On the Linear Capacity of Conditional Disclosure of Secrets

Abstract

Conditional disclosure of secrets (CDS) is the problem of disclosing as efficiently as possible, one secret from Alice and Bob to Carol if and only if the inputs at Alice and Bob satisfy some function f . The information theoretic capacity of CDS is the maximum number of bits of the secret that can be securely disclosed per bit of total communication. All CDS instances, where the capacity is the highest and is equal to 1/2, are recently characterized through a noise and signal alignment approach and are described using a graph representation of the function f . In this work, we go beyond the best case scenarios and further develop the alignment approach to characterize the linear capacity of a class of CDS instances to be (ρ − 1)/(2ρ), where ρ is a covering parameter of the graph representation of f .

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

“…Remark 2 As in CDS and CDMS, we can use a bipartite graph to specify two-database SPIR constraints. As introduced in [52], [53], CDS can be viewed as a data storage system over a bipartite graph where the nodes in each side of the graph are used to denote the input values in each party, and the connectivity of the links is used to indicate the satisfaction of the condition after selecting two nodes (input values) from two parties. In the extension to CDMS, we assign a distinct color c k to each independent secret S k .…”

“…Since CDS itself functions as an essential building block in applications such as secret sharing and attribute based encryption [49]- [51], CDS has also attracted significant attention as a stand-alone computer science problem. Recently, information-theoretic CDS is formulated in [52], [53] to characterize the maximum number of secret bits that can be securely disclosed per communication bit whenever a pre-defined condition is satisfied.…”

On Extremal Rates of Secure Storage over Graphs

“…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.…”