Conditional Disclosure of Secrets: A Noise and Signal Alignment Approach

Abstract

In the conditional disclosure of secrets (CDS) problem, Alice and Bob (each holds an input and a common secret) wish to disclose, as efficiently as possible, the secret to Carol if and only if their inputs satisfy some function. The capacity of CDS is the maximum number of bits of the secret that can be securely disclosed per bit of total communication. We characterize the necessary and sufficient condition for the extreme case where the capacity of CDS is the highest and is equal to 1/2. For the simplest instance where the capacity is smaller than 1/2, we show that the linear capacity is 2/5.

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 the Linear Capacity of Conditional Disclosure of Secrets

“…The conditional disclosure of secrets (CDS) problem is a classical cryptographic primitive with rich connections to many other primitives such as symmetric private information retrieval [1] and secret sharing [2,3]. For more background and applications of CDS, we refer to the introduction section of [4] and references therein. The goal of the CDS problem is to find the most efficient way for Alice and Bob to disclose a common secret to Carol if and only if the inputs at Alice and Bob satisfy some function f (see Fig.…”

“…The aim is to characterize the maximum rate, termed the capacity of CDS, for a fixed function f . In [4], we obtain a complete characterization for all functions f where the CDS capacity is the highest, and is equal to 1/2. In describing this result, we find it convenient to represent the function f by a bipartite graph, where each node denotes a possible signal for certain input and two types (colors) of edges are used to denote whether f is 1 or 0 (see Fig.…”

“…Beyond the best rate scenarios, the simplest uncovered case is also considered in [4] (see Theo-rem 2), where the linear capacity 1 has been found and this is our starting point. Our goal in this work is to further develop the alignment approach to characterize the linear capacity of a larger class of CDS instances.…”