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A user wants to retrieve a file from a database without revealing theidentity of the file retrieved at the database, which is known as the problemof private information retrieval (PIR). If it is further required that the userobtains no information about the database other than the desired file, theconcept of symmetric private information retrieval (SPIR) is introduced toguarantee privacy for both parties. In this paper, the problem of SPIR isstudied for a database stored among $N$ nodes in a distributed way, by using an$(N,M)$-MDS storage code. The information-theoretic capacity of SPIR, definedas the maximum number of symbols of the desired file retrieved per downloadedsymbol, for the coded database is derived. It is shown that the SPIR capacityfor coded database is $1-\frac{M}{N}$, when the amount of the shared commonrandomness of distributed nodes (unavailable at the user) is at least$\frac{M}{N-M}$ times the file size. Otherwise, the SPIR capacity for the codeddatabase equals zero.

Symmetric Private Information Retrieval For MDS Coded Distributed Storage