The Capacity of Private Information Retrieval From Uncoded Storage Constrained Databases

Multi-User Blind Symmetric Private Information Retrieval from Coded Servers

“…The scheme will happen over S = 2 rounds, and in round s ∈ [2] each user can decode the P = λ = 3 symbols in the s-th column of the desired file W (θ1,θ2) .…”

“…During round s ∈ [2], each user m ∈ [2] independently and uniformly generates F m λT m = 6F m random variables…”

“…By employing the received queries {Q m,s n } m∈ [2] from the M = 2 users and the intermediate polynomials φ s 1 (α), φ s 2 (α), φ s 3 (α) as coefficients, server n computes a linear combination of the stored encoded symbols Y n , and then responds the sum of the linear combination and the randomness Z s n = ψ s (α n ) stored by server n for the users:…”

“…Since the appearance of [29], a series of works is interested in exploring the fundamental limits of PIR under various variants of the classical model. This includes PIR with Tprivate queries and replicated storage [31], PIR with MDS coded storage [3], [36], RIR with optimal file length [32], [40], [55], [58], [57], PIR with T -private queries and MDS coded storage [16], [33], PIR with secure storage [18], [19], [20], [48], PIR with unresponsive and/or Byzantine servers [4], [19], [37], PIR with arbitrary collusion patterns [38], [50], multiround PIR [34], multi-message PIR [5], storage constrained PIR [2], [39], [60], PIR with side information [8], [22], [47], symmetric PIR [30], [42], [44], [45], as well as extending PIR to private computation [25], [26], [35], private search [9], federated submodel learning [21], etc.…”

“…We assume that each file is divided into K blocks, and each block is divided into λ stripes. 2 WLOG, we represent the file W (f1,...,fM ) by a random matrix of dimension λ × K, with each entry choosing independently and uniformly over the finite field F q for some prime power q, i.e., for any H(W (f1,...,fM ) ) = F L, where the entropy function H(•) is calculated with logarithm q.…”