Distributed Keyless Secret Sharing Over Noiseless Channels

Abstract

In traditional secret sharing, a central trusted authority must divide a secret into multiple parts, called shares, such that the secret can only be recovered when a certain number of shares are available for reconstruction [1], [2]. In this paper, we consider a secret sharing problem in which each share must be created separately by independent entities such that no collaboration or shared cryptographic keys are required; we call this the distributed keyless secret sharing problem. For this problem, general tradeoffs between compression and secrecy are characterized yielding the impossibility result that perfect secrecy is unachievable. In response to this impossibility, we define a practical measure of secrecy and design a low-cost solution based on this measure of secrecy.

Distributed keyless security for correlated data with applications in visual sensor networks

“…In addition, R(D) = 0 is necessary for unconditional secrecy, and so although allowing non-zero distortion does increase secrecy from the distortionless case (when R(D) = H(S)), it is not for free. Finally Theorem 1 can also be shown to match our previous distortionless result when D = 0 in [16].…”

“…The main novel contribution in this paper is the analysis of the compression-secrecy tradeoff when the base station is permitted a non-zero distortion reconstruction of the nodes' data; this extends our previous work in which we required perfect reconstruction at the base station [16,17]. The extension involves the application of rate-distortion and multiterminal source coding theory.…”

“…In this section we briefly review some of the coding schemes that can either achieve or come close to achieving the capacity regions for distortionless distributed secret sharing (DSS) [16] and distributed encryption (DE) [17] problems. The interpretation of the proofs in Appendix A allow us to easily apply these codes to some of the non-zero distortion cases.…”

“…Specifically, we look at how our coding theorems fit the more conventional image encryption algorithms designed to date. We outline how to encrypt an ideal image model using the codes presented in our previous papers [16,17].…”

Secure lossy source coding with side information

“…This corollary can be obtained from Theorem 1 by noting the fact that I(X; Y |U ) − I(X; Z|U ) ≤ I(X; Y ) − I(X; Z) in view of the Markov chain in (6), where the equality can be attained by setting U = φ. Corollary 1 implies that in the degraded case, the relative equivocation is not affected by the choice of V , and hence, there is no tension between the achievable rate and the achievable relative equivocation originating from the choice of V . This also implies that the use of optimal compression rate for the given distortion level is optimal.…”