Staircase-PIR: Universally Robust Private Information Retrieval
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We consider the problem of designing private information retrieval (PIR) schemes on data of m files replicated on n servers that can possibly collude. We focus on devising robust PIR schemes that can tolerate stragglers, i.e., slow or unresponsive servers. In many settings, the number of stragglers is not known a priori or may change with time. We define universally robust PIR as schemes that achieve asymptotic, in m, PIR capacity, i.e., asymptotically optimal download rate, simultaneously for any number of stragglers up to a given threshold. We introduce Staircase-PIR schemes and prove that they are universally robust. Towards that end, we establish an equivalence between robust PIR and communication efficient secret sharing.
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