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تسجيل مستخدم جديدA Code Equivalence between Secure Network and Index Coding
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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.
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We extend the equivalence between network coding and index coding by Effros, El Rouayheb, and Langberg to the secure communication setting in the presence of an eavesdropper. Specifically, we show that the most gener
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We study the fundamental problem of index coding under an additional privacy constraint that requires each receiver to learn nothing more about the collection of messages beyond its demanded messages from the server and what is available to it as sid
e information. To enable such private communication, we allow the use of a collection of independent secret keys, each of which is shared amongst a subset of users and is known to the server. The goal is to study properties of the key access structures which make the problem feasible and then design encoding and decoding schemes efficient in the size of the server transmission as well as the sizes of the secret keys. We call this the private index coding problem. We begin by characterizing the key access structures that make private index coding feasible. We also give conditions to check if a given linear scheme is a valid private index code. For up to three users, we characterize the rate region of feasible server transmission and key rates, and show that all feasible rates can be achieved using scalar linear coding and time sharing; we also show that scalar linear codes are sub-optimal for four receivers. The outer bounds used in the case of three users are extended to arbitrary number of users and seen as a generalized version of the well-known polymatroidal bounds for the standard non-private index coding. We also show that the presence of common randomness and private randomness does not change the rate region. Furthermore, we study the case where no keys are shared among the users and provide some necessary and sufficient conditions for feasibility in this setting under a weaker notion of privacy. If the server has the ability to multicast to any subset of users, we demonstrate how this flexibility can be used to provide privacy and characterize the minimum number of server multicasts required.
Information-theoretic security is considered in the paradigm of network coding in the presence of wiretappers, who can access one arbitrary edge subset up to a certain size, also referred to as the security level. Secure network coding is applied to
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