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IEEE Information Theory Workshop (ITW)

Strong Converse for Distributed Source Coding with Encryption Using Correlated Keys

Yasutada Oohama, Bagus Santoso

Published Oct 17, 2021• 2 citations
Publisher

Abstract

We pose and investigate the distributed secure source coding based on the common key cryptosystem. This cryptosystem includes the secrecy amplification problem for distributed encrypted sources with correlated keys using post-encryption-compression, which was previously studied by Santoso and Oohama. In this paper we propose another new security criterion which is generally more strict compared with the commonly used security criterion based on the upper-bound of mutual information between the plaintext and the ciphertext. Under this criterion, we establish the necessary and sufficient condition for the secure transmission of correlated sources.

DOI
10.1109/itw48936.2021.9611414

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We pose and investigate the distributed secure source coding based on the common key cryptosystem. This cryptosystem includes the secrecy amplification problem for distributed encrypted sources with correlated keys using post-encryption-compression, which was previously studied by Santoso and Oohama. In this paper we propose another new security criterion which is generally more strict compared with the commonly used security criterion based on the upper-bound of mutual information between the plaintext and the ciphertext. Under this criterion, we establish the necessary and sufficient condition for the secure transmission of correlated sources.
We reinvestigate the general distributed secure source coding based on the common key cryptosystem proposed by Oohama and Santoso (ITW 2021). They proposed a framework of distributed source encryption and derived the necessary and sufficient conditions to have reliable and secure transmission. However, the bounds of the rate region, which specifies both necessary and sufficient conditions to have reliable and secure transmission under the proposed cryptosystem, were derived based on a self-tailored non-standard} security criterion. In this paper we adopt the standard security criterion, i.e., standard mutual information. We successfully establish the bounds of the rate region based on this security criterion. Information spectrum method and a variant of Birkhoff-von Neumann theorem play an important role in deriving the result.
In this paper, we propose a framework of source encryption, where cryptographic processing is applied to a prescribed fixed length source code. The proposed source encryption framework is based on the secure communication framework of the Shannon cipher system. In the proposed framework, we use the mutual information as a measure of information leakage to an adversary. For the proposed framework, we explicitly establish the necessary and sufficient condition for reliable and secure communication under the condition that error probability and information leakage, respectively, are upper bounded by prescribed constants ε∈(0,1)ε\in (0,1)ε∈(0,1) and δ∈(0,∞)δ\in (0,\infty)δ∈(0,∞). We also show that the obtained necessary and sufficient condition does not depend on the constants ε∈(0,1)ε\in (0,1)ε∈(0,1) and δ∈(0,∞)δ\in (0,\infty)δ∈(0,∞), demonstrating that we have the strong converse theorem for the proposed framework of source encryption. We further prove the existence of encryption/decryption schemes, which are universal in the sense that they work effectively for any distributions of the plain text and those of the key used for the encryption.
We study the universal coding problem for the general framework of source encryption with a symmetric key under the side-channel attacks, which is posed and investigated by Oohama and Santoso (2022). The reliable and secure rate region indicating the trade off between the compression rate of the ciphertext and the rate constraint imposed on the adversary for secure source transmission was established by Oohama and Santoso (2022). In this paper we focus on our attention to strengthening the direct coding theorem. We prove the existence of encryption/decryption schemes, which are universal in the sense that they work effectively for any distributions of the plain text, any noisy channels through which the adversary observe the corrupted version of the key, and any measurement device used for collecting the physical information. Those schemes have a good performance such that if we compress the ciphertext with rate within the reliable and secure rate region, then: (1) anyone with secret key will be able to decrypt and decode the ciphertext correctly, but (2) any adversary who obtains the ciphertext and also the side physical information will not be able to obtain any information about the hidden source as long as the leaked physical information is encoded with a rate within the rate constraint.
Starting with Shannon's perfect secrecy theorem, information theory has provided a tool for quantifying the amount of secrecy available for a fixed transmission setup. In this paper, we derive tight upper bounds on the secrecy offered for a broad class of problems consisting of distributed encryption and joint decryption. In particular, we consider the scenario where correlated messages must be encrypted independently, transmitted through perfect channels to a common receiver, and jointly decrypted. The main result we present is a theorem stating that the secrecy of a distributed system does not depend on whether dependent messages are encrypted jointly or separately, as long as joint decryption is allowed. This result is analogous to the Slepian-Wolf theorem for data compression, which states that asymptotically, distributed data compression performs as well as joint compression. We show that the equivalence of distributed and joint encryption is true whether the system uses a key or not, and consequently we demonstrate that if the system does not rely on a key, no secrecy can be offered. We briefly discuss how the results obtained may be applied to the problem of drone or sensor networks, as well as parallel encryption
We study side-channel attacks for the Shannon cipher system. To pose side channel-attacks to the Shannon cipher system, we regard them as a signal estimation via encoded data from two distributed sensors. This can be formulated as the one helper source coding problem posed and investigated by Ahlswede, Körner(1975), and Wyner(1975). We further investigate the posed problem to derive new secrecy bounds. Our results are derived by a coupling of the result Watanabe and Oohama(2012) obtained on bounded storage evasdropper with the exponential strong converse theorem Oohama(2015) established for the one helper source coding problem.
The distributed source coding problem is extended by positing that noisy measurements of a remote source are the correlated random variables that should be reconstructed at another terminal. We consider a secure and private distributed lossy source coding problem with two encoders and one decoder such that (i) all terminals noncausally observe a noisy measurement of the remote source; (ii) a private key is available to each legitimate encoder and all private keys are available to the decoder; (iii) rate-limited noiseless communication links are available between each encoder and the decoder; (iv) the amount of information leakage to an eavesdropper about the correlated random variables is defined assecrecyleakage, andprivacyleakage is measured with respect to the remote source; and (v) two passive attack scenarios are considered, where a strong eavesdropper can access both communication links and a weak eavesdropper can choose only one of the links to access. Inner and outer bounds on the rate regions defined under secrecy, privacy, communication, and distortion constraints are derived for both passive attack scenarios. When one or both sources should be reconstructed reliably, the rate region bounds are simplified.