Storage efficient and unconditionally secure private information retrieval
A method of storing and retrieving a set of original data (E 1 , . . . , En) in and from a plurality of remote servers (SP 1 , . . . , SPI+1), comprises a coding step which consists in creating a set of coded data (S 1 , . . . , SN) from the set of original data (E 1 , . . . , En), a storing step which consists in storing the set of coded data (S 1 , . . . , SN) into the plurality of remote servers (SP 1 , . . . , SPI+1). Each server (SP 1 , . . . , SPI+1) of the said plurality of servers stores only a respective part of the set of coded data (S 1 , . . . , SN) and the method comprises a step which consists in generating a table (T 1 , T 2 ) which indicates which respective part of the set of coded data (S 1 , . . . , SN) is stored in which server of the said plurality of remote servers (SP 1 , . . . , SPI+1).
1. A method of storing a set of original data elements in a plurality of remote servers such that any data element of the set of original data can be retrieved without communicating the identity of the retrieved data element to the plurality of remote servers, the method comprising:
storing a set of original data elements by:
using a locally decodable code with a locality value that is one fewer than the number of remote servers, creating a set of coded data symbols from the set of original data,
dividing the set of coded data symbols into distinct groups of coded data symbols, each group defining a hyperplane in an ambient space, such that no one group of coded data symbols contains a coded data symbol that is contained by any other group of coded data symbols,
generating a first table associating each symbol of the set of coded data symbols with a respective group of coded data symbols,
storing each group of coded data symbols in to a respective server of the plurality of remote servers, such that each coded data symbol is stored on only one of the plurality of remote servers, and
generating a second table associating each group of coded data symbols with the respective server,
such that a selected original data element of the set of original data elements can be retrieved by:
generating, using the locally decodable code, a query for each respective one of the plurality of remote servers based on the first table, the second table, and a string,
each query including a request for at least one coded data symbol, the included coded data symbols constituting a direction which is transverse to each hyperplane defined by each group of coded data symbols such that the selected original data element can be computed based on the plurality of results returned from each respective one of the plurality of remote servers.
2. The method according to claim 1 , further comprising generating the query for each respective one of the plurality of remote servers based on the first table, the second table, and a string and receiving the at least one coded data symbol from each respective one of the plurality of remote servers.
3. The method according to claim 2 , further comprising decoding the selected original data element from the one coded data symbol from each respective one of the plurality of remote servers.
4. The method according to claim 3 , wherein the decoding is carried out using the locally decodable code.