A method (500) includes initializing a client state (250) on a client device (120) be executing a private batched sum retrieval instruction (200) to compute c sums O of data blocks (102) from an untrusted storage device (150). Each computed sum O stored on memory hardware (122) 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 (300) 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 (302).