Quantifying the Cost of Privately Storing Data in Distributed Storage Systems

Consider a user who wishes to store file in multiple servers such that at least $t$ are needed reconstruct the file, and notation="LaTeX">$z$ colluding cannot learn any information about file. Unlike traditional secret-sharing models, where perfectly secure channels assumed be available no cost between each server, we assume can only send data via public channel, server share an individual secret key with length notation="LaTeX">$n$ . For given , determine maximal of store, thus quantify necessary certain length, terms keys needs servers. Additionally, for this (i) optimal amount local randomness user, (ii) communication from servers, (iii) storage requirement