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Register a new userAlphabet Size Reduction for Secure Network Coding: A Graph Theoretic Approach
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Added by
Xuan Guang
Publication date
2016
fields
Informatics Engineering
and research's language is
English
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We consider a communication network where there exist wiretappers who can access a subset of channels, called a wiretap set, which is chosen from a given collection of wiretap sets. The collection of wiretap sets can be arbitrary. Secure network coding is applied to prevent the source information from being leaked to the wiretappers. In secure network coding, the required alphabet size is an open problem not only of theoretical interest but also of practical importance, because it is closely related to the implementation of such coding schemes in terms of computational complexity and storage requirement. In this paper, we develop a systematic graph-theoretic approach for improving Cai and Yeungs lower bound on the required alphabet size for the existence of secure network codes. The new lower bound thus obtained, which depends only on the network topology and the collection of wiretap sets, can be significantly smaller than Cai and Yeungs lower bound. A polynomial-time algorithm is devised for efficient computation of the new lower bound.
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Modern medical wireless systems, such as wireless body area networks (WBANs), are applications of wireless networks that can be used as a tool of data transmission between patients and doctors. Accuracy of data transmission is an important requirement for such systems. In this paper, we will propose a WBAN which is robust against erasures and describe its properties using graph theoretic techniques.
A code equivalence between index coding and network coding was established, which shows that any index-coding instance can be mapped to a network-coding instance, for which any index code can be translated to a network code with the same decoding-error performance, and vice versa. Also, any network-coding instance can be mapped to an index-coding instance with a similar code translation. In this paper, we extend the equivalence to secure index coding and secure network coding, where eavesdroppers are present in the networks, and any code construction needs to guarantee security constraints in addition to decoding-error performance.
A fundamental problem in quantum computation and quantum information is finding the minimum quantum dimension needed for a task. For tasks involving state preparation and measurements, this problem can be addressed using only the input-output correlations. This has been applied to Bell, prepare-and-measure, and Kochen-Specker contextuality scenarios. Here, we introduce a novel approach to quantum dimension witnessing for scenarios with one preparation and several measurements, which uses the graphs of mutual exclusivity between sets of measurement events. We present the concepts and tools needed for graph-theoretic quantum dimension witnessing and illustrate their use by identifying novel quantum dimension witnesses, including a family that can certify arbitrarily high quantum dimensions with few events.
Topological Coding consists of two different kinds of mathematics: topological structure and mathematical relation. The colorings and labelings of graph theory are main techniques in topological coding applied in asymmetric encryption system. Topsnut-gpws (also, colored graphs) have the following advantages: (1) Run fast in communication networks because they are saved in computer by popular matrices rather than pictures. (2) Produce easily text-based (number-based) strings for encrypt files. (3) Diversity of asymmetric ciphers, one public-key corresponds to more private-keys, or more public-keys correspond more private-keys. (4) Irreversibility, Topsnut-gpws can generate quickly text-based (number-based) strings with bytes as long as desired, but these strings can not reconstruct the original Topsnut-gpws. (5) Computational security, since there are many non-polynomial (NP-complete, NP-hard) algorithms in creating Topsnut-gpws. (6) Provable security, since there are many mathematical conjectures (open problems) in graph labelings and graph colorings. We are committed to create more kinds of new Topsnut-gpws to approximate practical applications and antiquantum computation, and try to use algebraic method and Topsnut-gpws to establish graphic group, graphic lattice, graph homomorphism etc.
We study the information leakage to a guessing adversary in zero-error source coding. The source coding problem is defined by a confusion graph capturing the distinguishability between source symbols. The information leakage is measured by the ratio of the adversarys successful guessing probability after and before eavesdropping the codeword, maximized over all possible source distributions. Such measurement under the basic adversarial model where the adversary makes a single guess and allows no distortion between its estimator and the true sequence is known as the maximum min-entropy leakage or the maximal leakage in the literature. We develop a single-letter characterization of the optimal normalized leakage under the basic adversarial model, together with an optimum-achieving scalar stochastic mapping scheme. An interesting observation is that the optimal normalized leakage is equal to the optimal compression rate with fixed-length source codes, both of which can be simultaneously achieved by some deterministic coding schemes. We then extend the leakage measurement to generalized adversarial models where the adversary makes multiple guesses and allows certain level of distortion, for which we derive single-letter lower and upper bounds.
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