Communication Cost of Two-Database Symmetric Private Information Retrieval: A Conditional Disclosure of Multiple Secrets Perspective

Wang, Zhusheng; Ulukuş, Şennur

doi:10.48550/arxiv.2201.12327

Cited by 2 publications

(4 citation statements)

References 17 publications

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“…In the case of K = 3, M 1 and M 2 both take the value 3, after converting the random reliability constraint and user privacy constraint into pairwise constraints as in ( 22)-( 25), we can proceed with the converse steps. As in the converse proof in the case of K = 2 above, the concrete process is to utilize the converse proof of [46,Theorem 2] once more after eliminating the influence of retrieval strategy randomness and its generated queries. Thus, we have the same conclusions as the one in [46,Theorem 2] in the case of K = 3,…”

Section: Converse Proofmentioning

confidence: 99%

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Digital Blind Box: Random Symmetric Private Information Retrieval

Wang¹,

Ulukuş²

2022

Preprint

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We introduce the problem of random symmetric private information retrieval (RSPIR). In canonical PIR, a user downloads a message out of K messages from N non-colluding and replicated databases in such a way that no database can know which message the user has downloaded (user privacy). In SPIR, the privacy is symmetric, in that, not only that the databases cannot know which message the user has downloaded, the user itself cannot learn anything further than the particular message it has downloaded (database privacy). In RSPIR, different from SPIR, the user does not have an input to the databases, i.e., the user does not pick a specific message to download, instead is content with any one of the messages. In RSPIR, the databases need to send symbols to the user in such a way that the user is guaranteed to download a message correctly (random reliability), the databases do not know which message the user has received (user privacy), and the user does not learn anything further than the one message it has received (database privacy). This is the digital version of a blind box, also known as gachapon, which implements the above specified setting with physical objects for entertainment. This is also the blind version of 1-out-of-K oblivious transfer (OT), an important cryptographic primitive. We study the information-theoretic capacity of RSPIR for the case of N = 2 databases. We determine its exact capacity for the cases of K = 2, 3, 4 messages. While we provide a general achievable scheme that is applicable to any number of messages, the capacity for K ≥ 5 remains open.

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Section: Converse Proofmentioning

confidence: 99%

“…As in the converse proof in the case of K = 2 above, the concrete process is to utilize the converse proof of [46,Theorem 2] once more after eliminating the influence of retrieval strategy randomness and its generated queries. Thus, we have the same conclusions as the one in [46,Theorem 2] in the case of K = 3,…”

Section: Converse Proofmentioning

confidence: 99%

Digital Blind Box: Random Symmetric Private Information Retrieval

Wang¹,

Ulukuş²

2022

Preprint

Self Cite

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“…First, when the graph G is bipartite (e.g., Fig. 1), the secure storage problem can be viewed a generalization of the conditional disclosure of secrets (CDS) problem [1][2][3][4][5]. To see this, we view the nodes on one side (e.g., V 1 , V 2 , V 3 , V 4 in Fig.…”

Section: Introductionmentioning

confidence: 99%

“…If and only if the signal indices (node indices) satisfy some function (i.e., the type of the edge corresponds to some source symbols), Carol who receives both signals can recover the corresponding secrets. Compared to the classic CDS problem where there is only one secret (source symbol) to disclose, the secure storage problem generalizes to include multiple secrets [5]; further, an arbitrary subset of all secrets can be conditionally disclosed.…”

Section: Introductionmentioning

confidence: 99%

On Extremal Rates of Secure Storage over Graphs

Li¹,

Sun²

2022

Preprint

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A secure storage code maps K source symbols, each of L w bits, to N coded symbols, each of L v bits, such that each coded symbol is stored in a node of a graph. Each edge of the graph is either associated with D of the K source symbols such that from the pair of nodes connected by the edge, we can decode the D source symbols and learn no information about the remaining K − D source symbols; or the edge is associated with no source symbols such that from the pair of nodes connected by the edge, nothing about the K source symbols is revealed. The ratio L w /L v is called the symbol rate of a secure storage code and the highest possible symbol rate is called the capacity.We characterize all graphs over which the capacity of a secure storage code is equal to 1, when D = 1. This result is generalized to D > 1, i.e., we characterize all graphs over which the capacity of a secure storage code is equal to 1/D under a mild condition that for any node, the source symbols associated with each of its connected edges do not include a common element. Further, we characterize all graphs over which the capacity of a secure storage code is equal to 2/D.

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Communication Cost of Two-Database Symmetric Private Information Retrieval: A Conditional Disclosure of Multiple Secrets Perspective

Cited by 2 publications

References 17 publications

Digital Blind Box: Random Symmetric Private Information Retrieval

Digital Blind Box: Random Symmetric Private Information Retrieval

On Extremal Rates of Secure Storage over Graphs

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