A method includes initializing a client state on a client device be executing a private batched sum retrieval instruction to compute c sums O of data blocks from an untrusted storage device. Each computed sum O stored on memory hardware of the client device and including a sum of a corresponding subset S of exactly k data blocks. The method also includes a query instruction to retrieve a query block Bq stored on the untrusted storage device by iterating through each of the c sums O of data blocks to identify one of the c sums O that does not include the query block Bq, instructing a service to pseudorandomly partition the untrusted storage device into partitions and sum the data blocks in each partition to determine a corresponding encrypted data block sum.