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IEEE International Symposium on Information Theory (ISIT)

Universal Source Encryption under Side-Channel Attacks

Yasutada Oohama, Bagus Santoso

Published Jul 7, 2024• 0 citations
Publisher

Abstract

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.

DOI
10.1109/isit57864.2024.10619496

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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.
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 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.
The problem of secure source coding with multiple terminals is extended by considering a remote source whose noisy measurements are the correlated random variables used for secure source reconstruction. The main additions to the problem include 1) all terminals noncausally observe a noisy measurement of the remote source; 2) a private key is available to all legitimate terminals; 3) the public communication link between the encoder and decoder is rate-limited; and 4) the secrecy leakage to the eavesdropper is measured with respect to the encoder input, whereas the privacy leakage is measured with respect to the remote source. Exact rate regions are characterized for a lossy source coding problem with a private key, remote source, and decoder side information under security, privacy, communication, and distortion constraints. By replacing the distortion constraint with a reliability constraint, we obtain the exact rate region also for the lossless case. Furthermore, the lossy rate region for scalar discrete-time Gaussian sources and measurement channels is established.
We extend the problem of secure source coding by considering a remote source whose noisy measurements are correlated random variables used for secure source reconstruction. The main additions to the problem are as follows: (1) all terminals noncausally observe a noisy measurement of the remote source; (2) a private key is available to all legitimate terminals; (3) the public communication link between the encoder and decoder is rate-limited; and (4) the secrecy leakage to the eavesdropper is measured with respect to the encoder input, whereas the privacy leakage is measured with respect to the remote source. Exact rate regions are characterized for a lossy source coding problem with a private key, remote source, and decoder side information under security, privacy, communication, and distortion constraints. By replacing the distortion constraint with a reliability constraint, we obtain the exact rate region for the lossless case as well. Furthermore, the lossy rate region for scalar discrete-time Gaussian sources and measurement channels is established. An achievable lossy rate region that can be numerically computed is also provided for binary-input multiple additive discrete-time Gaussian noise measurement channels.
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 problem of transmitting a remote source via multiple agents to a single destination is considered with secrecy constraints. In particular, noisy versions of a source are observed by multiple agents who then encode and transmit their observations to a decoder over dedicated noisy channel. The decoder should be able to reconstruct the remote source within a certain distortion limit. In addition, there exists an eavesdropper with correlated side information to the source who is capable of wiretapping the links from the agents to the decoder so as to extract as much information as possible about the source. Therefore, the agents should encode their observations in such a way that while as less information as possible is leaked to the eavesdropper the decoder can satisfy the distortion constraint. For this problem, we study the tradeoffs among agents' transmission rates, experienced distortion at the destination, and equivocation rates at the eavesdropper, and provide an achievable region.