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Register a new userCoded Caching in the Presence of a Wire and a Cache Tapping Adversary of Type II
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Added by
Mohamed Nafea
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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This paper introduces the notion of cache-tapping into the information theoretic models of coded caching. The wiretap channel II in the presence of multiple receivers equipped with fixed-size cache memories, and an adversary which selects symbols to tap into from cache placement and/or delivery is introduced. The legitimate terminals know neither whether placement, delivery, or both are tapped, nor the positions in which they are tapped. Only the size of the overall tapped set is known. For two receivers and two files, the strong secrecy capacity -- the maximum achievable file rate while keeping the overall library strongly secure -- is identified. Lower and upper bounds on the strong secrecy file rate are derived when the library has more than two files. Achievability relies on a code design which combines wiretap coding, security embedding codes, one-time pad keys, and coded caching. A genie-aided upper bound, in which the transmitter is provided with user demands before placement, establishes the converse for the two-files case. For more than two files, the upper bound is constructed by three successive channel transformations. Our results establish provable security guarantees against a powerful adversary which optimizes its tapping over both phases of communication in a cache-aided system.
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This paper considers a cache-aided device-to-device (D2D) system where the users are equipped with cache memories of different size. During low traffic hours, a server places content in the users cache memories, knowing that the files requested by the users during peak traffic hours will have to be delivered by D2D transmissions only. The worst-case D2D delivery load is minimized by jointly designing the uncoded cache placement and linear coded D2D delivery. Next, a novel lower bound on the D2D delivery load with uncoded placement is proposed and used in explicitly characterizing the minimum D2D delivery load (MD2DDL) with uncoded placement for several cases of interest. In particular, having characterized the MD2DDL for equal cache sizes, it is shown that the same delivery load can be achieved in the network with users of unequal cache sizes, provided that the smallest cache size is greater than a certain threshold. The MD2DDL is also characterized in the small cache size regime, the large cache size regime, and the three-user case. Comparisons of the server-based delivery load with the D2D delivery load are provided. Finally, connections and mathematical parallels between cache-aided D2D systems and coded distributed computing (CDC) systems are discussed.
If Alice must communicate with Bob over a channel shared with the adversarial Eve, then Bob must be able to validate the authenticity of the message. In particular we consider the model where Alice and Eve share a discrete memoryless multiple access channel with Bob, thus allowing simultaneous transmissions from Alice and Eve. By traditional random coding arguments, we demonstrate an inner bound on the rate at which Alice may transmit, while still granting Bob the ability to authenticate. Furthermore this is accomplished in spite of Alice and Bob lacking a pre-shared key, as well as allowing Eve prior knowledge of both the codebook Alice and Bob share and the messages Alice transmits.
We consider the coded caching problem with an additional privacy constraint that a user should not get any information about the demands of the other users. We first show that a demand-private scheme for $N$ files and $K$ users can be obtained from a non-private scheme that serves only a subset of the demands for the $N$ files and $NK$ users problem. We further use this fact to construct a demand-private scheme for $N$ files and $K$ users from a particular known non-private scheme for $N$ files and $NK-K+1$ users. It is then demonstrated that, the memory-rate pair $(M,min {N,K}(1-M/N))$, which is achievable for non-private schemes with uncoded transmissions, is also achievable under demand privacy. We further propose a scheme that improves on these ideas by removing some redundant transmissions. The memory-rate trade-off achieved using our schemes is shown to be within a multiplicative factor of 3 from the optimal when $K < N$ and of 8 when $Nleq K$. Finally, we give the exact memory-rate trade-off for demand-private coded caching problems with $Ngeq K=2$.
We address a centralized caching problem with unequal cache sizes. We consider a system with a server of files connected through a shared error-free link to a group of cache-enabled users where one subgroup has a larger cache size than the other. We propose an explicit caching scheme for the considered system aimed at minimizing the load of worst-case demands over the shared link. As suggested by numerical evaluations, our scheme improves upon the best existing explicit scheme by having a lower worst-case load; also, our scheme performs within a multiplicative factor of 1.11 from the scheme that can be obtained by solving an optimisation problem in which the number of parameters grows exponentially with the number of users.
The coded caching problem with secrecy constraint i.e., the users should not be able to gain any information about the content of the files that they did not demand, is known as the secretive coded caching problem. This was proposed by Ravindrakumar et al. in the paper titled ``Private Coded Caching that appeared in emph{ IEEE Transactions on Information Forensics and Security}, 2018 and is characterised by subpacketization levels growing exponentially with the number of users. In the context of coded caching without secrecy, coded caching schemes at subexponential subpacketization levels are feasible by representing the caching system in the form of a Placement Delivery Array (PDA) and designing placement and delivery policies from it. Motivated by this, we propose a secretive coded caching scheme with low subpacketization using PDA, for users with dedicated caches in the centralized setting. When our scheme is applied to a special class of PDA known as MN PDA, the scheme proposed by Ravindrakumar et al. is recovered.
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