15 research outputs found

    Dynamics of heart rate variability in rats with streptozotocin-induced diabetes

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    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

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    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) ------------------------------------------------------------------------------------------------------------------ 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’Π•Π‘HNOLOGY Π‘Π•NTΠ•R, 188. doi: http://doi.org/10.15587/978-617-7319-31-2 ------------------------------------------------------------------------------------------------------------------ Indexing:                    Π ΠΎΠ·Π²ΠΈΡ‚ΠΎΠΊ сучасної світової ΡΠΏΡ–Π»ΡŒΠ½ΠΎΡ‚ΠΈ тісно пов’язаний Π· досягнСннями Π² області ΠΎΠ±Ρ‡ΠΈΡΠ»ΡŽΠ²Π°Π»ΡŒΠ½ΠΈΡ… рСсурсів Ρ– кібСрпростору. Ѐормування Ρ‚Π° Ρ€ΠΎΠ·ΡˆΠΈΡ€Π΅Π½Π½Ρ асортимСнту послуг Π±Π°Π·ΡƒΡ”Ρ‚ΡŒΡΡ Π½Π° досягнСннях Π»ΡŽΠ΄ΡΡ‚Π²Π° Ρƒ Π³Π°Π»ΡƒΠ·Ρ– високих Ρ‚Π΅Ρ…Π½ΠΎΠ»ΠΎΠ³Ρ–ΠΉ. Однак стрімкС зростання ΠΎΠ±Ρ‡ΠΈΡΠ»ΡŽΠ²Π°Π»ΡŒΠ½ΠΈΡ… рСсурсів, поява ΠΏΠΎΠ²Π½ΠΎΠΌΠ°ΡΡˆΡ‚Π°Π±Π½ΠΎΠ³ΠΎ ΠΊΠ²Π°Π½Ρ‚ΠΎΠ²ΠΎΠ³ΠΎ ΠΊΠΎΠΌΠΏβ€™ΡŽΡ‚Π΅Ρ€Π° ΠΏΠΎΡΠΈΠ»ΡŽΡ” Π²ΠΈΠΌΠΎΠ³ΠΈ Π΄ΠΎ систСм Π±Π΅Π·ΠΏΠ΅ΠΊΠΈ Π½Π΅ Ρ‚Ρ–Π»ΡŒΠΊΠΈ Ρ–Π½Ρ„ΠΎΡ€ΠΌΠ°Ρ†Ρ–ΠΉΠ½ΠΎ-ΠΊΠΎΠΌΡƒΠ½Ρ–ΠΊΠ°Ρ†Ρ–ΠΉΠ½ΠΈΡ…, Π°Π»Π΅ Ρ– Π΄ΠΎ ΠΊΡ–Π±Π΅Ρ€Ρ„Ρ–Π·ΠΈΡ‡Π½ΠΈΡ… систСм Ρ– Ρ‚Π΅Ρ…Π½ΠΎΠ»ΠΎΠ³Ρ–ΠΉ. Π£ ΠΏΠ΅Ρ€ΡˆΠΎΠΌΡƒ Ρ€ΠΎΠ·Π΄Ρ–Π»Ρ– ΠΎΠ±Π³ΠΎΠ²ΠΎΡ€ΡŽΡŽΡ‚ΡŒΡΡ ΠΌΠ΅Ρ‚ΠΎΠ΄ΠΎΠ»ΠΎΠ³Ρ–Ρ‡Π½Ρ– основи ΠΏΠΎΠ±ΡƒΠ΄ΠΎΠ²ΠΈ систСм Π±Π΅Π·ΠΏΠ΅ΠΊΠΈ для ΠΎΠ±'Ρ”ΠΊΡ‚Ρ–Π² ΠΊΡ€ΠΈΡ‚ΠΈΡ‡Π½ΠΎΡ— інфраструктури Π½Π° основі модСлювання процСсів ΠΏΠΎΠ²Π΅Π΄Ρ–Π½ΠΊΠΈ антагоністичних Π°Π³Π΅Π½Ρ‚Ρ–Π² Ρƒ систСм Π±Π΅Π·ΠΏΠ΅ΠΊΠΈ. Π£ Π΄Ρ€ΡƒΠ³ΠΎΠΌΡƒ Ρ€ΠΎΠ·Π΄Ρ–Π»Ρ– ΠΏΡ€ΠΎΠΏΠΎΠ½ΡƒΡ”Ρ‚ΡŒΡΡ концСпція Ρ–Π½Ρ„ΠΎΡ€ΠΌΠ°Ρ†Ρ–ΠΉΠ½ΠΎΡ— Π±Π΅Π·ΠΏΠ΅ΠΊΠΈ Π² ΡΠΎΡ†Ρ–Π°Π»ΡŒΠ½ΠΈΡ… ΠΌΠ΅Ρ€Π΅ΠΆΠ°Ρ…, яка заснована Π½Π° ΠΌΠ°Ρ‚Π΅ΠΌΠ°Ρ‚ΠΈΡ‡Π½ΠΈΡ… модСлях захисту Π΄Π°Π½ΠΈΡ…, Π· урахуванням Π²ΠΏΠ»ΠΈΠ²Ρƒ ΠΊΠΎΠ½ΠΊΡ€Π΅Ρ‚Π½ΠΈΡ… ΠΏΠ°Ρ€Π°ΠΌΠ΅Ρ‚Ρ€Ρ–Π² ΡΠΎΡ†Ρ–Π°Π»ΡŒΠ½ΠΎΡ— ΠΌΠ΅Ρ€Π΅ΠΆΡ– Ρ‚Π° наслідків для Π½Π΅Ρ—. Π’Ρ€Π°Ρ…ΠΎΠ²ΡƒΡŽΡ‚ΡŒΡΡ Π½Π΅Π»Ρ–Π½Ρ–ΠΉΠ½Ρ– Π²Π·Π°Ρ”ΠΌΠΎΠ·Π²'язки ΠΏΠ°Ρ€Π°ΠΌΠ΅Ρ‚Ρ€Ρ–Π² систСми захисту, Π°Ρ‚Π°ΠΊ, ΡΠΎΡ†Ρ–Π°Π»ΡŒΠ½ΠΈΡ… ΠΌΠ΅Ρ€Π΅ΠΆ, Π° Ρ‚Π°ΠΊΠΎΠΆ Π²ΠΏΠ»ΠΈΠ² Ρ–Π½Π΄ΠΈΠ²Ρ–Π΄ΡƒΠ°Π»ΡŒΠ½ΠΈΡ… характСристик користувачів Ρ– Ρ…Π°Ρ€Π°ΠΊΡ‚Π΅Ρ€Ρƒ взаємовідносин ΠΌΡ–ΠΆ Π½ΠΈΠΌΠΈ. Π£ Ρ‚Ρ€Π΅Ρ‚ΡŒΠΎΠΌΡƒ Ρ€ΠΎΠ·Π΄Ρ–Π»Ρ– Ρ€ΠΎΠ·Π³Π»ΡΠ΄Π°ΡŽΡ‚ΡŒΡΡ ΠΏΡ€Π°ΠΊΡ‚ΠΈΡ‡Π½Ρ– аспСкти ΠΌΠ΅Ρ‚ΠΎΠ΄ΠΎΠ»ΠΎΠ³Ρ–Ρ— ΠΏΠΎΠ±ΡƒΠ΄ΠΎΠ²ΠΈ постквантових Π°Π»Π³ΠΎΡ€ΠΈΡ‚ΠΌΡ–Π² для асимСтричних криптосистСм Мак-Еліса Ρ‚Π° НідСррСйтСра Π½Π° Π°Π»Π³Π΅Π±Ρ€Π°Ρ—Ρ‡Π½ΠΈΡ… ΠΊΠΎΠ΄Π°Ρ… (Π΅Π»Ρ–ΠΏΡ‚ΠΈΡ‡Π½ΠΈΡ… Ρ‚Π° ΠΌΠΎΠ΄ΠΈΡ„Ρ–ΠΊΠΎΠ²Π°Π½ΠΈΡ… Π΅Π»Ρ–ΠΏΡ‚ΠΈΡ‡Π½ΠΈΡ… ΠΊΠΎΠ΄Π°Ρ…), Ρ—Ρ… ΠΌΠ°Ρ‚Π΅ΠΌΠ°Ρ‚ΠΈΡ‡Π½Ρ– ΠΌΠΎΠ΄Π΅Π»Ρ– Ρ‚Π° ΠΏΡ€Π°ΠΊΡ‚ΠΈΡ‡Π½Ρ– Π°Π»Π³ΠΎΡ€ΠΈΡ‚ΠΌΠΈ. Π—Π°ΠΏΡ€ΠΎΠΏΠΎΠ½ΠΎΠ²Π°Π½ΠΎ Π³Ρ–Π±Ρ€ΠΈΠ΄Π½Ρ– конструкції ΠΊΡ€ΠΈΠΏΡ‚ΠΎΠΊΠΎΠ΄Ρƒ Мак-Еліса Ρ‚Π° НідСррСйтСра Π½Π° Π΄Π΅Ρ„Π΅ΠΊΡ‚Π½ΠΈΡ… ΠΊΠΎΠ΄Π°Ρ…. Π’ΠΎΠ½ΠΈ Π΄ΠΎΠ·Π²ΠΎΠ»ΡΡŽΡ‚ΡŒ істотно Π·Π½ΠΈΠ·ΠΈΡ‚ΠΈ Π΅Π½Π΅Ρ€Π³Π΅Ρ‚ΠΈΡ‡Π½Ρ– Π²ΠΈΡ‚Ρ€Π°Ρ‚ΠΈ Π½Π° Ρ€Π΅Π°Π»Ρ–Π·Π°Ρ†Ρ–ΡŽ, Π·Π°Π±Π΅Π·ΠΏΠ΅Ρ‡ΡƒΡŽΡ‡ΠΈ ΠΏΡ€ΠΈ Ρ†ΡŒΠΎΠΌΡƒ Π½Π΅ΠΎΠ±Ρ…Ρ–Π΄Π½ΠΈΠΉ Ρ€Ρ–Π²Π΅Π½ΡŒ ΠΊΡ€ΠΈΠΏΡ‚ΠΎΠ³Ρ€Π°Ρ„Ρ–Ρ‡Π½ΠΎΡ— стійкості систСми Π² Ρ†Ρ–Π»ΠΎΠΌΡƒ. Π—Π°ΠΏΡ€ΠΎΠΏΠΎΠ½ΠΎΠ²Π°Π½ΠΎ ΠΊΠΎΠ½Ρ†Π΅ΠΏΡ†Ρ–ΡŽ Π±Π΅Π·ΠΏΠ΅ΠΊΠΈ ΠΊΠΎΡ€ΠΏΠΎΡ€Π°Ρ‚ΠΈΠ²Π½ΠΈΡ… Ρ–Π½Ρ„ΠΎΡ€ΠΌΠ°Ρ†Ρ–ΠΉΠ½ΠΈΡ… Ρ‚Π° освітніх систСм, які засновані Π½Π° ΠΏΠΎΠ±ΡƒΠ΄ΠΎΠ²Ρ– Π°Π΄Π°ΠΏΡ‚ΠΈΠ²Π½ΠΎΡ— систСми захисту Ρ–Π½Ρ„ΠΎΡ€ΠΌΠ°Ρ†Ρ–Ρ—. ISBN 978-617-7319-31-2 (on-line)ISBN 978-617-7319-32-9 (print) ------------------------------------------------------------------------------------------------------------------ Π―ΠΊ Ρ†ΠΈΡ‚ΡƒΠ²Π°Ρ‚ΠΈ: 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’Π•Π‘HNOLOGY Π‘Π•NTΠ•R, 188. doi: http://doi.org/10.15587/978-617-7319-31-2 ------------------------------------------------------------------------------------------------------------------ ІндСксація:                 &nbsp

    Electrical activity in rat retina in a streptozotocin-induced diabetes model

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    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

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    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

    No full text
    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 β€œSentences Repetition”, β€œMemory for Designs”, β€œInhibition”, β€œStatue”, and β€œDimensional 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

    Paper for the 2005 PAA Annual meeting

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    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

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    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·Ρ€ΠΎΠ±ΠΊΠ° Π³Ρ–Π±Ρ€ΠΈΠ΄Π½ΠΎΡ— ΠΊΡ€ΠΈΠΏΡ‚ΠΎ-ΠΊΠΎΠ΄ΠΎΠ²ΠΎΡ— конструкції Π½Ρ–Π΄Π΅Ρ€Ρ€Π°ΠΉΡ‚Π΅Ρ€Π° Π½Π° Π·Π±ΠΈΡ‚ΠΊΠΎΠ²ΠΈΡ… ΠΊΠΎΠ΄Π°Ρ…

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    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 cryptographyИспользованиС ΠΌΠΎΠ΄ΠΈΡ„ΠΈΡ†ΠΈΡ€ΠΎΠ²Π°Π½Π½ΠΎΠΉ ΠΊΡ€ΠΈΠΏΡ‚ΠΎ-ΠΊΠΎΠ΄ΠΎΠ²ΠΎΠΉ конструкции (МККК) НидСррайтСра с Π΄ΠΎΠΏΠΎΠ»Π½ΠΈΡ‚Π΅Π»ΡŒΠ½Ρ‹ΠΌΠΈ Π²Π΅ΠΊΡ‚ΠΎΡ€Π°ΠΌΠΈ ΠΈΠ½ΠΈΡ†ΠΈΠ°Π»ΠΈΠ·Π°Ρ†ΠΈΠΈ (с мноТСством нСдопустимых ΠΏΠΎΠ·ΠΈΡ†ΠΈΠΎΠ½Π½Ρ‹Ρ… Π²Π΅ΠΊΡ‚ΠΎΡ€ΠΎΠ² Π²Π΅ΠΊΡ‚ΠΎΡ€Π° ошибок ΠΈ мноТСством ΠΏΠΎΠ·ΠΈΡ†ΠΈΠΉ укорочСния Π²Π΅ΠΊΡ‚ΠΎΡ€Π° ошибки) Ρ‚Ρ€Π΅Π±ΡƒΠ΅Ρ‚ увСличСния быстродСйствия криптопрСобразования систСмы Π² Ρ†Π΅Π»ΠΎΠΌ. Для этого прСдлагаСтся ΠΈΡΠΏΠΎΠ»ΡŒΠ·ΠΎΠ²Π°Ρ‚ΡŒ ΡƒΡ‰Π΅Ρ€Π±Π½Ρ‹Π΅ ΠΊΠΎΠ΄Ρ‹. Π£Ρ‰Π΅Ρ€Π±Π½Ρ‹Π΅ ΠΊΠΎΠ΄Ρ‹ ΠΏΠΎΠ·Π²ΠΎΠ»ΡΡŽΡ‚ ΡƒΠ²Π΅Π»ΠΈΡ‡ΠΈΡ‚ΡŒ ΡΠΊΠΎΡ€ΠΎΡΡ‚ΡŒ ΠΊΠΎΠ΄ΠΎΠ²Ρ‹Ρ… ΠΏΡ€Π΅ΠΎΠ±Ρ€Π°Π·ΠΎΠ²Π°Π½ΠΈΠΉ Π·Π° счСт ΡƒΠΌΠ΅Π½ΡŒΡˆΠ΅Π½ΠΈΡ мощности поля ΠΏΡ€ΠΈ нанСсСнии ΡƒΡ‰Π΅Ρ€Π±Π° ΠΎΡ‚ΠΊΡ€Ρ‹Ρ‚Ρƒ тСксту ΠΈ ΡƒΠΌΠ΅Π½ΡŒΡˆΠΈΡ‚ΡŒ объСм ΠΏΠ΅Ρ€Π΅Π΄Π°Π²Π°Π΅ΠΌΡ‹Ρ… Π΄Π°Π½Π½Ρ‹Ρ… Π·Π° счСт нанСсСния ΡƒΡ‰Π΅Ρ€Π±Π° ΡˆΠΈΡ„Ρ€Ρ‚Π΅ΠΊΡΡ‚Ρƒ. Π’Π°ΠΊΠΎΠΉ ΠΏΠΎΠ΄Ρ…ΠΎΠ΄ позволяСт ΡΡ‚Ρ€ΠΎΠΈΡ‚ΡŒ Π³ΠΈΠ±Ρ€ΠΈΠ΄Π½Ρ‹Π΅ ΠΊΡ€ΠΈΠΏΡ‚ΠΎ-ΠΊΠΎΠ΄ΠΎΠ²Ρ‹Π΅ конструкции Π½Π° основС синтСза ΠΌΠΎΠ΄ΠΈΡ„ΠΈΡ†ΠΈΡ€ΠΎΠ²Π°Π½Π½Ρ‹Ρ… ΠΊΡ€ΠΈΠΏΡ‚ΠΎΠΊΠΎΠ΄ΠΎΠ²Ρ‹Ρ… конструкций НидСррайтСра Π½Π° ΠΌΠΎΠ΄ΠΈΡ„ΠΈΡ†ΠΈΡ€ΠΎΠ²Π°Π½Π½Ρ‹Ρ… (ΡƒΠΊΠΎΡ€ΠΎΡ‡Π΅Π½Π½Ρ‹Ρ… ΠΈΠ»ΠΈ ΡƒΠ΄Π»ΠΈΠ½Π΅Π½Π½Ρ‹Ρ…) ΠΊΠΎΠ΄Π°Ρ… Π½Π° эллиптичСских ΠΊΡ€ΠΈΠ²Ρ‹Ρ… с ΠΏΡ€ΠΎΡ†Π΅Π΄ΡƒΡ€Π°ΠΌΠΈ нанСсСния ΡƒΡ‰Π΅Ρ€Π±Π°. БущСствСнным ΠΎΡ‚Π»ΠΈΡ‡ΠΈΠ΅ΠΌ ΠΎΡ‚ классичСских Π³ΠΈΠ±Ρ€ΠΈΠ΄Π½Ρ‹Ρ… (комплСксных) криптосистСм являСтся использованиС нСсиммСтричной криптосистСмы для обСспСчСния бСзопасности Π΄Π°Π½Π½Ρ‹Ρ… с быстрыми ΠΏΡ€ΠΎΡ†Π΅Π΄ΡƒΡ€Π°ΠΌΠΈ криптопрСобразования (Ρ„ΠΎΡ€ΠΌΠΈΡ€ΠΎΠ²Π°Π½ΠΈΠ΅ ΠΈ раскодирования ΠΊΠΎΠ΄ΠΎΠ³Ρ€Π°ΠΌΠΌΡ‹). Π’ Ρ€Π°Π±ΠΎΡ‚Π΅ Ρ€Π°ΡΡΠΌΠ°Ρ‚Ρ€ΠΈΠ²Π°ΡŽΡ‚ΡΡ способы построСния ΡƒΡ‰Π΅Ρ€Π±Π½Ρ‹Ρ… ΠΊΠΎΠ΄ΠΎΠ² ΠΈ ΠΏΠΎΠ΄Ρ…ΠΎΠ΄Ρ‹ использования Π² Π³ΠΈΠ±Ρ€ΠΈΠ΄Π½ΠΎΠΉ ΠΊΡ€ΠΈΠΏΡ‚ΠΎ-ΠΊΠΎΠ΄ΠΎΠ²ΠΎΠΉ конструкции НидСррайтСра Π½Π° ΠΌΠΎΠ΄ΠΈΡ„ΠΈΡ†ΠΈΡ€ΠΎΠ²Π°Π½Π½Ρ‹Ρ… эллиптичСских ΠΊΠΎΠ΄Π°Ρ…. ΠŸΡ€Π΅Π΄Π»Π°Π³Π°ΡŽΡ‚ΡΡ практичСскиС Π°Π»Π³ΠΎΡ€ΠΈΡ‚ΠΌΡ‹ использования ΠΌΠ΅Ρ…Π°Π½ΠΈΠ·ΠΌΠ° нанСсСния ΡƒΡ‰Π΅Ρ€Π±Π° MV2 Π² ΠΊΡ€ΠΈΠΏΡ‚ΠΎ-ΠΊΠΎΠ΄ΠΎΠ²ΠΎΠΉ конструкции НидСррайтСра Π½Π° ΠΌΠΎΠ΄ΠΈΡ„ΠΈΡ†ΠΈΡ€ΠΎΠ²Π°Π½Π½Ρ‹Ρ… эллиптичСских ΠΊΠΎΠ΄Π°Ρ…, Ρ‡Ρ‚ΠΎ позволяСт Ρ€Π΅Π°Π»ΠΈΠ·ΠΎΠ²Π°Ρ‚ΡŒ Π³ΠΈΠ±Ρ€ΠΈΠ΄Π½ΡƒΡŽ ΠΊΡ€ΠΈΠΏΡ‚ΠΎ-ΠΊΠΎΠ΄ΠΎΠ²ΡƒΡŽ ΠΊΠΎΠ½ΡΡ‚Ρ€ΡƒΠΊΡ†ΠΈΡŽ. ΠŸΡ€ΠΈΠ²Π΅Π΄Π΅Π½Ρ‹ Ρ€Π΅Π·ΡƒΠ»ΡŒΡ‚Π°Ρ‚Ρ‹ ΡΡ€Π°Π²Π½ΠΈΡ‚Π΅Π»ΡŒΠ½ΠΎΠΉ ΠΎΡ†Π΅Π½ΠΊΠΈ энСргозатрат Π½Π° Ρ„ΠΎΡ€ΠΌΠΈΡ€ΠΎΠ²Π°Π½ΠΈΠ΅ ΠΈΠ½Ρ„ΠΎΡ€ΠΌΠ°Ρ†ΠΈΠΎΠ½Π½ΠΎΠΉ посылки ΠΏΡ€ΠΈ Ρ€Π°Π·Π»ΠΈΡ‡Π½Ρ‹Ρ… способах нанСсСния ΡƒΡ‰Π΅Ρ€Π±Π°, Ρ‡Ρ‚ΠΎ ΠΎΠΏΡ€Π΅Π΄Π΅Π»ΠΈΠ»ΠΎ Π²Ρ‹Π±ΠΎΡ€ способа нанСсСния ΡƒΡ‰Π΅Ρ€Π±Π° Π² практичСских Π°Π»Π³ΠΎΡ€ΠΈΡ‚ΠΌΠ°Ρ…. ΠŸΡ€ΠΎΠ²Π΅Π΄Π΅Π½Π½Ρ‹Π΅ исслСдования ΠΏΠΎΠ΄Ρ‚Π²Π΅Ρ€ΠΆΠ΄Π°ΡŽΡ‚ ΠΊΠΎΠ½ΠΊΡƒΡ€Π΅Π½Ρ‚ΡƒΡŽ ΡΡ„Ρ„Π΅ΠΊΡ‚ΠΈΠ²Π½ΠΎΡΡ‚ΡŒ ΠΏΡ€Π΅Π΄Π»ΠΎΠΆΠ΅Π½Π½ΠΎΠΉ криптосистСмы Π² Π˜Π½Ρ‚Π΅Ρ€Π½Π΅Ρ‚-тСхнологиях ΠΈ ΠΌΠΎΠ±ΠΈΠ»ΡŒΠ½Ρ‹Ρ… сСтях, обСспСчСния практичСской Ρ€Π΅Π°Π»ΠΈΠ·Π°Ρ†ΠΈΠΈ Π½Π° соврСмСнных ΠΏΠ»Π°Ρ‚Ρ„ΠΎΡ€ΠΌΠ°Ρ… ΠΈ Π½Π΅ΠΎΠ±Ρ…ΠΎΠ΄ΠΈΠΌΠΎΠΉ криптостойкости Π² условиях постквантовой криптографииВикористання ΠΌΠΎΠ΄ΠΈΡ„Ρ–ΠΊΠΎΠ²Π°Π½ΠΎΡ— ΠΊΡ€ΠΈΠΏΡ‚ΠΎ-ΠΊΠΎΠ΄ΠΎΠ²ΠΎΡ— конструкції (МККК) НідСррайтСра Π· Π΄ΠΎΠ΄Π°Ρ‚ΠΊΠΎΠ²ΠΈΠΌΠΈ Π²Π΅ΠΊΡ‚ΠΎΡ€Π°ΠΌΠΈ Ρ–Π½Ρ–Ρ†Ρ–Π°Π»Ρ–Π·Π°Ρ†Ρ–Ρ— (Π· мноТиною нСприпустимих ΠΏΠΎΠ·ΠΈΡ†Ρ–ΠΉΠ½ΠΈΡ… Π²Π΅ΠΊΡ‚ΠΎΡ€Ρ–Π² Π²Π΅ΠΊΡ‚ΠΎΡ€Π° ΠΏΠΎΠΌΠΈΠ»ΠΎΠΊ Ρ– мноТиною ΠΏΠΎΠ·ΠΈΡ†Ρ–ΠΉ укорочСння Π²Π΅ΠΊΡ‚ΠΎΡ€Π° ΠΏΠΎΠΌΠΈΠ»ΠΊΠΈ) Π²ΠΈΠΌΠ°Π³Π°Ρ” Π·Π±Ρ–Π»ΡŒΡˆΠ΅Π½Π½Ρ ΡˆΠ²ΠΈΠ΄ΠΊΠΎΠ΄Ρ–Ρ— ΠΊΡ€ΠΈΠΏΡ‚ΠΎΠΏΠ΅Ρ€Π΅Ρ‚Π²ΠΎΡ€Π΅Π½ΡŒ систСми Π²Ρ†Ρ–Π»ΠΎΠΌΡƒ. Для Ρ†ΡŒΠΎΠ³ΠΎ ΠΏΡ€ΠΎΠΏΠΎΠ½ΡƒΡ”Ρ‚ΡŒΡΡ використовувати Π·Π±ΠΈΡ‚ΠΊΠΎΠ²Ρ– ΠΊΠΎΠ΄ΠΈ. Π—Π±ΠΈΡ‚ΠΊΠΎΠ²Ρ– ΠΊΠΎΠ΄ΠΈ Π΄ΠΎΠ·Π²ΠΎΠ»ΡΡŽΡ‚ΡŒ Π·Π±Ρ–Π»ΡŒΡˆΠΈΡ‚ΠΈ ΡˆΠ²ΠΈΠ΄ΠΊΡ–ΡΡ‚ΡŒ ΠΊΠΎΠ΄ΠΎΠ²ΠΈΡ… ΠΏΠ΅Ρ€Π΅Ρ‚Π²ΠΎΡ€Π΅Π½ΡŒ Π·Π° Ρ€Π°Ρ…ΡƒΠ½ΠΎΠΊ змСншСння потуТності поля ΠΏΡ€ΠΈ нанСсСнні Π·Π±ΠΈΡ‚ΠΊΡƒ Π²Ρ–Π΄ΠΊΡ€ΠΈΡ‚ΠΎΠ³ΠΎ тСксту Ρ– Π·ΠΌΠ΅Π½ΡˆΠΈΡ‚ΠΈ обсяг ΠΏΠ΅Ρ€Π΅Π΄Π°Π½ΠΈΡ… Π΄Π°Π½ΠΈΡ… Π·Π° Ρ€Π°Ρ…ΡƒΠ½ΠΎΠΊ нанСсСння шкоди ΡˆΠΈΡ„Ρ€Ρ‚Π΅ΠΊΡΡ‚Ρƒ. Π’Π°ΠΊΡ–ΠΉ ΠΏΡ–Π΄Ρ…Ρ–Π΄ дозволяє Π±ΡƒΠ΄ΡƒΠ²Π°Ρ‚ΠΈ Π³Ρ–Π±Ρ€ΠΈΠ΄Π½Ρ– ΠΊΡ€ΠΈΠΏΡ‚ΠΎ-ΠΊΠΎΠ΄ΠΎΠ²Ρ– конструкції Π½Π° основі синтСзу ΠΌΠΎΠ΄ΠΈΡ„Ρ–ΠΊΠΎΠ²Π°Π½ΠΈΡ… ΠΊΡ€ΠΈΠΏΡ‚ΠΎΠΊΠΎΠ΄ΠΎΠ²ΠΈΡ… конструкцій НідСррайтСра Π½Π° ΠΌΠΎΠ΄ΠΈΡ„Ρ–ΠΊΠΎΠ²Π°Π½ΠΈΡ… (ΡƒΠΊΠΎΡ€ΠΎΡ‡Π΅Π½ΠΈΡ… Π°Π±ΠΎ ΠΏΠΎΠ΄ΠΎΠ²ΠΆΠ΅Π½ΠΈΡ…) ΠΊΠΎΠ΄Π°Ρ… Π½Π° Π΅Π»Ρ‹ΠΏΡ‚ΠΈΡ‡Π½ΠΈΡ… ΠΊΡ€ΠΈΠ²ΠΈΡ… Π· ΠΏΡ€ΠΎΡ†Π΅Π΄ΡƒΡ€Π°ΠΌΠΈ нанСсСння Π·Π±ΠΈΡ‚ΠΊΡƒ. Π‘ΡƒΡ‚Ρ‚Ρ”Π²ΠΎΡŽ Π²Ρ–Π΄ΠΌΡ–Π½Π½Ρ–ΡΡ‚ΡŽ Π²Ρ–Π΄ класичних Π³Ρ–Π±Ρ€ΠΈΠ΄Π½ΠΈΡ… (комплСксних) криптосистСм Ρ” використання нСсимСтричної криптосистСми для забСзпСчСння Π±Π΅Π·ΠΏΠ΅ΠΊΠΈ Π΄Π°Π½ΠΈΡ… Π· ΡˆΠ²Ρ–Π΄ΠΊΠΈΠΌΠΈ ΠΏΡ€ΠΎΡ†Π΅Π΄ΡƒΡ€Π°ΠΌΠΈ ΠΊΡ€ΠΈΠΏΡ‚ΠΎΠΏΠ΅Ρ€Π΅Ρ‚Π²ΠΎΡ€Π΅Π½ΡŒ (формування Ρ‚Π° розкодування ΠΊΠΎΠ΄ΠΎΠ³Ρ€Π°ΠΌΠΈ). Π’ Ρ€ΠΎΠ±ΠΎΡ‚Ρ– Ρ€ΠΎΠ·Π³Π»ΡΠ΄Π°ΡŽΡ‚ΡŒΡΡ способи ΠΏΠΎΠ±ΡƒΠ΄ΠΎΠ²ΠΈ Π·Π±ΠΈΡ‚ΠΊΠΎΠ²ΠΈΡ… ΠΊΠΎΠ΄Ρ–Π² Ρ– ΠΏΡ–Π΄Ρ…ΠΎΠ΄ΠΈ використання Π² Π³Ρ–Π±Ρ€ΠΈΠ΄Π½ΠΎΡ— ΠΊΡ€ΠΈΠΏΡ‚ΠΎ-ΠΊΠΎΠ΄ΠΎΠ²ΠΎΡ— конструкції НідСррайтСра Π½Π° ΠΌΠΎΠ΄ΠΈΡ„Ρ–ΠΊΠΎΠ²Π°Π½ΠΈΡ… Π΅Π»Ρ–ΠΏΡ‚ΠΈΡ‡Π½ΠΈΡ… ΠΊΠΎΠ΄Π°Ρ…. ΠŸΡ€ΠΎΠΏΠΎΠ½ΡƒΡŽΡ‚ΡŒΡΡ ΠΏΡ€Π°ΠΊΡ‚ΠΈΡ‡Π½Ρ– Π°Π»Π³ΠΎΡ€ΠΈΡ‚ΠΌΠΈ використання ΠΌΠ΅Ρ…Π°Π½Ρ–Π·ΠΌΡƒ нанСсСння Π·Π±ΠΈΡ‚ΠΊΡƒ MV2 Π² ΠΊΡ€ΠΈΠΏΡ‚ΠΎ-ΠΊΠΎΠ΄ΠΎΠ²ΠΎΡ— конструкції НідСррайтСра Π½Π° ΠΌΠΎΠ΄ΠΈΡ„Ρ–ΠΊΠΎΠ²Π°Π½ΠΈΡ… Π΅Π»Ρ–ΠΏΡ‚ΠΈΡ‡Π½ΠΈΡ… ΠΊΠΎΠ΄Π°Ρ…, Ρ‰ΠΎ дозволяє Ρ€Π΅Π°Π»Ρ–Π·ΡƒΠ²Π°Ρ‚ΠΈ Π³Ρ–Π±Ρ€ΠΈΠ΄Π½Ρƒ ΠΊΡ€ΠΈΠΏΡ‚ΠΎ-ΠΊΠΎΠ΄ΠΎΠ²Ρƒ ΠΊΠΎΠ½ΡΡ‚Ρ€ΡƒΠΊΡ†Ρ–ΡŽ. НавСдСні Ρ€Π΅Π·ΡƒΠ»ΡŒΡ‚Π°Ρ‚ΠΈ ΠΏΠΎΡ€Ρ–Π²Π½ΡΠ»ΡŒΠ½ΠΎΡ— ΠΎΡ†Ρ–Π½ΠΊΠΈ Π΅Π½Π΅Ρ€Π³ΠΎΠ²ΠΈΡ‚Ρ€Π°Ρ‚ Π½Π° формування Ρ–Π½Ρ„ΠΎΡ€ΠΌΠ°Ρ†Ρ–ΠΉΠ½ΠΎΡ— посилки ΠΏΡ€ΠΈ Ρ€Ρ–Π·Π½ΠΈΡ… способах нанСсСння Π·Π±ΠΈΡ‚ΠΊΡƒ, Ρ‰ΠΎ Π²ΠΈΠ·Π½Π°Ρ‡ΠΈΠ»ΠΎ Π²ΠΈΠ±Ρ–Ρ€ способу нанСсСння Π·Π±ΠΈΡ‚ΠΊΡƒ Π² ΠΏΡ€Π°ΠΊΡ‚ΠΈΡ‡Π½ΠΈΡ… Π°Π»Π³ΠΎΡ€ΠΈΡ‚ΠΌΠ°Ρ…. ΠŸΡ€ΠΎΠ²Π΅Π΄Π΅Π½Ρ– дослідТСння ΠΏΡ–Π΄Ρ‚Π²Π΅Ρ€ΠΆΡƒΡŽΡ‚ΡŒ ΠΊΠΎΠ½ΠΊΡƒΡ€Π΅Π½Ρ‚Ρƒ ΡΠΏΡ€ΠΎΠΌΠΎΠΆΠ½Ρ–ΡΡ‚ΡŒ Π·Π°ΠΏΡ€ΠΎΠΏΠΎΠ½ΠΎΠ²Π°Π½ΠΎΡ— криптосистСми Π² Π†Π½Ρ‚Π΅Ρ€Π½Π΅Ρ‚-тСхнологіях Ρ‚Π° ΠΌΠΎΠ±Ρ–Π»ΡŒΠ½ΠΈΡ… ΠΌΠ΅Ρ€Π΅ΠΆΠ°Ρ…, забСзпСчСння ΠΏΡ€Π°ΠΊΡ‚ΠΈΡ‡Π½ΠΎΡ— Ρ€Π΅Π°Π»Ρ–Π·Π°Ρ†Ρ–Ρ— Π½Π° сучасних ΠΏΠ»Π°Ρ‚Ρ„ΠΎΡ€ΠΌΠ°Ρ… Ρ‚Π° Π½Π΅ΠΎΠ±Ρ…Ρ–Π΄Π½ΠΎΡ— криптостійкості Π² ΡƒΠΌΠΎΠ²Π°Ρ… постквантової ΠΊΡ€ΠΈΠΏΡ‚ΠΎΠ³Ρ€Π°Ρ„Ρ–

    Π ΠΎΠ·Ρ€ΠΎΠ±ΠΊΠ° Π³Ρ–Π±Ρ€ΠΈΠ΄Π½ΠΎΡ— ΠΊΡ€ΠΈΠΏΡ‚ΠΎ-ΠΊΠΎΠ΄ΠΎΠ²ΠΎΡ— конструкції Π½Ρ–Π΄Π΅Ρ€Ρ€Π°ΠΉΡ‚Π΅Ρ€Π° Π½Π° Π·Π±ΠΈΡ‚ΠΊΠΎΠ²ΠΈΡ… ΠΊΠΎΠ΄Π°Ρ…

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    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 cryptographyИспользованиС ΠΌΠΎΠ΄ΠΈΡ„ΠΈΡ†ΠΈΡ€ΠΎΠ²Π°Π½Π½ΠΎΠΉ ΠΊΡ€ΠΈΠΏΡ‚ΠΎ-ΠΊΠΎΠ΄ΠΎΠ²ΠΎΠΉ конструкции (МККК) НидСррайтСра с Π΄ΠΎΠΏΠΎΠ»Π½ΠΈΡ‚Π΅Π»ΡŒΠ½Ρ‹ΠΌΠΈ Π²Π΅ΠΊΡ‚ΠΎΡ€Π°ΠΌΠΈ ΠΈΠ½ΠΈΡ†ΠΈΠ°Π»ΠΈΠ·Π°Ρ†ΠΈΠΈ (с мноТСством нСдопустимых ΠΏΠΎΠ·ΠΈΡ†ΠΈΠΎΠ½Π½Ρ‹Ρ… Π²Π΅ΠΊΡ‚ΠΎΡ€ΠΎΠ² Π²Π΅ΠΊΡ‚ΠΎΡ€Π° ошибок ΠΈ мноТСством ΠΏΠΎΠ·ΠΈΡ†ΠΈΠΉ укорочСния Π²Π΅ΠΊΡ‚ΠΎΡ€Π° ошибки) Ρ‚Ρ€Π΅Π±ΡƒΠ΅Ρ‚ увСличСния быстродСйствия криптопрСобразования систСмы Π² Ρ†Π΅Π»ΠΎΠΌ. Для этого прСдлагаСтся ΠΈΡΠΏΠΎΠ»ΡŒΠ·ΠΎΠ²Π°Ρ‚ΡŒ ΡƒΡ‰Π΅Ρ€Π±Π½Ρ‹Π΅ ΠΊΠΎΠ΄Ρ‹. Π£Ρ‰Π΅Ρ€Π±Π½Ρ‹Π΅ ΠΊΠΎΠ΄Ρ‹ ΠΏΠΎΠ·Π²ΠΎΠ»ΡΡŽΡ‚ ΡƒΠ²Π΅Π»ΠΈΡ‡ΠΈΡ‚ΡŒ ΡΠΊΠΎΡ€ΠΎΡΡ‚ΡŒ ΠΊΠΎΠ΄ΠΎΠ²Ρ‹Ρ… ΠΏΡ€Π΅ΠΎΠ±Ρ€Π°Π·ΠΎΠ²Π°Π½ΠΈΠΉ Π·Π° счСт ΡƒΠΌΠ΅Π½ΡŒΡˆΠ΅Π½ΠΈΡ мощности поля ΠΏΡ€ΠΈ нанСсСнии ΡƒΡ‰Π΅Ρ€Π±Π° ΠΎΡ‚ΠΊΡ€Ρ‹Ρ‚Ρƒ тСксту ΠΈ ΡƒΠΌΠ΅Π½ΡŒΡˆΠΈΡ‚ΡŒ объСм ΠΏΠ΅Ρ€Π΅Π΄Π°Π²Π°Π΅ΠΌΡ‹Ρ… Π΄Π°Π½Π½Ρ‹Ρ… Π·Π° счСт нанСсСния ΡƒΡ‰Π΅Ρ€Π±Π° ΡˆΠΈΡ„Ρ€Ρ‚Π΅ΠΊΡΡ‚Ρƒ. Π’Π°ΠΊΠΎΠΉ ΠΏΠΎΠ΄Ρ…ΠΎΠ΄ позволяСт ΡΡ‚Ρ€ΠΎΠΈΡ‚ΡŒ Π³ΠΈΠ±Ρ€ΠΈΠ΄Π½Ρ‹Π΅ ΠΊΡ€ΠΈΠΏΡ‚ΠΎ-ΠΊΠΎΠ΄ΠΎΠ²Ρ‹Π΅ конструкции Π½Π° основС синтСза ΠΌΠΎΠ΄ΠΈΡ„ΠΈΡ†ΠΈΡ€ΠΎΠ²Π°Π½Π½Ρ‹Ρ… ΠΊΡ€ΠΈΠΏΡ‚ΠΎΠΊΠΎΠ΄ΠΎΠ²Ρ‹Ρ… конструкций НидСррайтСра Π½Π° ΠΌΠΎΠ΄ΠΈΡ„ΠΈΡ†ΠΈΡ€ΠΎΠ²Π°Π½Π½Ρ‹Ρ… (ΡƒΠΊΠΎΡ€ΠΎΡ‡Π΅Π½Π½Ρ‹Ρ… ΠΈΠ»ΠΈ ΡƒΠ΄Π»ΠΈΠ½Π΅Π½Π½Ρ‹Ρ…) ΠΊΠΎΠ΄Π°Ρ… Π½Π° эллиптичСских ΠΊΡ€ΠΈΠ²Ρ‹Ρ… с ΠΏΡ€ΠΎΡ†Π΅Π΄ΡƒΡ€Π°ΠΌΠΈ нанСсСния ΡƒΡ‰Π΅Ρ€Π±Π°. БущСствСнным ΠΎΡ‚Π»ΠΈΡ‡ΠΈΠ΅ΠΌ ΠΎΡ‚ классичСских Π³ΠΈΠ±Ρ€ΠΈΠ΄Π½Ρ‹Ρ… (комплСксных) криптосистСм являСтся использованиС нСсиммСтричной криптосистСмы для обСспСчСния бСзопасности Π΄Π°Π½Π½Ρ‹Ρ… с быстрыми ΠΏΡ€ΠΎΡ†Π΅Π΄ΡƒΡ€Π°ΠΌΠΈ криптопрСобразования (Ρ„ΠΎΡ€ΠΌΠΈΡ€ΠΎΠ²Π°Π½ΠΈΠ΅ ΠΈ раскодирования ΠΊΠΎΠ΄ΠΎΠ³Ρ€Π°ΠΌΠΌΡ‹). Π’ Ρ€Π°Π±ΠΎΡ‚Π΅ Ρ€Π°ΡΡΠΌΠ°Ρ‚Ρ€ΠΈΠ²Π°ΡŽΡ‚ΡΡ способы построСния ΡƒΡ‰Π΅Ρ€Π±Π½Ρ‹Ρ… ΠΊΠΎΠ΄ΠΎΠ² ΠΈ ΠΏΠΎΠ΄Ρ…ΠΎΠ΄Ρ‹ использования Π² Π³ΠΈΠ±Ρ€ΠΈΠ΄Π½ΠΎΠΉ ΠΊΡ€ΠΈΠΏΡ‚ΠΎ-ΠΊΠΎΠ΄ΠΎΠ²ΠΎΠΉ конструкции НидСррайтСра Π½Π° ΠΌΠΎΠ΄ΠΈΡ„ΠΈΡ†ΠΈΡ€ΠΎΠ²Π°Π½Π½Ρ‹Ρ… эллиптичСских ΠΊΠΎΠ΄Π°Ρ…. ΠŸΡ€Π΅Π΄Π»Π°Π³Π°ΡŽΡ‚ΡΡ практичСскиС Π°Π»Π³ΠΎΡ€ΠΈΡ‚ΠΌΡ‹ использования ΠΌΠ΅Ρ…Π°Π½ΠΈΠ·ΠΌΠ° нанСсСния ΡƒΡ‰Π΅Ρ€Π±Π° MV2 Π² ΠΊΡ€ΠΈΠΏΡ‚ΠΎ-ΠΊΠΎΠ΄ΠΎΠ²ΠΎΠΉ конструкции НидСррайтСра Π½Π° ΠΌΠΎΠ΄ΠΈΡ„ΠΈΡ†ΠΈΡ€ΠΎΠ²Π°Π½Π½Ρ‹Ρ… эллиптичСских ΠΊΠΎΠ΄Π°Ρ…, Ρ‡Ρ‚ΠΎ позволяСт Ρ€Π΅Π°Π»ΠΈΠ·ΠΎΠ²Π°Ρ‚ΡŒ Π³ΠΈΠ±Ρ€ΠΈΠ΄Π½ΡƒΡŽ ΠΊΡ€ΠΈΠΏΡ‚ΠΎ-ΠΊΠΎΠ΄ΠΎΠ²ΡƒΡŽ ΠΊΠΎΠ½ΡΡ‚Ρ€ΡƒΠΊΡ†ΠΈΡŽ. ΠŸΡ€ΠΈΠ²Π΅Π΄Π΅Π½Ρ‹ Ρ€Π΅Π·ΡƒΠ»ΡŒΡ‚Π°Ρ‚Ρ‹ ΡΡ€Π°Π²Π½ΠΈΡ‚Π΅Π»ΡŒΠ½ΠΎΠΉ ΠΎΡ†Π΅Π½ΠΊΠΈ энСргозатрат Π½Π° Ρ„ΠΎΡ€ΠΌΠΈΡ€ΠΎΠ²Π°Π½ΠΈΠ΅ ΠΈΠ½Ρ„ΠΎΡ€ΠΌΠ°Ρ†ΠΈΠΎΠ½Π½ΠΎΠΉ посылки ΠΏΡ€ΠΈ Ρ€Π°Π·Π»ΠΈΡ‡Π½Ρ‹Ρ… способах нанСсСния ΡƒΡ‰Π΅Ρ€Π±Π°, Ρ‡Ρ‚ΠΎ ΠΎΠΏΡ€Π΅Π΄Π΅Π»ΠΈΠ»ΠΎ Π²Ρ‹Π±ΠΎΡ€ способа нанСсСния ΡƒΡ‰Π΅Ρ€Π±Π° Π² практичСских Π°Π»Π³ΠΎΡ€ΠΈΡ‚ΠΌΠ°Ρ…. ΠŸΡ€ΠΎΠ²Π΅Π΄Π΅Π½Π½Ρ‹Π΅ исслСдования ΠΏΠΎΠ΄Ρ‚Π²Π΅Ρ€ΠΆΠ΄Π°ΡŽΡ‚ ΠΊΠΎΠ½ΠΊΡƒΡ€Π΅Π½Ρ‚ΡƒΡŽ ΡΡ„Ρ„Π΅ΠΊΡ‚ΠΈΠ²Π½ΠΎΡΡ‚ΡŒ ΠΏΡ€Π΅Π΄Π»ΠΎΠΆΠ΅Π½Π½ΠΎΠΉ криптосистСмы Π² Π˜Π½Ρ‚Π΅Ρ€Π½Π΅Ρ‚-тСхнологиях ΠΈ ΠΌΠΎΠ±ΠΈΠ»ΡŒΠ½Ρ‹Ρ… сСтях, обСспСчСния практичСской Ρ€Π΅Π°Π»ΠΈΠ·Π°Ρ†ΠΈΠΈ Π½Π° соврСмСнных ΠΏΠ»Π°Ρ‚Ρ„ΠΎΡ€ΠΌΠ°Ρ… ΠΈ Π½Π΅ΠΎΠ±Ρ…ΠΎΠ΄ΠΈΠΌΠΎΠΉ криптостойкости Π² условиях постквантовой криптографииВикористання ΠΌΠΎΠ΄ΠΈΡ„Ρ–ΠΊΠΎΠ²Π°Π½ΠΎΡ— ΠΊΡ€ΠΈΠΏΡ‚ΠΎ-ΠΊΠΎΠ΄ΠΎΠ²ΠΎΡ— конструкції (МККК) НідСррайтСра Π· Π΄ΠΎΠ΄Π°Ρ‚ΠΊΠΎΠ²ΠΈΠΌΠΈ Π²Π΅ΠΊΡ‚ΠΎΡ€Π°ΠΌΠΈ Ρ–Π½Ρ–Ρ†Ρ–Π°Π»Ρ–Π·Π°Ρ†Ρ–Ρ— (Π· мноТиною нСприпустимих ΠΏΠΎΠ·ΠΈΡ†Ρ–ΠΉΠ½ΠΈΡ… Π²Π΅ΠΊΡ‚ΠΎΡ€Ρ–Π² Π²Π΅ΠΊΡ‚ΠΎΡ€Π° ΠΏΠΎΠΌΠΈΠ»ΠΎΠΊ Ρ– мноТиною ΠΏΠΎΠ·ΠΈΡ†Ρ–ΠΉ укорочСння Π²Π΅ΠΊΡ‚ΠΎΡ€Π° ΠΏΠΎΠΌΠΈΠ»ΠΊΠΈ) Π²ΠΈΠΌΠ°Π³Π°Ρ” Π·Π±Ρ–Π»ΡŒΡˆΠ΅Π½Π½Ρ ΡˆΠ²ΠΈΠ΄ΠΊΠΎΠ΄Ρ–Ρ— ΠΊΡ€ΠΈΠΏΡ‚ΠΎΠΏΠ΅Ρ€Π΅Ρ‚Π²ΠΎΡ€Π΅Π½ΡŒ систСми Π²Ρ†Ρ–Π»ΠΎΠΌΡƒ. Для Ρ†ΡŒΠΎΠ³ΠΎ ΠΏΡ€ΠΎΠΏΠΎΠ½ΡƒΡ”Ρ‚ΡŒΡΡ використовувати Π·Π±ΠΈΡ‚ΠΊΠΎΠ²Ρ– ΠΊΠΎΠ΄ΠΈ. Π—Π±ΠΈΡ‚ΠΊΠΎΠ²Ρ– ΠΊΠΎΠ΄ΠΈ Π΄ΠΎΠ·Π²ΠΎΠ»ΡΡŽΡ‚ΡŒ Π·Π±Ρ–Π»ΡŒΡˆΠΈΡ‚ΠΈ ΡˆΠ²ΠΈΠ΄ΠΊΡ–ΡΡ‚ΡŒ ΠΊΠΎΠ΄ΠΎΠ²ΠΈΡ… ΠΏΠ΅Ρ€Π΅Ρ‚Π²ΠΎΡ€Π΅Π½ΡŒ Π·Π° Ρ€Π°Ρ…ΡƒΠ½ΠΎΠΊ змСншСння потуТності поля ΠΏΡ€ΠΈ нанСсСнні Π·Π±ΠΈΡ‚ΠΊΡƒ Π²Ρ–Π΄ΠΊΡ€ΠΈΡ‚ΠΎΠ³ΠΎ тСксту Ρ– Π·ΠΌΠ΅Π½ΡˆΠΈΡ‚ΠΈ обсяг ΠΏΠ΅Ρ€Π΅Π΄Π°Π½ΠΈΡ… Π΄Π°Π½ΠΈΡ… Π·Π° Ρ€Π°Ρ…ΡƒΠ½ΠΎΠΊ нанСсСння шкоди ΡˆΠΈΡ„Ρ€Ρ‚Π΅ΠΊΡΡ‚Ρƒ. Π’Π°ΠΊΡ–ΠΉ ΠΏΡ–Π΄Ρ…Ρ–Π΄ дозволяє Π±ΡƒΠ΄ΡƒΠ²Π°Ρ‚ΠΈ Π³Ρ–Π±Ρ€ΠΈΠ΄Π½Ρ– ΠΊΡ€ΠΈΠΏΡ‚ΠΎ-ΠΊΠΎΠ΄ΠΎΠ²Ρ– конструкції Π½Π° основі синтСзу ΠΌΠΎΠ΄ΠΈΡ„Ρ–ΠΊΠΎΠ²Π°Π½ΠΈΡ… ΠΊΡ€ΠΈΠΏΡ‚ΠΎΠΊΠΎΠ΄ΠΎΠ²ΠΈΡ… конструкцій НідСррайтСра Π½Π° ΠΌΠΎΠ΄ΠΈΡ„Ρ–ΠΊΠΎΠ²Π°Π½ΠΈΡ… (ΡƒΠΊΠΎΡ€ΠΎΡ‡Π΅Π½ΠΈΡ… Π°Π±ΠΎ ΠΏΠΎΠ΄ΠΎΠ²ΠΆΠ΅Π½ΠΈΡ…) ΠΊΠΎΠ΄Π°Ρ… Π½Π° Π΅Π»Ρ‹ΠΏΡ‚ΠΈΡ‡Π½ΠΈΡ… ΠΊΡ€ΠΈΠ²ΠΈΡ… Π· ΠΏΡ€ΠΎΡ†Π΅Π΄ΡƒΡ€Π°ΠΌΠΈ нанСсСння Π·Π±ΠΈΡ‚ΠΊΡƒ. Π‘ΡƒΡ‚Ρ‚Ρ”Π²ΠΎΡŽ Π²Ρ–Π΄ΠΌΡ–Π½Π½Ρ–ΡΡ‚ΡŽ Π²Ρ–Π΄ класичних Π³Ρ–Π±Ρ€ΠΈΠ΄Π½ΠΈΡ… (комплСксних) криптосистСм Ρ” використання нСсимСтричної криптосистСми для забСзпСчСння Π±Π΅Π·ΠΏΠ΅ΠΊΠΈ Π΄Π°Π½ΠΈΡ… Π· ΡˆΠ²Ρ–Π΄ΠΊΠΈΠΌΠΈ ΠΏΡ€ΠΎΡ†Π΅Π΄ΡƒΡ€Π°ΠΌΠΈ ΠΊΡ€ΠΈΠΏΡ‚ΠΎΠΏΠ΅Ρ€Π΅Ρ‚Π²ΠΎΡ€Π΅Π½ΡŒ (формування Ρ‚Π° розкодування ΠΊΠΎΠ΄ΠΎΠ³Ρ€Π°ΠΌΠΈ). Π’ Ρ€ΠΎΠ±ΠΎΡ‚Ρ– Ρ€ΠΎΠ·Π³Π»ΡΠ΄Π°ΡŽΡ‚ΡŒΡΡ способи ΠΏΠΎΠ±ΡƒΠ΄ΠΎΠ²ΠΈ Π·Π±ΠΈΡ‚ΠΊΠΎΠ²ΠΈΡ… ΠΊΠΎΠ΄Ρ–Π² Ρ– ΠΏΡ–Π΄Ρ…ΠΎΠ΄ΠΈ використання Π² Π³Ρ–Π±Ρ€ΠΈΠ΄Π½ΠΎΡ— ΠΊΡ€ΠΈΠΏΡ‚ΠΎ-ΠΊΠΎΠ΄ΠΎΠ²ΠΎΡ— конструкції НідСррайтСра Π½Π° ΠΌΠΎΠ΄ΠΈΡ„Ρ–ΠΊΠΎΠ²Π°Π½ΠΈΡ… Π΅Π»Ρ–ΠΏΡ‚ΠΈΡ‡Π½ΠΈΡ… ΠΊΠΎΠ΄Π°Ρ…. ΠŸΡ€ΠΎΠΏΠΎΠ½ΡƒΡŽΡ‚ΡŒΡΡ ΠΏΡ€Π°ΠΊΡ‚ΠΈΡ‡Π½Ρ– Π°Π»Π³ΠΎΡ€ΠΈΡ‚ΠΌΠΈ використання ΠΌΠ΅Ρ…Π°Π½Ρ–Π·ΠΌΡƒ нанСсСння Π·Π±ΠΈΡ‚ΠΊΡƒ MV2 Π² ΠΊΡ€ΠΈΠΏΡ‚ΠΎ-ΠΊΠΎΠ΄ΠΎΠ²ΠΎΡ— конструкції НідСррайтСра Π½Π° ΠΌΠΎΠ΄ΠΈΡ„Ρ–ΠΊΠΎΠ²Π°Π½ΠΈΡ… Π΅Π»Ρ–ΠΏΡ‚ΠΈΡ‡Π½ΠΈΡ… ΠΊΠΎΠ΄Π°Ρ…, Ρ‰ΠΎ дозволяє Ρ€Π΅Π°Π»Ρ–Π·ΡƒΠ²Π°Ρ‚ΠΈ Π³Ρ–Π±Ρ€ΠΈΠ΄Π½Ρƒ ΠΊΡ€ΠΈΠΏΡ‚ΠΎ-ΠΊΠΎΠ΄ΠΎΠ²Ρƒ ΠΊΠΎΠ½ΡΡ‚Ρ€ΡƒΠΊΡ†Ρ–ΡŽ. НавСдСні Ρ€Π΅Π·ΡƒΠ»ΡŒΡ‚Π°Ρ‚ΠΈ ΠΏΠΎΡ€Ρ–Π²Π½ΡΠ»ΡŒΠ½ΠΎΡ— ΠΎΡ†Ρ–Π½ΠΊΠΈ Π΅Π½Π΅Ρ€Π³ΠΎΠ²ΠΈΡ‚Ρ€Π°Ρ‚ Π½Π° формування Ρ–Π½Ρ„ΠΎΡ€ΠΌΠ°Ρ†Ρ–ΠΉΠ½ΠΎΡ— посилки ΠΏΡ€ΠΈ Ρ€Ρ–Π·Π½ΠΈΡ… способах нанСсСння Π·Π±ΠΈΡ‚ΠΊΡƒ, Ρ‰ΠΎ Π²ΠΈΠ·Π½Π°Ρ‡ΠΈΠ»ΠΎ Π²ΠΈΠ±Ρ–Ρ€ способу нанСсСння Π·Π±ΠΈΡ‚ΠΊΡƒ Π² ΠΏΡ€Π°ΠΊΡ‚ΠΈΡ‡Π½ΠΈΡ… Π°Π»Π³ΠΎΡ€ΠΈΡ‚ΠΌΠ°Ρ…. ΠŸΡ€ΠΎΠ²Π΅Π΄Π΅Π½Ρ– дослідТСння ΠΏΡ–Π΄Ρ‚Π²Π΅Ρ€ΠΆΡƒΡŽΡ‚ΡŒ ΠΊΠΎΠ½ΠΊΡƒΡ€Π΅Π½Ρ‚Ρƒ ΡΠΏΡ€ΠΎΠΌΠΎΠΆΠ½Ρ–ΡΡ‚ΡŒ Π·Π°ΠΏΡ€ΠΎΠΏΠΎΠ½ΠΎΠ²Π°Π½ΠΎΡ— криптосистСми Π² Π†Π½Ρ‚Π΅Ρ€Π½Π΅Ρ‚-тСхнологіях Ρ‚Π° ΠΌΠΎΠ±Ρ–Π»ΡŒΠ½ΠΈΡ… ΠΌΠ΅Ρ€Π΅ΠΆΠ°Ρ…, забСзпСчСння ΠΏΡ€Π°ΠΊΡ‚ΠΈΡ‡Π½ΠΎΡ— Ρ€Π΅Π°Π»Ρ–Π·Π°Ρ†Ρ–Ρ— Π½Π° сучасних ΠΏΠ»Π°Ρ‚Ρ„ΠΎΡ€ΠΌΠ°Ρ… Ρ‚Π° Π½Π΅ΠΎΠ±Ρ…Ρ–Π΄Π½ΠΎΡ— криптостійкості Π² ΡƒΠΌΠΎΠ²Π°Ρ… постквантової ΠΊΡ€ΠΈΠΏΡ‚ΠΎΠ³Ρ€Π°Ρ„Ρ–

    Development of A Modified UMAC Algorithm Based on CryptoΒ­code Constructions

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    The development of computer technology has determined the vector for the expansion of services based on the Internet and β€œG” 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
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