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.
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.
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, Korner(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 eavesdropper with the exponential strong converse theorem Oohama(2015) established for the one helper source coding problem.
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 the secure cooperative source-coding problem that we consider, Encoder 1 and Decoder 1 observe, respectively, a pair of independent identically distributed (i.i.d.) correlated sources and wish to communicate the first source to Decoder 2 subject to a distortion constraint. Encoder 1 sends a message to both the decoders over a public nonsecure channel, and then Decoder 1-the helper-sends a message just to Decoder 2 over a secure channel. An eavesdropper, which has access to memoryless side-information that is correlated with the first source, intercepts the message sent by Encoder 1 and based on both wishes to minimize its uncertainty about the first source. The secrecy measure of the system is the equivocation of the first source at the eavesdropper. We determine the rates equivocation region for this problem assuming that conditioned on the side-information of Decoder 1 the eavesdropper's side-information is independent of the first source. To that end, we derive an inner and an outer bound that depend explicitly on the proportional rate that Encoder 1 spends in the cooperation process. Subsequently, we evaluate this region for the case of a doubly symmetric binary source and Hamming distortion.
We consider a secure source coding problem with a rate-limited helper. In particular, Alice observes an independent and identically distributed (i.i.d.) source X and wishes to transmit this source losslessly to Bob over a rate-limited link. A helper (Helen), observes an i.i.d. correlated source Y and can transmit information to Bob over a separate rate-limited link. A passive eavesdropper (Eve) can observe the coded output of Alice, i.e., the link from Alice to Bob is public. The uncertainty about the source X at Eve, is measured by the conditional entropy of the source given the coded output of Alice. We completely characterize the rate-equivocation region for this secure source coding model, where we show that Slepian-Wolf binning of X with respect to the coded side information received at Bob is optimal. We next consider a modification of this model in which Alice also has access to the coded output of Helen. For the two-sided helper model, we characterize the rate-equivocation region. While the availability of side information at Alice does not reduce the rate of transmission from Alice, it significantly enhances the resulting equivocation at Eve. In particular, the resulting equivocation for the two-sided helper case is shown to be min(H(X),R_y), i.e., one bit from the two-sided helper provides one bit of uncertainty at Eve. From this result, we infer that Slepian-Wolf binning of X is suboptimal and one can further decrease the information leakage to the eavesdropper by utilizing the side information at Alice. We finally generalize these results to the case in which there is additional un-coded side information W available at Bob and characterize the rate-equivocation regions under the assumption that Y-X-W forms a Markov chain.
Recently, a secrecy measure based on list-reconstruction has been proposed [2], in which a wiretapper is allowed to produce a list of 2mRL reconstruction sequences and the secrecy is measured by the minimum distortion over the entire list. In this paper, we show that this list secrecy problem is equivalent to the one with secrecy measured by a new quantity \emph{lossy-equivocation}, which is proven to be the minimum optimistic 1-achievable source coding rate (the minimum coding rate needed to reconstruct the source within target distortion with positive probability for \emph{infinitely many blocklengths}) of the source with the wiretapped signal as two-sided information, and also can be seen as a lossy extension of conventional equivocation. Upon this (or list) secrecy measure, we study source-channel secrecy problem in the discrete memoryless Shannon cipher system with \emph{noisy} wiretap channel. Two inner bounds and an outer bound on the achievable region of secret key rate, list rate, wiretapper distortion, and distortion of legitimate user are given. The inner bounds are derived by using uncoded scheme and (operationally) separate scheme, respectively. Thanks to the equivalence between lossy-equivocation secrecy and list secrecy, information spectrum method is leveraged to prove the outer bound. As special cases, the admissible region for the case of degraded wiretap channel or lossless communication for legitimate user has been characterized completely. For both these two cases, separate scheme is proven to be optimal. Interestingly, however, separation indeed suffers performance loss for other certain cases. Besides, we also extend our results to characterize the achievable region for Gaussian communication case. As a side product optimistic lossy source coding has also been addressed.
Recently, a secrecy measure based on list-reconstruction has been proposed, in which a wiretapper is allowed to produce a list of 2mRLreconstruction sequences and the secrecy is measured by the minimum distortion over the entire list. In this paper, we show that this list secrecy problem is equivalent to the one with secrecy measured by a new quantity lossy equivocation, which is proved to be the minimum optimistic one-achievable source coding rate (the minimum coding rate needed to reconstruct the source within target distortion with positive probability for infinitely many blocklengths) of the source with the wiretapped signal as two-sided information, and also can be seen as a lossy extension of conventional equivocation. Upon this (or list) secrecy measure, we study source-channel secrecy problem in the discrete memoryless Shannon cipher system with noisy wiretap channel. Two inner bounds and an outer bound on the achievable region of secret key rate, list rate, wiretapper distortion, and distortion of legitimate user are given. The inner bounds are derived by using uncoded scheme and (operationally) separate scheme, respectively. Thanks to the equivalence between lossy-equivocation secrecy and list secrecy, information spectrum method is leveraged to prove the outer bound. As special cases, the admissible region for the case of degraded wiretap channel or lossless communication for legitimate user has been characterized completely. For both these two cases, separate scheme is proved to be optimal. Interestingly, however, separation indeed suffers performance loss for other certain cases. Besides, we also extend our results to characterize the achievable region for Gaussian communication case. As a side product, optimistic lossy source coding has also been addressed.