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We study private information retrieval (PIR) on coded data with possiblycolluding servers. Devising PIR schemes with optimal download rate in the caseof collusion and coded data is still open in general. We provide a liftingoperation that can transform what we call one-shot PIR schemes for two messagesinto schemes for any number of messages. We apply this lifting operation onexisting PIR schemes and describe two immediate implications. First, we obtainnovel PIR schemes with improved download rate in the case of MDS coded data andserver collusion. Second, we provide a simplified description of existingoptimal PIR schemes on replicated data as lifted secret sharing based PIR.

Lifting Private Information Retrieval from Two to any Number of Messages