6 research outputs found

    Nonparametric Anomaly Detection and Secure Communication

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    Two major security challenges in information systems are detection of anomalous data patterns that reflect malicious intrusions into data storage systems and protection of data from malicious eavesdropping during data transmissions. The first problem typically involves design of statistical tests to identify data variations, and the second problem generally involves design of communication schemes to transmit data securely in the presence of malicious eavesdroppers. The main theme of this thesis is to exploit information theoretic and statistical tools to address the above two security issues in order to provide information theoretically provable security, i.e., anomaly detection with vanishing probability of error and guaranteed secure communication with vanishing leakage rate at eavesdroppers. First, the anomaly detection problem is investigated, in which typical and anomalous patterns (i.e., distributions that generate data) are unknown \emph{a priori}. Two types of problems are investigated. The first problem considers detection of the existence of anomalous geometric structures over networks, and the second problem considers the detection of a set of anomalous data streams out of a large number of data streams. In both problems, anomalous data are assumed to be generated by a distribution qq, which is different from a distribution pp generating typical samples. For both problems, kernel-based tests are proposed, which are based on maximum mean discrepancy (MMD) that measures the distance between mean embeddings of distributions into a reproducing kernel Hilbert space. These tests are nonparametric without exploiting the information about pp and qq and are universally applicable to arbitrary pp and qq. Furthermore, these tests are shown to be statistically consistent under certain conditions on the parameters of the problems. These conditions are further shown to be necessary or nearly necessary, which implies that the MMD-based tests are order level optimal or nearly order level optimal. Numerical results are provided to demonstrate the performance of the proposed tests. The secure communication problem is then investigated, for which the focus is on degraded broadcast channels. In such channels, one transmitter sends messages to multiple receivers, the channel quality of which can be ordered. Two specific models are studied. In the first model, layered decoding and layered secrecy are required, i.e., each receiver decodes one more message than the receiver with one level worse channel quality, and this message should be kept secure from all receivers with worse channel qualities. In the second model, secrecy only outside a bounded range is required, i.e., each message is required to be kept secure from the receiver with two-level worse channel quality. Communication schemes for both models are designed and the corresponding achievable rate regions (i.e., inner bounds on the capacity region) are characterized. Furthermore, outer bounds on the capacity region are developed, which match the inner bounds, and hence the secrecy capacity regions are established for both models

    Π’Π΅ΠΎΡ€Π΅Ρ‚ΠΈΠΊΠΎ-ΠΈΠ½Ρ„ΠΎΡ€ΠΌΠ°Ρ†ΠΈΠΎΠ½Π½ΠΎΠ΅ прСдставлСниС Π²ΠΈΡ€Ρ‚ΡƒΠ°Π»ΠΈΠ·Π°Ρ†ΠΈΠΈ сСтСвого ΠΊΠ°Π½Π°Π»Π° ΠΏΠ΅Ρ€Π΅Ρ…Π²Π°Ρ‚Π°

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    The most difficult task of secure telecommunication systems using symmetric encryption, due to the need for preliminary and resource-intensive organization of secret channels for delivering keys to network correspondents, is key management. An alternative is the generating keys methods through open communication channels. In information theory, it is shown that these methods are implemented under the condition that the channel information rate of correspondents exceeds the rate of the intruder interception channel. The search for methods that provide the informational advantage of correspondents is being updated. The goal is to determine the information-theoretical conditions for the formation of a virtual network and an interception channel, for which the best ratio of information speeds for correspondents is provided compared to the ratio of the original network and interception channel. The paper proposes an information transfer model that includes a connectivity model and an information transfer method for asymptotic lengths of code words. The model includes three correspondents and is characterized by the introduction of an ideal broadcast channel in addition to an errored broadcast channel. The model introduces a source of "noisy" information, which is transmitted over the channel with errors, so the transmission of code words using the known method of random coding is carried out over the channel without errors. For asymptotic lengths of code words, all actions of correspondents in processing and transmitting information in the model are reduced to the proposed method of transmitting information. The use of the method by correspondents within the framework of the transmission model makes it possible to simultaneously form for them a new virtual broadcast channel with information rate as in the original channel with errors, and for the intruder a new virtual broadcast interception channel with a rate lower than the information rate of the initial interception channel. The information-theoretic conditions for deterioration of the interception channel are proved in the statement. The practical significance of the results obtained lies in the possibility of using the latter to assess the information efficiency of open network key formation in the proposed information transfer model, as well as in the development of well-known scientific achievements of open key agreement. The proposed transmission model can be useful for researching key management systems and protecting information transmitted over open channels. Further research is related to the information-theoretic assessment of the network key throughput, which is the potential information-theoretic speed of network key formation.БлоТнСйшСй Π·Π°Π΄Π°Ρ‡Π΅ΠΉ Π·Π°Ρ‰ΠΈΡ‰Π΅Π½Π½Ρ‹Ρ… Ρ‚Π΅Π»Π΅ΠΊΠΎΠΌΠΌΡƒΠ½ΠΈΠΊΠ°Ρ†ΠΈΠΎΠ½Π½Ρ‹Ρ… систСм, ΠΈΡΠΏΠΎΠ»ΡŒΠ·ΡƒΡŽΡ‰ΠΈΡ… симмСтричноС ΡˆΠΈΡ„Ρ€ΠΎΠ²Π°Π½ΠΈΠ΅, Π² связи с Π½Π΅ΠΎΠ±Ρ…ΠΎΠ΄ΠΈΠΌΠΎΡΡ‚ΡŒΡŽ ΠΏΡ€Π΅Π΄Π²Π°Ρ€ΠΈΡ‚Π΅Π»ΡŒΠ½ΠΎΠΉ ΠΈ рСсурсоСмкой ΠΎΡ€Π³Π°Π½ΠΈΠ·Π°Ρ†ΠΈΠΈ сСкрСтных ΠΊΠ°Π½Π°Π»ΠΎΠ² доставки ΠΊΠ»ΡŽΡ‡Π΅ΠΉ сСтСвым коррСспондСнтам, являСтся ΡƒΠΏΡ€Π°Π²Π»Π΅Π½ΠΈΠ΅ ΠΊΠ»ΡŽΡ‡Π°ΠΌΠΈ. ΠΠ»ΡŒΡ‚Π΅Ρ€Π½Π°Ρ‚ΠΈΠ²ΠΎΠΉ Π²Ρ‹ΡΡ‚ΡƒΠΏΠ°ΡŽΡ‚ ΠΌΠ΅Ρ‚ΠΎΠ΄Ρ‹ формирования ΠΊΠ»ΡŽΡ‡Π΅ΠΉ ΠΏΠΎ ΠΎΡ‚ΠΊΡ€Ρ‹Ρ‚Ρ‹ΠΌ ΠΊΠ°Π½Π°Π»Π°ΠΌ связи. Π’ Ρ‚Π΅ΠΎΡ€ΠΈΠΈ ΠΈΠ½Ρ„ΠΎΡ€ΠΌΠ°Ρ†ΠΈΠΈ ΠΏΠΎΠΊΠ°Π·Π°Π½ΠΎ, Ρ‡Ρ‚ΠΎ эти ΠΌΠ΅Ρ‚ΠΎΠ΄Ρ‹ Ρ€Π΅Π°Π»ΠΈΠ·ΡƒΡŽΡ‚ΡΡ ΠΏΡ€ΠΈ условии ΠΏΡ€Π΅Π²Ρ‹ΡˆΠ΅Π½ΠΈΡ ΠΈΠ½Ρ„ΠΎΡ€ΠΌΠ°Ρ†ΠΈΠΎΠ½Π½ΠΎΠΉ скорости ΠΊΠ°Π½Π°Π»Π° коррСспондСнтов Π½Π°Π΄ ΡΠΊΠΎΡ€ΠΎΡΡ‚ΡŒΡŽ ΠΊΠ°Π½Π°Π»Π° ΠΏΠ΅Ρ€Π΅Ρ…Π²Π°Ρ‚Π° Π½Π°Ρ€ΡƒΡˆΠΈΡ‚Π΅Π»Ρ. АктуализируСтся поиск ΠΌΠ΅Ρ‚ΠΎΠ΄ΠΎΠ², ΠΎΠ±Π΅ΡΠΏΠ΅Ρ‡ΠΈΠ²Π°ΡŽΡ‰ΠΈΡ… ΠΏΠΎΠ»ΡƒΡ‡Π΅Π½ΠΈΠ΅ ΠΈΠ½Ρ„ΠΎΡ€ΠΌΠ°Ρ†ΠΈΠΎΠ½Π½ΠΎΠ³ΠΎ прСимущСства коррСспондСнтов. ЦСль Π·Π°ΠΊΠ»ΡŽΡ‡Π°Π΅Ρ‚ΡΡ Π² ΠΎΠΏΡ€Π΅Π΄Π΅Π»Π΅Π½ΠΈΠΈ Ρ‚Π΅ΠΎΡ€Π΅Ρ‚ΠΈΠΊΠΎ-ΠΈΠ½Ρ„ΠΎΡ€ΠΌΠ°Ρ†ΠΈΠΎΠ½Π½Ρ‹Ρ… условий формирования Π²ΠΈΡ€Ρ‚ΡƒΠ°Π»ΡŒΠ½Ρ‹Ρ… сСти ΠΈ ΠΊΠ°Π½Π°Π»Π° ΠΏΠ΅Ρ€Π΅Ρ…Π²Π°Ρ‚Π°, для ΠΊΠΎΡ‚ΠΎΡ€Ρ‹Ρ… обСспСчиваСтся Π»ΡƒΡ‡ΡˆΠ΅Π΅ Ρƒ коррСспондСнтов ΠΎΡ‚Π½ΠΎΡˆΠ΅Π½ΠΈΠ΅ ΠΈΠ½Ρ„ΠΎΡ€ΠΌΠ°Ρ†ΠΈΠΎΠ½Π½Ρ‹Ρ… скоростСй ΠΏΠΎ ΡΡ€Π°Π²Π½Π΅Π½ΠΈΡŽ с ΠΎΡ‚Π½ΠΎΡˆΠ΅Π½ΠΈΠ΅ΠΌ исходных сСти ΠΈ ΠΊΠ°Π½Π°Π»Π° ΠΏΠ΅Ρ€Π΅Ρ…Π²Π°Ρ‚Π°. Π’ Ρ€Π°Π±ΠΎΡ‚Π΅ прСдлагаСтся модСль ΠΏΠ΅Ρ€Π΅Π΄Π°Ρ‡ΠΈ ΠΈΠ½Ρ„ΠΎΡ€ΠΌΠ°Ρ†ΠΈΠΈ, Π²ΠΊΠ»ΡŽΡ‡Π°ΡŽΡ‰Π°Ρ модСль связности ΠΈ ΠΌΠ΅Ρ‚ΠΎΠ΄ ΠΏΠ΅Ρ€Π΅Π΄Π°Ρ‡ΠΈ ΠΈΠ½Ρ„ΠΎΡ€ΠΌΠ°Ρ†ΠΈΠΈ для асимптотичСских Π΄Π»ΠΈΠ½ ΠΊΠΎΠ΄ΠΎΠ²Ρ‹Ρ… слов. МодСль Π²ΠΊΠ»ΡŽΡ‡Π°Π΅Ρ‚ Ρ‚Ρ€Π΅Ρ… коррСспондСнтов ΠΈ отличаСтся Π²Π²Π΅Π΄Π΅Π½ΠΈΠ΅ΠΌ идСального ΡˆΠΈΡ€ΠΎΠΊΠΎΠ²Π΅Ρ‰Π°Ρ‚Π΅Π»ΡŒΠ½ΠΎΠ³ΠΎ ΠΊΠ°Π½Π°Π»Π° Π² Π΄ΠΎΠΏΠΎΠ»Π½Π΅Π½ΠΈΠ΅ ΠΊ ΡˆΠΈΡ€ΠΎΠΊΠΎΠ²Π΅Ρ‰Π°Ρ‚Π΅Π»ΡŒΠ½ΠΎΠΌΡƒ ΠΊΠ°Π½Π°Π»Ρƒ с ошибками. Π’ ΠΌΠΎΠ΄Π΅Π»ΠΈ Π²Π²Π΅Π΄Π΅Π½ источник Β«Π·Π°ΡˆΡƒΠΌΠ»ΡΡŽΡ‰Π΅ΠΉΒ» ΠΈΠ½Ρ„ΠΎΡ€ΠΌΠ°Ρ†ΠΈΠΈ, которая пСрСдаСтся ΠΏΠΎ ΠΊΠ°Π½Π°Π»Ρƒ с ошибками, поэтому ΠΏΠ΅Ρ€Π΅Π΄Π°Ρ‡Π° ΠΊΠΎΠ΄ΠΎΠ²Ρ‹Ρ… слов с использованиСм извСстного ΠΌΠ΅Ρ‚ΠΎΠ΄Π° случайного кодирования производится ΠΏΠΎ ΠΊΠ°Π½Π°Π»Ρƒ Π±Π΅Π· ошибок. Для асимптотичСских Π΄Π»ΠΈΠ½ ΠΊΠΎΠ΄ΠΎΠ²Ρ‹Ρ… слов всС дСйствия коррСспондСнтов ΠΏΠΎ ΠΎΠ±Ρ€Π°Π±ΠΎΡ‚ΠΊΠ΅ ΠΈ ΠΏΠ΅Ρ€Π΅Π΄Π°Ρ‡Π΅ ΠΈΠ½Ρ„ΠΎΡ€ΠΌΠ°Ρ†ΠΈΠΈ Π² ΠΌΠΎΠ΄Π΅Π»ΠΈ свСдСны Π² ΠΏΡ€Π΅Π΄Π»Π°Π³Π°Π΅ΠΌΡ‹ΠΉ ΠΌΠ΅Ρ‚ΠΎΠ΄ ΠΏΠ΅Ρ€Π΅Π΄Π°Ρ‡ΠΈ ΠΈΠ½Ρ„ΠΎΡ€ΠΌΠ°Ρ†ΠΈΠΈ. ИспользованиС ΠΌΠ΅Ρ‚ΠΎΠ΄Π° коррСспондСнтами Π² Ρ€Π°ΠΌΠΊΠ°Ρ… ΠΌΠΎΠ΄Π΅Π»ΠΈ ΠΏΠ΅Ρ€Π΅Π΄Π°Ρ‡ΠΈ позволяСт ΠΎΠ΄Π½ΠΎΠ²Ρ€Π΅ΠΌΠ΅Π½Π½ΠΎ ΡΡ„ΠΎΡ€ΠΌΠΈΡ€ΠΎΠ²Π°Ρ‚ΡŒ для Π½ΠΈΡ… Π½ΠΎΠ²Ρ‹ΠΉ Π²ΠΈΡ€Ρ‚ΡƒΠ°Π»ΡŒΠ½Ρ‹ΠΉ ΡˆΠΈΡ€ΠΎΠΊΠΎΠ²Π΅Ρ‰Π°Ρ‚Π΅Π»ΡŒΠ½Ρ‹ΠΉ ΠΊΠ°Π½Π°Π» с ΠΈΠ½Ρ„ΠΎΡ€ΠΌΠ°Ρ†ΠΈΠΎΠ½Π½ΠΎΠΉ ΡΠΊΠΎΡ€ΠΎΡΡ‚ΡŒΡŽ, ΠΊΠ°ΠΊ ΠΈ Π² ΠΏΠ΅Ρ€Π²ΠΎΠ½Π°Ρ‡Π°Π»ΡŒΠ½ΠΎΠΌ ΠΊΠ°Π½Π°Π»Π΅ с ошибками, Π° для Π½Π°Ρ€ΡƒΡˆΠΈΡ‚Π΅Π»Ρ Π½ΠΎΠ²Ρ‹ΠΉ Π²ΠΈΡ€Ρ‚ΡƒΠ°Π»ΡŒΠ½Ρ‹ΠΉ ΡˆΠΈΡ€ΠΎΠΊΠΎΠ²Π΅Ρ‰Π°Ρ‚Π΅Π»ΡŒΠ½Ρ‹ΠΉ ΠΊΠ°Π½Π°Π» ΠΏΠ΅Ρ€Π΅Ρ…Π²Π°Ρ‚Π° со ΡΠΊΠΎΡ€ΠΎΡΡ‚ΡŒΡŽ мСньшСй ΠΈΠ½Ρ„ΠΎΡ€ΠΌΠ°Ρ†ΠΈΠΎΠ½Π½ΠΎΠΉ скорости ΠΏΠ΅Ρ€Π²ΠΎΠ½Π°Ρ‡Π°Π»ΡŒΠ½ΠΎΠ³ΠΎ ΠΊΠ°Π½Π°Π»Π° ΠΏΠ΅Ρ€Π΅Ρ…Π²Π°Ρ‚Π°. Π’Π΅ΠΎΡ€Π΅Ρ‚ΠΈΠΊΠΎ-ΠΈΠ½Ρ„ΠΎΡ€ΠΌΠ°Ρ†ΠΈΠΎΠ½Π½Ρ‹Π΅ условия ΡƒΡ…ΡƒΠ΄ΡˆΠ΅Π½ΠΈΡ ΠΊΠ°Π½Π°Π»Π° ΠΏΠ΅Ρ€Π΅Ρ…Π²Π°Ρ‚Π° доказываСтся Π² ΡƒΡ‚Π²Π΅Ρ€ΠΆΠ΄Π΅Π½ΠΈΠΈ. ΠŸΡ€Π°ΠΊΡ‚ΠΈΡ‡Π΅ΡΠΊΠ°Ρ Π·Π½Π°Ρ‡ΠΈΠΌΠΎΡΡ‚ΡŒ ΠΏΠΎΠ»ΡƒΡ‡Π΅Π½Π½Ρ‹Ρ… Ρ€Π΅Π·ΡƒΠ»ΡŒΡ‚Π°Ρ‚ΠΎΠ² Π·Π°ΠΊΠ»ΡŽΡ‡Π°Π΅Ρ‚ΡΡ Π² возмоТности использования послСдних для ΠΎΡ†Π΅Π½ΠΊΠΈ ΠΈΠ½Ρ„ΠΎΡ€ΠΌΠ°Ρ†ΠΈΠΎΠ½Π½ΠΎΠΉ эффСктивности ΠΎΡ‚ΠΊΡ€Ρ‹Ρ‚ΠΎΠ³ΠΎ сСтСвого формирования ΠΊΠ»ΡŽΡ‡Π΅ΠΉ Π² ΠΏΡ€Π΅Π΄Π»ΠΎΠΆΠ΅Π½Π½ΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ ΠΏΠ΅Ρ€Π΅Π΄Π°Ρ‡ΠΈ ΠΈΠ½Ρ„ΠΎΡ€ΠΌΠ°Ρ†ΠΈΠΈ, Π° Ρ‚Π°ΠΊΠΆΠ΅ Π² Ρ€Π°Π·Π²ΠΈΡ‚ΠΈΠΈ извСстных Π½Π°ΡƒΡ‡Π½Ρ‹Ρ… достиТСний ΠΎΡ‚ΠΊΡ€Ρ‹Ρ‚ΠΎΠ³ΠΎ ΠΊΠ»ΡŽΡ‡Π΅Π²ΠΎΠ³ΠΎ согласования. ΠŸΡ€Π΅Π΄Π»Π°Π³Π°Π΅ΠΌΠ°Ρ модСль ΠΏΠ΅Ρ€Π΅Π΄Π°Ρ‡ΠΈ ΠΌΠΎΠΆΠ΅Ρ‚ Π±Ρ‹Ρ‚ΡŒ ΠΏΠΎΠ»Π΅Π·Π½ΠΎΠΉ для провСдСния исслСдований систСм управлСния ΠΊΠ»ΡŽΡ‡Π°ΠΌΠΈ ΠΈ Π·Π°Ρ‰ΠΈΡ‚Ρ‹ ΠΈΠ½Ρ„ΠΎΡ€ΠΌΠ°Ρ†ΠΈΠΈ, ΠΏΠ΅Ρ€Π΅Π΄Π°Π²Π°Π΅ΠΌΠΎΠΉ ΠΏΠΎ ΠΎΡ‚ΠΊΡ€Ρ‹Ρ‚Ρ‹ΠΌ ΠΊΠ°Π½Π°Π»Π°ΠΌ. Π”Π°Π»ΡŒΠ½Π΅ΠΉΡˆΠΈΠ΅ исслСдования связаны с Ρ‚Π΅ΠΎΡ€Π΅Ρ‚ΠΈΠΊΠΎ-ΠΈΠ½Ρ„ΠΎΡ€ΠΌΠ°Ρ†ΠΈΠΎΠ½Π½ΠΎΠΉ ΠΎΡ†Π΅Π½ΠΊΠΎΠΉ сСтСвой ΠΊΠ»ΡŽΡ‡Π΅Π²ΠΎΠΉ пропускной способности, ΠΏΡ€Π΅Π΄ΡΡ‚Π°Π²Π»ΡΡŽΡ‰Π΅ΠΉ собой ΠΏΠΎΡ‚Π΅Π½Ρ†ΠΈΠ°Π»ΡŒΠ½ΡƒΡŽ Ρ‚Π΅ΠΎΡ€Π΅Ρ‚ΠΈΠΊΠΎ-ΠΈΠ½Ρ„ΠΎΡ€ΠΌΠ°Ρ†ΠΈΠΎΠ½Π½ΡƒΡŽ ΡΠΊΠΎΡ€ΠΎΡΡ‚ΡŒ формирования сСтСвого ΠΊΠ»ΡŽΡ‡Π°

    Degraded Broadcast Channel with Secrecy Outside a Bounded Range

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    The K-receiver degraded broadcast channel with secrecy outside a bounded range is studied, in which a transmitter sends K messages to K receivers, and the channel quality gradually degrades from receiver K to receiver 1. Each receiver k is required to decode message W 1 , ..., W k , for 1 ≀ k ≀ K, and to be kept ignorant of W k+2 , .. ., W K , fork = 1, ..., K -2. Thus, each message W k is kept secure from receivers with at least two-level worse channel quality, i.e., receivers 1, ..., k -2 . The secrecy capacity region is fully characterized. The achievable scheme designates one superposition layer to each message with binning employed for each layer. Joint embedded coding and binning are employed to protect all upper-layer messages from lower-layer receivers. Furthermore, the scheme allows adjacent layers to share rates so that part of the rate of each message can be shared with its immediate upper-layer message to enlarge the rate region. More importantly, an induction approach is developed to perform Fourier-Motzkin elimination of 2 K variables from the order of K 2 bounds to obtain a close-form achievable rate region. An outer bound is developed that matches the achievable rate region, whose proof involves recursive construction of the rate bounds and exploits the intuition gained from the achievable scheme

    Degraded Broadcast Channel With Secrecy Outside a Bounded Range

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