A method includes executing an instruction to execute a query for a data block, the data block associated with a corresponding memory level of a logarithmic number of memory levels (li) of memory, each memory level (li) including physical memory (RAMi) residing on memory hardware of a distributed system. The method also includes retrieving a value associated with the data block from an oblivious hash table using a corresponding key, and extracting un-queried key value pairs from the oblivious hash table associated with un-queried data blocks after executing a threshold number of queries for data blocks. The method also includes a multi-array shuffle routine on the extracted key value pairs from the oblivious hash table to generate an output array containing the un-queried key value pairs.