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arXiv:2605.04720

A Framework of Secure Source Coding using Mutual Information Security Criterion: Universal Coding, Strong Converse Theorem

Yasutada Oohama, Bagus Santoso

Published May 6, 2026• 0 citations
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Abstract

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 $ε\in (0,1)$ and $δ\in (0,\infty)$. We also show that the obtained necessary and sufficient condition does not depend on the constants $ε\in (0,1)$ and $δ\in (0,\infty)$, 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.

DOI
10.48550/arxiv.2605.04720

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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.
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.
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.
In this paper, coding theorems on the (t, m) -threshold scheme for a general source are discussed, where m means the number of the shares and t means a threshold. The (t,m) -threshold scheme treated in this paper encrypts n source outputs Xnto m shares at once and is required to satisfy the two conditions that 1) Xnis reproduced from arbitrary t shares, and 2) almost no information of Xnis revealed from any t - 1 shares. It is shown that the (t,m) -threshold scheme must satisfy certain inequalities including the limit inferiors in probability. One of the inequalities is closely related to the minimum length of the fair random bits needed to a dealer for realizing the (t, m) -threshold scheme. In addition, it is shown that a certain variation of Shamir's threshold scheme meets the two conditions. The same approach can be taken to the problems of Shannon's cipher system with the perfect secrecy and fixed-length source coding with vanishing decoding error probability. It is shown that the same kind of inequalities, which indicate the converse coding theorems, hold in both two cases.
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.
Reliable communication imposes an upper limit on the achievable rate, namely the Shannon capacity. Wyner's wiretap coding, which ensures a security constraint also in addition to reliability, results in decrease of the achievable rate. To mitigate the loss in the secrecy rate, we propose a coding scheme paper where we use sufficiently old messages as key and for this scheme prove that multiple messages are secure with respect to (w.r.t.) all the information possessed by the eavesdropper. We also show that we can achieve security in the strong sense. Next we consider a fading wiretap channel with full channel state information of the eavesdropper's channel and use our coding/decoding scheme to achieve secrecy capacity close to the Shannon capacity of the main channel (in the ergodic sense). Finally we also consider the case where the transmitter does not have the instantaneous information of the channel state of the eavesdropper, but only its distribution.