The distributed multi-user point function

Khalesi, Ali; Akhbari, Bahareh
Submitted to ArXiV, 17 January 2025

In this paper, we study the problem of information-theoretic distributed multi-user point function, involving a trusted master node, N ∈ N server nodes, and K ∈ N users, where each user has access to the contents of a subset of the storages of server nodes. Each user is associated with an independent point function fXk,Zk : {1, 2, . . . , T} → GF(q mRk ), T, mRk ∈ N. Using these point functions, the trusted master node encodes and places functional shares G1, G2, . . . , GN ∈ GF(q M), M ∈ N in the storage nodes such that each user can correctly recover its point function result from the response transmitted to itself and gains no information about the point functions of any other user, even with knowledge of all responses transmitted from its connected servers. For the first time, we propose a multi-user scheme that satisfies the correctness and information-theoretic privacy constraints, ensuring recovery for all point functions. We also characterize the inner and outer bounds on the capacity— the maximum achievable rate defined as the size of the range of each point function mRk relative to the storage size of the servers M—of the distributed multi-user point function scheme by presenting a novel converse argument. 


Type:
Conference
Date:
2025-01-17
Department:
Communication systems
Eurecom Ref:
8038
Copyright:
© EURECOM. Personal use of this material is permitted. The definitive version of this paper was published in Submitted to ArXiV, 17 January 2025 and is available at :
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PERMALINK : https://www.eurecom.fr/publication/8038