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- W3123459056 abstract "We study the equivalence between non-perfect secret sharing (NSS) and symmetric private information retrieval (SPIR) with arbitrary response and collusion patterns. NSS and SPIR are defined with an access structure, which corresponds to the authorized/forbidden sets for NSS and the response/collusion patterns for SPIR. We prove the equivalence between NSS and SPIR in the following two senses. 1) Given any SPIR protocol with an access structure, an NSS protocol is constructed with the same access structure and the same rate. 2) Given any linear NSS protocol with an access structure, a linear SPIR protocol is constructed with the same access structure and the same rate. We prove the first relation even if the SPIR protocol has imperfect correctness and secrecy. From the first relation, we derive an upper bound of the SPIR capacity for arbitrary response and collusion patterns. For the special case of <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$mathsf {n}$ </tex-math></inline-formula> -server SPIR with <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$mathsf {r}$ </tex-math></inline-formula> responsive and <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$mathsf {t}$ </tex-math></inline-formula> colluding servers, this upper bound proves that the SPIR capacity is <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$(mathsf {r}-mathsf {t})/mathsf {n}$ </tex-math></inline-formula> . From the second relation, we prove that a SPIR protocol exists for any response and collusion patterns." @default.
- W3123459056 created "2021-02-01" @default.
- W3123459056 creator A5024634142 @default.
- W3123459056 creator A5047793875 @default.
- W3123459056 date "2022-03-01" @default.
- W3123459056 modified "2023-10-02" @default.
- W3123459056 title "Equivalence of Non-Perfect Secret Sharing and Symmetric Private Information Retrieval With General Access Structure" @default.
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- W3123459056 doi "https://doi.org/10.1109/jsac.2022.3142375" @default.
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