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- W4386075129 abstract "The problem of X-secure T-private linear computation with graph based replicated storage (GXSTPLC) is to enable the user to retrieve a linear combination of messages privately from a set of N distributed servers where every message is only allowed to replicate among a subset of servers subject to an X-security constraint, i.e., any groups of up to X colluding servers must reveal nothing about the messages. Besides, any groups of up to T servers must reveal no information about the coefficients of the linear combination retrieved by the user. In this paper, inspired by a Vandermonde decomposition of Cauchy matrices, we propose an achievability scheme for GXSTPLC that achieves the rate of (ρ <inf xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>min</inf> −X −T)/N if every message is replicated at least ρ <inf xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>min</inf> times and ρ <inf xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>min</inf> > X + T, which coincides with a lower bound of the rate of X-secure T-private information retrieval with graph based replicated storage (GXSTPIR) by Jia and Jafar. Moreover, the asymptotic capacity of GXSTPLC is partially settled, including the setting where the storage forms a symmetric pattern." @default.
- W4386075129 created "2023-08-23" @default.
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- W4386075129 date "2023-06-25" @default.
- W4386075129 modified "2023-09-26" @default.
- W4386075129 title "X-Secure T-Private Linear Computation With Graph Based Replicated Storage" @default.
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- W4386075129 doi "https://doi.org/10.1109/isit54713.2023.10206837" @default.
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