Π±ΠΈΡΠΊΠΎΠ²Ρ ΠΊΠΎΠ΄ΠΈ. ΠΠ±ΠΈΡΠΊΠΎΠ²Ρ ΠΊΠΎΠ΄ΠΈ Π΄ΠΎΠ·Π²ΠΎΠ»ΡΡΡΡ Π·Π±ΡΠ»ΡΡΠΈΡΠΈ ΡΠ²ΠΈΠ΄ΠΊΡΡΡΡ ΠΊΠΎΠ΄ΠΎΠ²ΠΈΡ
ΠΏΠ΅ΡΠ΅ΡΠ²ΠΎΡΠ΅Π½Ρ Π·Π° ΡΠ°Ρ
ΡΠ½ΠΎΠΊ Π·ΠΌΠ΅Π½ΡΠ΅Π½Π½Ρ ΠΏΠΎΡΡΠΆΠ½ΠΎΡΡΡ ΠΏΠΎΠ»Ρ ΠΏΡΠΈ Π½Π°Π½Π΅ΡΠ΅Π½Π½Ρ Π·Π±ΠΈΡΠΊΡ Π²ΡΠ΄ΠΊΡΠΈΡΠΎΠ³ΠΎ ΡΠ΅ΠΊΡΡΡ Ρ Π·ΠΌΠ΅Π½ΡΠΈΡΠΈ ΠΎΠ±ΡΡΠ³ ΠΏΠ΅ΡΠ΅Π΄Π°Π½ΠΈΡ
Π΄Π°Π½ΠΈΡ
Π·Π° ΡΠ°Ρ
ΡΠ½ΠΎΠΊ Π½Π°Π½Π΅ΡΠ΅Π½Π½Ρ ΡΠΊΠΎΠ΄ΠΈ ΡΠΈΡΡΡΠ΅ΠΊΡΡΡ. Π’Π°ΠΊΡΠΉ ΠΏΡΠ΄Ρ
ΡΠ΄ Π΄ΠΎΠ·Π²ΠΎΠ»ΡΡ Π±ΡΠ΄ΡΠ²Π°ΡΠΈ Π³ΡΠ±ΡΠΈΠ΄Π½Ρ ΠΊΡΠΈΠΏΡΠΎ-ΠΊΠΎΠ΄ΠΎΠ²Ρ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΡΡ Π½Π° ΠΎΡΠ½ΠΎΠ²Ρ ΡΠΈΠ½ΡΠ΅Π·Ρ ΠΌΠΎΠ΄ΠΈΡΡΠΊΠΎΠ²Π°Π½ΠΈΡ
ΠΊΡΠΈΠΏΡΠΎΠΊΠΎΠ΄ΠΎΠ²ΠΈΡ
ΠΊΠΎΠ½ΡΡΡΡΠΊΡΡΠΉ ΠΡΠ΄Π΅ΡΡΠ°ΠΉΡΠ΅ΡΠ° Π½Π° ΠΌΠΎΠ΄ΠΈΡΡΠΊΠΎΠ²Π°Π½ΠΈΡ
(ΡΠΊΠΎΡΠΎΡΠ΅Π½ΠΈΡ
Π°Π±ΠΎ ΠΏΠΎΠ΄ΠΎΠ²ΠΆΠ΅Π½ΠΈΡ
) ΠΊΠΎΠ΄Π°Ρ
Π½Π° Π΅Π»ΡΠΏΡΠΈΡΠ½ΠΈΡ
ΠΊΡΠΈΠ²ΠΈΡ
Π· ΠΏΡΠΎΡΠ΅Π΄ΡΡΠ°ΠΌΠΈ Π½Π°Π½Π΅ΡΠ΅Π½Π½Ρ Π·Π±ΠΈΡΠΊΡ. Π‘ΡΡΡΡΠ²ΠΎΡ Π²ΡΠ΄ΠΌΡΠ½Π½ΡΡΡΡ Π²ΡΠ΄ ΠΊΠ»Π°ΡΠΈΡΠ½ΠΈΡ
Π³ΡΠ±ΡΠΈΠ΄Π½ΠΈΡ
(ΠΊΠΎΠΌΠΏΠ»Π΅ΠΊΡΠ½ΠΈΡ
) ΠΊΡΠΈΠΏΡΠΎΡΠΈΡΡΠ΅ΠΌ Ρ Π²ΠΈΠΊΠΎΡΠΈΡΡΠ°Π½Π½Ρ Π½Π΅ΡΠΈΠΌΠ΅ΡΡΠΈΡΠ½ΠΎΡ ΠΊΡΠΈΠΏΡΠΎΡΠΈΡΡΠ΅ΠΌΠΈ Π΄Π»Ρ Π·Π°Π±Π΅Π·ΠΏΠ΅ΡΠ΅Π½Π½Ρ Π±Π΅Π·ΠΏΠ΅ΠΊΠΈ Π΄Π°Π½ΠΈΡ
Π· ΡΠ²ΡΠ΄ΠΊΠΈΠΌΠΈ ΠΏΡΠΎΡΠ΅Π΄ΡΡΠ°ΠΌΠΈ ΠΊΡΠΈΠΏΡΠΎΠΏΠ΅ΡΠ΅ΡΠ²ΠΎΡΠ΅Π½Ρ (ΡΠΎΡΠΌΡΠ²Π°Π½Π½Ρ ΡΠ° ΡΠΎΠ·ΠΊΠΎΠ΄ΡΠ²Π°Π½Π½Ρ ΠΊΠΎΠ΄ΠΎΠ³ΡΠ°ΠΌΠΈ). Π ΡΠΎΠ±ΠΎΡΡ ΡΠΎΠ·Π³Π»ΡΠ΄Π°ΡΡΡΡΡ ΡΠΏΠΎΡΠΎΠ±ΠΈ ΠΏΠΎΠ±ΡΠ΄ΠΎΠ²ΠΈ Π·Π±ΠΈΡΠΊΠΎΠ²ΠΈΡ
ΠΊΠΎΠ΄ΡΠ² Ρ ΠΏΡΠ΄Ρ
ΠΎΠ΄ΠΈ Π²ΠΈΠΊΠΎΡΠΈΡΡΠ°Π½Π½Ρ Π² Π³ΡΠ±ΡΠΈΠ΄Π½ΠΎΡ ΠΊΡΠΈΠΏΡΠΎ-ΠΊΠΎΠ΄ΠΎΠ²ΠΎΡ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΡΡ ΠΡΠ΄Π΅ΡΡΠ°ΠΉΡΠ΅ΡΠ° Π½Π° ΠΌΠΎΠ΄ΠΈΡΡΠΊΠΎΠ²Π°Π½ΠΈΡ
Π΅Π»ΡΠΏΡΠΈΡΠ½ΠΈΡ
ΠΊΠΎΠ΄Π°Ρ
. ΠΡΠΎΠΏΠΎΠ½ΡΡΡΡΡΡ ΠΏΡΠ°ΠΊΡΠΈΡΠ½Ρ Π°Π»Π³ΠΎΡΠΈΡΠΌΠΈ Π²ΠΈΠΊΠΎΡΠΈΡΡΠ°Π½Π½Ρ ΠΌΠ΅Ρ
Π°Π½ΡΠ·ΠΌΡ Π½Π°Π½Π΅ΡΠ΅Π½Π½Ρ Π·Π±ΠΈΡΠΊΡ MV2 Π² ΠΊΡΠΈΠΏΡΠΎ-ΠΊΠΎΠ΄ΠΎΠ²ΠΎΡ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΡΡ ΠΡΠ΄Π΅ΡΡΠ°ΠΉΡΠ΅ΡΠ° Π½Π° ΠΌΠΎΠ΄ΠΈΡΡΠΊΠΎΠ²Π°Π½ΠΈΡ
Π΅Π»ΡΠΏΡΠΈΡΠ½ΠΈΡ
ΠΊΠΎΠ΄Π°Ρ
, ΡΠΎ Π΄ΠΎΠ·Π²ΠΎΠ»ΡΡ ΡΠ΅Π°Π»ΡΠ·ΡΠ²Π°ΡΠΈ Π³ΡΠ±ΡΠΈΠ΄Π½Ρ ΠΊΡΠΈΠΏΡΠΎ-ΠΊΠΎΠ΄ΠΎΠ²Ρ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΡΡ. ΠΠ°Π²Π΅Π΄Π΅Π½Ρ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠΈ ΠΏΠΎΡΡΠ²Π½ΡΠ»ΡΠ½ΠΎΡ ΠΎΡΡΠ½ΠΊΠΈ Π΅Π½Π΅ΡΠ³ΠΎΠ²ΠΈΡΡΠ°Ρ Π½Π° ΡΠΎΡΠΌΡΠ²Π°Π½Π½Ρ ΡΠ½ΡΠΎΡΠΌΠ°ΡΡΠΉΠ½ΠΎΡ ΠΏΠΎΡΠΈΠ»ΠΊΠΈ ΠΏΡΠΈ ΡΡΠ·Π½ΠΈΡ
ΡΠΏΠΎΡΠΎΠ±Π°Ρ
Π½Π°Π½Π΅ΡΠ΅Π½Π½Ρ Π·Π±ΠΈΡΠΊΡ, ΡΠΎ Π²ΠΈΠ·Π½Π°ΡΠΈΠ»ΠΎ Π²ΠΈΠ±ΡΡ ΡΠΏΠΎΡΠΎΠ±Ρ Π½Π°Π½Π΅ΡΠ΅Π½Π½Ρ Π·Π±ΠΈΡΠΊΡ Π² ΠΏΡΠ°ΠΊΡΠΈΡΠ½ΠΈΡ
Π°Π»Π³ΠΎΡΠΈΡΠΌΠ°Ρ
. ΠΡΠΎΠ²Π΅Π΄Π΅Π½Ρ Π΄ΠΎΡΠ»ΡΠ΄ΠΆΠ΅Π½Π½Ρ ΠΏΡΠ΄ΡΠ²Π΅ΡΠΆΡΡΡΡ ΠΊΠΎΠ½ΠΊΡΡΠ΅Π½ΡΡ ΡΠΏΡΠΎΠΌΠΎΠΆΠ½ΡΡΡΡ Π·Π°ΠΏΡΠΎΠΏΠΎΠ½ΠΎΠ²Π°Π½ΠΎΡ ΠΊΡΠΈΠΏΡΠΎΡΠΈΡΡΠ΅ΠΌΠΈ Π² ΠΠ½ΡΠ΅ΡΠ½Π΅Ρ-ΡΠ΅Ρ
Π½ΠΎΠ»ΠΎΠ³ΡΡΡ
ΡΠ° ΠΌΠΎΠ±ΡΠ»ΡΠ½ΠΈΡ
ΠΌΠ΅ΡΠ΅ΠΆΠ°Ρ
, Π·Π°Π±Π΅Π·ΠΏΠ΅ΡΠ΅Π½Π½Ρ ΠΏΡΠ°ΠΊΡΠΈΡΠ½ΠΎΡ ΡΠ΅Π°Π»ΡΠ·Π°ΡΡΡ Π½Π° ΡΡΡΠ°ΡΠ½ΠΈΡ
ΠΏΠ»Π°ΡΡΠΎΡΠΌΠ°Ρ
ΡΠ° Π½Π΅ΠΎΠ±Ρ
ΡΠ΄Π½ΠΎΡ ΠΊΡΠΈΠΏΡΠΎΡΡΡΠΉΠΊΠΎΡΡΡ Π² ΡΠΌΠΎΠ²Π°Ρ
ΠΏΠΎΡΡΠΊΠ²Π°Π½ΡΠΎΠ²ΠΎΡ ΠΊΡΠΈΠΏΡΠΎΠ³ΡΠ°ΡΡ
Π ΠΎΠ·ΡΠΎΠ±ΠΊΠ° Π³ΡΠ±ΡΠΈΠ΄Π½ΠΎΡ ΠΊΡΠΈΠΏΡΠΎ-ΠΊΠΎΠ΄ΠΎΠ²ΠΎΡ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΡΡ Π½ΡΠ΄Π΅ΡΡΠ°ΠΉΡΠ΅ΡΠ° Π½Π° Π·Π±ΠΈΡΠΊΠΎΠ²ΠΈΡ ΠΊΠΎΠ΄Π°Ρ
The use of the Niederreiter modified crypto-code structure (MCCS) with additional initialization vectors (with many invalid positional vectors of the error vector and multiple positions of shortening the error vector) requires an increase in the speed of cryptographic transformation of the system as a whole. For this purpose, it is proposed to use flawed codes. Flawed codes allow you to increase the speed of code transformations by reducing the power of the field while damaging the plaintext and reducing the amount of data transferred by damaging the ciphertext. This approach allows the construction of hybrid crypto-code structures based on the synthesis of Niederreiter modified crypto-code structures on modified (shortened or extended) codes on elliptic curves with damaging procedures. A significant difference from classical hybrid (complex) cryptosystems is the use of asymmetric cryptosystems to ensure data security with fast crypto-transformation procedures (generation and decoding of a codogram). The paper discusses methods for constructing flawed codes and approaches for using the Niederreiter hybrid crypto-code structure on modified elliptic codes. Practical algorithms are proposed for using the MV2 damage mechanism in the Niederreiter crypto-code structure on modified elliptic codes, which makes it possible to implement a hybrid crypto-code structure. The results of a comparative assessment of energy consumption for the formation of an information package with various methods of damage, which determined the choice of damage method in practical algorithms. The conducted studies confirm the competitive efficiency of the proposed cryptosystem in Internet technologies and mobile networks, ensuring practical implementation on modern platforms and the necessary cryptographic strength under post-quantum cryptographyΠΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅ ΠΌΠΎΠ΄ΠΈΡΠΈΡΠΈΡΠΎΠ²Π°Π½Π½ΠΎΠΉ ΠΊΡΠΈΠΏΡΠΎ-ΠΊΠΎΠ΄ΠΎΠ²ΠΎΠΉ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠΈ (ΠΠΠΠ) ΠΠΈΠ΄Π΅ΡΡΠ°ΠΉΡΠ΅ΡΠ° Ρ Π΄ΠΎΠΏΠΎΠ»Π½ΠΈΡΠ΅Π»ΡΠ½ΡΠΌΠΈ Π²Π΅ΠΊΡΠΎΡΠ°ΠΌΠΈ ΠΈΠ½ΠΈΡΠΈΠ°Π»ΠΈΠ·Π°ΡΠΈΠΈ (Ρ ΠΌΠ½ΠΎΠΆΠ΅ΡΡΠ²ΠΎΠΌ Π½Π΅Π΄ΠΎΠΏΡΡΡΠΈΠΌΡΡ
ΠΏΠΎΠ·ΠΈΡΠΈΠΎΠ½Π½ΡΡ
Π²Π΅ΠΊΡΠΎΡΠΎΠ² Π²Π΅ΠΊΡΠΎΡΠ° ΠΎΡΠΈΠ±ΠΎΠΊ ΠΈ ΠΌΠ½ΠΎΠΆΠ΅ΡΡΠ²ΠΎΠΌ ΠΏΠΎΠ·ΠΈΡΠΈΠΉ ΡΠΊΠΎΡΠΎΡΠ΅Π½ΠΈΡ Π²Π΅ΠΊΡΠΎΡΠ° ΠΎΡΠΈΠ±ΠΊΠΈ) ΡΡΠ΅Π±ΡΠ΅Ρ ΡΠ²Π΅Π»ΠΈΡΠ΅Π½ΠΈΡ Π±ΡΡΡΡΠΎΠ΄Π΅ΠΉΡΡΠ²ΠΈΡ ΠΊΡΠΈΠΏΡΠΎΠΏΡΠ΅ΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°Π½ΠΈΡ ΡΠΈΡΡΠ΅ΠΌΡ Π² ΡΠ΅Π»ΠΎΠΌ. ΠΠ»Ρ ΡΡΠΎΠ³ΠΎ ΠΏΡΠ΅Π΄Π»Π°Π³Π°Π΅ΡΡΡ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°ΡΡ ΡΡΠ΅ΡΠ±Π½ΡΠ΅ ΠΊΠΎΠ΄Ρ. Π£ΡΠ΅ΡΠ±Π½ΡΠ΅ ΠΊΠΎΠ΄Ρ ΠΏΠΎΠ·Π²ΠΎΠ»ΡΡΡ ΡΠ²Π΅Π»ΠΈΡΠΈΡΡ ΡΠΊΠΎΡΠΎΡΡΡ ΠΊΠΎΠ΄ΠΎΠ²ΡΡ
ΠΏΡΠ΅ΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°Π½ΠΈΠΉ Π·Π° ΡΡΠ΅Ρ ΡΠΌΠ΅Π½ΡΡΠ΅Π½ΠΈΡ ΠΌΠΎΡΠ½ΠΎΡΡΠΈ ΠΏΠΎΠ»Ρ ΠΏΡΠΈ Π½Π°Π½Π΅ΡΠ΅Π½ΠΈΠΈ ΡΡΠ΅ΡΠ±Π° ΠΎΡΠΊΡΡΡΡ ΡΠ΅ΠΊΡΡΡ ΠΈ ΡΠΌΠ΅Π½ΡΡΠΈΡΡ ΠΎΠ±ΡΠ΅ΠΌ ΠΏΠ΅ΡΠ΅Π΄Π°Π²Π°Π΅ΠΌΡΡ
Π΄Π°Π½Π½ΡΡ
Π·Π° ΡΡΠ΅Ρ Π½Π°Π½Π΅ΡΠ΅Π½ΠΈΡ ΡΡΠ΅ΡΠ±Π° ΡΠΈΡΡΡΠ΅ΠΊΡΡΡ. Π’Π°ΠΊΠΎΠΉ ΠΏΠΎΠ΄Ρ
ΠΎΠ΄ ΠΏΠΎΠ·Π²ΠΎΠ»ΡΠ΅Ρ ΡΡΡΠΎΠΈΡΡ Π³ΠΈΠ±ΡΠΈΠ΄Π½ΡΠ΅ ΠΊΡΠΈΠΏΡΠΎ-ΠΊΠΎΠ΄ΠΎΠ²ΡΠ΅ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠΈ Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ ΡΠΈΠ½ΡΠ΅Π·Π° ΠΌΠΎΠ΄ΠΈΡΠΈΡΠΈΡΠΎΠ²Π°Π½Π½ΡΡ
ΠΊΡΠΈΠΏΡΠΎΠΊΠΎΠ΄ΠΎΠ²ΡΡ
ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠΉ ΠΠΈΠ΄Π΅ΡΡΠ°ΠΉΡΠ΅ΡΠ° Π½Π° ΠΌΠΎΠ΄ΠΈΡΠΈΡΠΈΡΠΎΠ²Π°Π½Π½ΡΡ
(ΡΠΊΠΎΡΠΎΡΠ΅Π½Π½ΡΡ
ΠΈΠ»ΠΈ ΡΠ΄Π»ΠΈΠ½Π΅Π½Π½ΡΡ
) ΠΊΠΎΠ΄Π°Ρ
Π½Π° ΡΠ»Π»ΠΈΠΏΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΊΡΠΈΠ²ΡΡ
Ρ ΠΏΡΠΎΡΠ΅Π΄ΡΡΠ°ΠΌΠΈ Π½Π°Π½Π΅ΡΠ΅Π½ΠΈΡ ΡΡΠ΅ΡΠ±Π°. Π‘ΡΡΠ΅ΡΡΠ²Π΅Π½Π½ΡΠΌ ΠΎΡΠ»ΠΈΡΠΈΠ΅ΠΌ ΠΎΡ ΠΊΠ»Π°ΡΡΠΈΡΠ΅ΡΠΊΠΈΡ
Π³ΠΈΠ±ΡΠΈΠ΄Π½ΡΡ
(ΠΊΠΎΠΌΠΏΠ»Π΅ΠΊΡΠ½ΡΡ
) ΠΊΡΠΈΠΏΡΠΎΡΠΈΡΡΠ΅ΠΌ ΡΠ²Π»ΡΠ΅ΡΡΡ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅ Π½Π΅ΡΠΈΠΌΠΌΠ΅ΡΡΠΈΡΠ½ΠΎΠΉ ΠΊΡΠΈΠΏΡΠΎΡΠΈΡΡΠ΅ΠΌΡ Π΄Π»Ρ ΠΎΠ±Π΅ΡΠΏΠ΅ΡΠ΅Π½ΠΈΡ Π±Π΅Π·ΠΎΠΏΠ°ΡΠ½ΠΎΡΡΠΈ Π΄Π°Π½Π½ΡΡ
Ρ Π±ΡΡΡΡΡΠΌΠΈ ΠΏΡΠΎΡΠ΅Π΄ΡΡΠ°ΠΌΠΈ ΠΊΡΠΈΠΏΡΠΎΠΏΡΠ΅ΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°Π½ΠΈΡ (ΡΠΎΡΠΌΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ ΠΈ ΡΠ°ΡΠΊΠΎΠ΄ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΊΠΎΠ΄ΠΎΠ³ΡΠ°ΠΌΠΌΡ). Π ΡΠ°Π±ΠΎΡΠ΅ ΡΠ°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°ΡΡΡΡ ΡΠΏΠΎΡΠΎΠ±Ρ ΠΏΠΎΡΡΡΠΎΠ΅Π½ΠΈΡ ΡΡΠ΅ΡΠ±Π½ΡΡ
ΠΊΠΎΠ΄ΠΎΠ² ΠΈ ΠΏΠΎΠ΄Ρ
ΠΎΠ΄Ρ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΡ Π² Π³ΠΈΠ±ΡΠΈΠ΄Π½ΠΎΠΉ ΠΊΡΠΈΠΏΡΠΎ-ΠΊΠΎΠ΄ΠΎΠ²ΠΎΠΉ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠΈ ΠΠΈΠ΄Π΅ΡΡΠ°ΠΉΡΠ΅ΡΠ° Π½Π° ΠΌΠΎΠ΄ΠΈΡΠΈΡΠΈΡΠΎΠ²Π°Π½Π½ΡΡ
ΡΠ»Π»ΠΈΠΏΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΊΠΎΠ΄Π°Ρ
. ΠΡΠ΅Π΄Π»Π°Π³Π°ΡΡΡΡ ΠΏΡΠ°ΠΊΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ Π°Π»Π³ΠΎΡΠΈΡΠΌΡ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΡ ΠΌΠ΅Ρ
Π°Π½ΠΈΠ·ΠΌΠ° Π½Π°Π½Π΅ΡΠ΅Π½ΠΈΡ ΡΡΠ΅ΡΠ±Π° MV2 Π² ΠΊΡΠΈΠΏΡΠΎ-ΠΊΠΎΠ΄ΠΎΠ²ΠΎΠΉ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠΈ ΠΠΈΠ΄Π΅ΡΡΠ°ΠΉΡΠ΅ΡΠ° Π½Π° ΠΌΠΎΠ΄ΠΈΡΠΈΡΠΈΡΠΎΠ²Π°Π½Π½ΡΡ
ΡΠ»Π»ΠΈΠΏΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΊΠΎΠ΄Π°Ρ
, ΡΡΠΎ ΠΏΠΎΠ·Π²ΠΎΠ»ΡΠ΅Ρ ΡΠ΅Π°Π»ΠΈΠ·ΠΎΠ²Π°ΡΡ Π³ΠΈΠ±ΡΠΈΠ΄Π½ΡΡ ΠΊΡΠΈΠΏΡΠΎ-ΠΊΠΎΠ΄ΠΎΠ²ΡΡ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΡ. ΠΡΠΈΠ²Π΅Π΄Π΅Π½Ρ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ ΡΡΠ°Π²Π½ΠΈΡΠ΅Π»ΡΠ½ΠΎΠΉ ΠΎΡΠ΅Π½ΠΊΠΈ ΡΠ½Π΅ΡΠ³ΠΎΠ·Π°ΡΡΠ°Ρ Π½Π° ΡΠΎΡΠΌΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΎΠ½Π½ΠΎΠΉ ΠΏΠΎΡΡΠ»ΠΊΠΈ ΠΏΡΠΈ ΡΠ°Π·Π»ΠΈΡΠ½ΡΡ
ΡΠΏΠΎΡΠΎΠ±Π°Ρ
Π½Π°Π½Π΅ΡΠ΅Π½ΠΈΡ ΡΡΠ΅ΡΠ±Π°, ΡΡΠΎ ΠΎΠΏΡΠ΅Π΄Π΅Π»ΠΈΠ»ΠΎ Π²ΡΠ±ΠΎΡ ΡΠΏΠΎΡΠΎΠ±Π° Π½Π°Π½Π΅ΡΠ΅Π½ΠΈΡ ΡΡΠ΅ΡΠ±Π° Π² ΠΏΡΠ°ΠΊΡΠΈΡΠ΅ΡΠΊΠΈΡ
Π°Π»Π³ΠΎΡΠΈΡΠΌΠ°Ρ
. ΠΡΠΎΠ²Π΅Π΄Π΅Π½Π½ΡΠ΅ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ ΠΏΠΎΠ΄ΡΠ²Π΅ΡΠΆΠ΄Π°ΡΡ ΠΊΠΎΠ½ΠΊΡΡΠ΅Π½ΡΡΡ ΡΡΡΠ΅ΠΊΡΠΈΠ²Π½ΠΎΡΡΡ ΠΏΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½Π½ΠΎΠΉ ΠΊΡΠΈΠΏΡΠΎΡΠΈΡΡΠ΅ΠΌΡ Π² ΠΠ½ΡΠ΅ΡΠ½Π΅Ρ-ΡΠ΅Ρ
Π½ΠΎΠ»ΠΎΠ³ΠΈΡΡ
ΠΈ ΠΌΠΎΠ±ΠΈΠ»ΡΠ½ΡΡ
ΡΠ΅ΡΡΡ
, ΠΎΠ±Π΅ΡΠΏΠ΅ΡΠ΅Π½ΠΈΡ ΠΏΡΠ°ΠΊΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΡΠ΅Π°Π»ΠΈΠ·Π°ΡΠΈΠΈ Π½Π° ΡΠΎΠ²ΡΠ΅ΠΌΠ΅Π½Π½ΡΡ
ΠΏΠ»Π°ΡΡΠΎΡΠΌΠ°Ρ
ΠΈ Π½Π΅ΠΎΠ±Ρ
ΠΎΠ΄ΠΈΠΌΠΎΠΉ ΠΊΡΠΈΠΏΡΠΎΡΡΠΎΠΉΠΊΠΎΡΡΠΈ Π² ΡΡΠ»ΠΎΠ²ΠΈΡΡ
ΠΏΠΎΡΡΠΊΠ²Π°Π½ΡΠΎΠ²ΠΎΠΉ ΠΊΡΠΈΠΏΡΠΎΠ³ΡΠ°ΡΠΈΠΈΠΠΈΠΊΠΎΡΠΈΡΡΠ°Π½Π½Ρ ΠΌΠΎΠ΄ΠΈΡΡΠΊΠΎΠ²Π°Π½ΠΎΡ ΠΊΡΠΈΠΏΡΠΎ-ΠΊΠΎΠ΄ΠΎΠ²ΠΎΡ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΡΡ (ΠΠΠΠ) ΠΡΠ΄Π΅ΡΡΠ°ΠΉΡΠ΅ΡΠ° Π· Π΄ΠΎΠ΄Π°ΡΠΊΠΎΠ²ΠΈΠΌΠΈ Π²Π΅ΠΊΡΠΎΡΠ°ΠΌΠΈ ΡΠ½ΡΡΡΠ°Π»ΡΠ·Π°ΡΡΡ (Π· ΠΌΠ½ΠΎΠΆΠΈΠ½ΠΎΡ Π½Π΅ΠΏΡΠΈΠΏΡΡΡΠΈΠΌΠΈΡ
ΠΏΠΎΠ·ΠΈΡΡΠΉΠ½ΠΈΡ
Π²Π΅ΠΊΡΠΎΡΡΠ² Π²Π΅ΠΊΡΠΎΡΠ° ΠΏΠΎΠΌΠΈΠ»ΠΎΠΊ Ρ ΠΌΠ½ΠΎΠΆΠΈΠ½ΠΎΡ ΠΏΠΎΠ·ΠΈΡΡΠΉ ΡΠΊΠΎΡΠΎΡΠ΅Π½Π½Ρ Π²Π΅ΠΊΡΠΎΡΠ° ΠΏΠΎΠΌΠΈΠ»ΠΊΠΈ) Π²ΠΈΠΌΠ°Π³Π°Ρ Π·Π±ΡΠ»ΡΡΠ΅Π½Π½Ρ ΡΠ²ΠΈΠ΄ΠΊΠΎΠ΄ΡΡ ΠΊΡΠΈΠΏΡΠΎΠΏΠ΅ΡΠ΅ΡΠ²ΠΎΡΠ΅Π½Ρ ΡΠΈΡΡΠ΅ΠΌΠΈ Π²ΡΡΠ»ΠΎΠΌΡ. ΠΠ»Ρ ΡΡΠΎΠ³ΠΎ ΠΏΡΠΎΠΏΠΎΠ½ΡΡΡΡΡΡ Π²ΠΈΠΊΠΎΡΠΈΡΡΠΎΠ²ΡΠ²Π°ΡΠΈ Π·Π±ΠΈΡΠΊΠΎΠ²Ρ ΠΊΠΎΠ΄ΠΈ. ΠΠ±ΠΈΡΠΊΠΎΠ²Ρ ΠΊΠΎΠ΄ΠΈ Π΄ΠΎΠ·Π²ΠΎΠ»ΡΡΡΡ Π·Π±ΡΠ»ΡΡΠΈΡΠΈ ΡΠ²ΠΈΠ΄ΠΊΡΡΡΡ ΠΊΠΎΠ΄ΠΎΠ²ΠΈΡ
ΠΏΠ΅ΡΠ΅ΡΠ²ΠΎΡΠ΅Π½Ρ Π·Π° ΡΠ°Ρ
ΡΠ½ΠΎΠΊ Π·ΠΌΠ΅Π½ΡΠ΅Π½Π½Ρ ΠΏΠΎΡΡΠΆΠ½ΠΎΡΡΡ ΠΏΠΎΠ»Ρ ΠΏΡΠΈ Π½Π°Π½Π΅ΡΠ΅Π½Π½Ρ Π·Π±ΠΈΡΠΊΡ Π²ΡΠ΄ΠΊΡΠΈΡΠΎΠ³ΠΎ ΡΠ΅ΠΊΡΡΡ Ρ Π·ΠΌΠ΅Π½ΡΠΈΡΠΈ ΠΎΠ±ΡΡΠ³ ΠΏΠ΅ΡΠ΅Π΄Π°Π½ΠΈΡ
Π΄Π°Π½ΠΈΡ
Π·Π° ΡΠ°Ρ
ΡΠ½ΠΎΠΊ Π½Π°Π½Π΅ΡΠ΅Π½Π½Ρ ΡΠΊΠΎΠ΄ΠΈ ΡΠΈΡΡΡΠ΅ΠΊΡΡΡ. Π’Π°ΠΊΡΠΉ ΠΏΡΠ΄Ρ
ΡΠ΄ Π΄ΠΎΠ·Π²ΠΎΠ»ΡΡ Π±ΡΠ΄ΡΠ²Π°ΡΠΈ Π³ΡΠ±ΡΠΈΠ΄Π½Ρ ΠΊΡΠΈΠΏΡΠΎ-ΠΊΠΎΠ΄ΠΎΠ²Ρ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΡΡ Π½Π° ΠΎΡΠ½ΠΎΠ²Ρ ΡΠΈΠ½ΡΠ΅Π·Ρ ΠΌΠΎΠ΄ΠΈΡΡΠΊΠΎΠ²Π°Π½ΠΈΡ
ΠΊΡΠΈΠΏΡΠΎΠΊΠΎΠ΄ΠΎΠ²ΠΈΡ
ΠΊΠΎΠ½ΡΡΡΡΠΊΡΡΠΉ ΠΡΠ΄Π΅ΡΡΠ°ΠΉΡΠ΅ΡΠ° Π½Π° ΠΌΠΎΠ΄ΠΈΡΡΠΊΠΎΠ²Π°Π½ΠΈΡ
(ΡΠΊΠΎΡΠΎΡΠ΅Π½ΠΈΡ
Π°Π±ΠΎ ΠΏΠΎΠ΄ΠΎΠ²ΠΆΠ΅Π½ΠΈΡ
) ΠΊΠΎΠ΄Π°Ρ
Π½Π° Π΅Π»ΡΠΏΡΠΈΡΠ½ΠΈΡ
ΠΊΡΠΈΠ²ΠΈΡ
Π· ΠΏΡΠΎΡΠ΅Π΄ΡΡΠ°ΠΌΠΈ Π½Π°Π½Π΅ΡΠ΅Π½Π½Ρ Π·Π±ΠΈΡΠΊΡ. Π‘ΡΡΡΡΠ²ΠΎΡ Π²ΡΠ΄ΠΌΡΠ½Π½ΡΡΡΡ Π²ΡΠ΄ ΠΊΠ»Π°ΡΠΈΡΠ½ΠΈΡ
Π³ΡΠ±ΡΠΈΠ΄Π½ΠΈΡ
(ΠΊΠΎΠΌΠΏΠ»Π΅ΠΊΡΠ½ΠΈΡ
) ΠΊΡΠΈΠΏΡΠΎΡΠΈΡΡΠ΅ΠΌ Ρ Π²ΠΈΠΊΠΎΡΠΈΡΡΠ°Π½Π½Ρ Π½Π΅ΡΠΈΠΌΠ΅ΡΡΠΈΡΠ½ΠΎΡ ΠΊΡΠΈΠΏΡΠΎΡΠΈΡΡΠ΅ΠΌΠΈ Π΄Π»Ρ Π·Π°Π±Π΅Π·ΠΏΠ΅ΡΠ΅Π½Π½Ρ Π±Π΅Π·ΠΏΠ΅ΠΊΠΈ Π΄Π°Π½ΠΈΡ
Π· ΡΠ²ΡΠ΄ΠΊΠΈΠΌΠΈ ΠΏΡΠΎΡΠ΅Π΄ΡΡΠ°ΠΌΠΈ ΠΊΡΠΈΠΏΡΠΎΠΏΠ΅ΡΠ΅ΡΠ²ΠΎΡΠ΅Π½Ρ (ΡΠΎΡΠΌΡΠ²Π°Π½Π½Ρ ΡΠ° ΡΠΎΠ·ΠΊΠΎΠ΄ΡΠ²Π°Π½Π½Ρ ΠΊΠΎΠ΄ΠΎΠ³ΡΠ°ΠΌΠΈ). Π ΡΠΎΠ±ΠΎΡΡ ΡΠΎΠ·Π³Π»ΡΠ΄Π°ΡΡΡΡΡ ΡΠΏΠΎΡΠΎΠ±ΠΈ ΠΏΠΎΠ±ΡΠ΄ΠΎΠ²ΠΈ Π·Π±ΠΈΡΠΊΠΎΠ²ΠΈΡ
ΠΊΠΎΠ΄ΡΠ² Ρ ΠΏΡΠ΄Ρ
ΠΎΠ΄ΠΈ Π²ΠΈΠΊΠΎΡΠΈΡΡΠ°Π½Π½Ρ Π² Π³ΡΠ±ΡΠΈΠ΄Π½ΠΎΡ ΠΊΡΠΈΠΏΡΠΎ-ΠΊΠΎΠ΄ΠΎΠ²ΠΎΡ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΡΡ ΠΡΠ΄Π΅ΡΡΠ°ΠΉΡΠ΅ΡΠ° Π½Π° ΠΌΠΎΠ΄ΠΈΡΡΠΊΠΎΠ²Π°Π½ΠΈΡ
Π΅Π»ΡΠΏΡΠΈΡΠ½ΠΈΡ
ΠΊΠΎΠ΄Π°Ρ
. ΠΡΠΎΠΏΠΎΠ½ΡΡΡΡΡΡ ΠΏΡΠ°ΠΊΡΠΈΡΠ½Ρ Π°Π»Π³ΠΎΡΠΈΡΠΌΠΈ Π²ΠΈΠΊΠΎΡΠΈΡΡΠ°Π½Π½Ρ ΠΌΠ΅Ρ
Π°Π½ΡΠ·ΠΌΡ Π½Π°Π½Π΅ΡΠ΅Π½Π½Ρ Π·Π±ΠΈΡΠΊΡ MV2 Π² ΠΊΡΠΈΠΏΡΠΎ-ΠΊΠΎΠ΄ΠΎΠ²ΠΎΡ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΡΡ ΠΡΠ΄Π΅ΡΡΠ°ΠΉΡΠ΅ΡΠ° Π½Π° ΠΌΠΎΠ΄ΠΈΡΡΠΊΠΎΠ²Π°Π½ΠΈΡ
Π΅Π»ΡΠΏΡΠΈΡΠ½ΠΈΡ
ΠΊΠΎΠ΄Π°Ρ
, ΡΠΎ Π΄ΠΎΠ·Π²ΠΎΠ»ΡΡ ΡΠ΅Π°Π»ΡΠ·ΡΠ²Π°ΡΠΈ Π³ΡΠ±ΡΠΈΠ΄Π½Ρ ΠΊΡΠΈΠΏΡΠΎ-ΠΊΠΎΠ΄ΠΎΠ²Ρ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΡΡ. ΠΠ°Π²Π΅Π΄Π΅Π½Ρ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠΈ ΠΏΠΎΡΡΠ²Π½ΡΠ»ΡΠ½ΠΎΡ ΠΎΡΡΠ½ΠΊΠΈ Π΅Π½Π΅ΡΠ³ΠΎΠ²ΠΈΡΡΠ°Ρ Π½Π° ΡΠΎΡΠΌΡΠ²Π°Π½Π½Ρ ΡΠ½ΡΠΎΡΠΌΠ°ΡΡΠΉΠ½ΠΎΡ ΠΏΠΎΡΠΈΠ»ΠΊΠΈ ΠΏΡΠΈ ΡΡΠ·Π½ΠΈΡ
ΡΠΏΠΎΡΠΎΠ±Π°Ρ
Π½Π°Π½Π΅ΡΠ΅Π½Π½Ρ Π·Π±ΠΈΡΠΊΡ, ΡΠΎ Π²ΠΈΠ·Π½Π°ΡΠΈΠ»ΠΎ Π²ΠΈΠ±ΡΡ ΡΠΏΠΎΡΠΎΠ±Ρ Π½Π°Π½Π΅ΡΠ΅Π½Π½Ρ Π·Π±ΠΈΡΠΊΡ Π² ΠΏΡΠ°ΠΊΡΠΈΡΠ½ΠΈΡ
Π°Π»Π³ΠΎΡΠΈΡΠΌΠ°Ρ
. ΠΡΠΎΠ²Π΅Π΄Π΅Π½Ρ Π΄ΠΎΡΠ»ΡΠ΄ΠΆΠ΅Π½Π½Ρ ΠΏΡΠ΄ΡΠ²Π΅ΡΠΆΡΡΡΡ ΠΊΠΎΠ½ΠΊΡΡΠ΅Π½ΡΡ ΡΠΏΡΠΎΠΌΠΎΠΆΠ½ΡΡΡΡ Π·Π°ΠΏΡΠΎΠΏΠΎΠ½ΠΎΠ²Π°Π½ΠΎΡ ΠΊΡΠΈΠΏΡΠΎΡΠΈΡΡΠ΅ΠΌΠΈ Π² ΠΠ½ΡΠ΅ΡΠ½Π΅Ρ-ΡΠ΅Ρ
Π½ΠΎΠ»ΠΎΠ³ΡΡΡ
ΡΠ° ΠΌΠΎΠ±ΡΠ»ΡΠ½ΠΈΡ
ΠΌΠ΅ΡΠ΅ΠΆΠ°Ρ
, Π·Π°Π±Π΅Π·ΠΏΠ΅ΡΠ΅Π½Π½Ρ ΠΏΡΠ°ΠΊΡΠΈΡΠ½ΠΎΡ ΡΠ΅Π°Π»ΡΠ·Π°ΡΡΡ Π½Π° ΡΡΡΠ°ΡΠ½ΠΈΡ
ΠΏΠ»Π°ΡΡΠΎΡΠΌΠ°Ρ
ΡΠ° Π½Π΅ΠΎΠ±Ρ
ΡΠ΄Π½ΠΎΡ ΠΊΡΠΈΠΏΡΠΎΡΡΡΠΉΠΊΠΎΡΡΡ Π² ΡΠΌΠΎΠ²Π°Ρ
ΠΏΠΎΡΡΠΊΠ²Π°Π½ΡΠΎΠ²ΠΎΡ ΠΊΡΠΈΠΏΡΠΎΠ³ΡΠ°ΡΡ
Development of A Modified UMAC Algorithm Based on CryptoΒcode Constructions
The development of computer technology has determined the vector for the expansion of services based on the Internet and βGβ technologies. The main requirements for modern services in the banking sector are security and reliability. At the same time, security is considered not only as ensuring the confidentiality and integrity of transactions, but also their authenticity. However, in the post-quantum period, US NIST specialists question the durability of modern means of providing basic security services based on symmetric and asymmetric cryptography algorithms. The increase in computing resources allows attackers to use modern threats in combination. Thus, there is a need to search for new and/or modify known algorithms for generating MAC (message authentication codes). In addition, the growth of services increases the amount of information that needs to be authenticated. Among the well-known hash algorithms, the hash functions of universal hashing are distinguished, which allow initially determining the number of collisions and their uniform distribution over the entire set of hash codes. Possibilities of modifying the cascade hashing algorithm UMAC (message authentication code based on universal hashing, universal MAC) based on the use of McEliece crypto-code construction on algebrogeometric (elliptic codes (EC), modified elliptic codes (MEC) and damaged codes (DC). This approach allows preserving the uniqueness property, in contrast to the classical UMAC scheme based on a block symmetric cipher (AES). The presented algorithms for evaluating the properties of universality and strict universality of hash codes make it possible to evaluate the security of the proposed hashing constructs based on universal hash functions, taking into account the preservation of the universality propert