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Large matrix multiplications commonly take place in large-scale machine-learning applications. Often, the sheer size of these matrices prevent carrying out the multiplication at a single server. Therefore, these operations are typically offloaded to a distributed computing platform with a master server and a large amount of workers in the cloud, operating in parallel. For such distributed platforms, it has been recently shown that coding over the input data matrices can reduce the computational delay by introducing a tolerance against straggling workers, i.e., workers for which execution time significantly lags with respect to the average. In addition to exact recovery, we impose a security constraint on both matrices to be multiplied. Specifically, we assume that workers can collude and eavesdrop on the content of these matrices. For this problem, we introduce a new class of polynomial codes with fewer non-zero coefficients than the degree +1. We provide closed-form expressions for the recovery threshold and show that our construction improves the recovery threshold of existing schemes in the literature, in particular for larger matrix dimensions and a moderate to large number of colluding workers. In the absence of any security constraints, we show that our construction is optimal in terms of recovery threshold.
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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.
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With the emergence of wireless networks, cooperation for secrecy is recognized as an attractive way to establish secure communications. Departing from cryptographic techniques, secrecy can be provided by exploiting the wireless channel characteristics; that is, some error-correcting codes besides reliability have been shown to achieve information-theoretic security. In this paper, we propose a polar-coding-based technique for the primitive relay wiretap channel and show that this technique is suitable to provide information-theoretic security. Specifically, we integrate at the relay an additional functionality, which allows it to smartly decide whether it will cooperate or not based on the decoding detector result. In the case of cooperation, the relay operates in a decode-and-forward mode and assists the communication by transmitting a complementary message to the destination in order to correctly decode the initial source's message. Otherwise, the communication is completed with direct transmission from source to the destination. Finally, we first prove that the proposed encoding scheme achieves weak secrecy, then, in order to overcome the obstacle of misaligned bits, we implement a double-chaining construction, which achieves strong secrecy.
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A polar coding scheme is proposed for the Wiretap Broadcast Channel with two legitimate receivers and one eavesdropper. We consider a model in which the transmitter wishes to send the same private (non-confidential) message and the same confidential message reliably to two different legitimate receivers, and the confidential message must also be (strongly) secured from the eavesdropper. The coding scheme aims to use the optimal rate of randomness and does not make any assumption regarding the symmetry or degradedness of the channel. This paper extends previous work on polar codes for the wiretap channel by proposing a new chaining construction that allows to reliably and securely send the same confidential message to two different receivers. This construction introduces new dependencies between the random variables involved in the coding scheme that need to be considered in the secrecy analysis.
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As accessibility of networked devices becomes more and more ubiquitous, groundbreaking applications of the Internet of Things (IoT) find their place in many aspects of our society. The exploitation of these devices is the main reason for the cyberattacks in IoT networks. Security design is still an open problem and a crucial step in making IoT applications successful. In dicey environments, such as e-health, smart grid, and smart cities, real-time commands must reach the end devices in the scale of milliseconds. Traditional public-key cryptosystem, albeit necessary in the context of general Internet security, falls short in establishing new session keys in the scale of milliseconds for critical messages. In this paper, a systematic perspective for securing IoT communication, specifically satisfying the real-time constraint against certain adversaries in realistic settings. First, at the network layer, we propose a secret random route computation scheme using the software-defined network (SDN) based on a capability scheme using the network actions. The computed routes are random in the eyes of the eavesdropper. Second, at the application layer, the source breaks command messages into secret shares and sends them through the network to the destination. Only the legitimate destination device can reconstruct the command. The secret sharing scheme is efficient compared to PKI and comes with information-theoretic security against adversaries. Our proof formalizes the notion of security of the proposed scheme, and our simulations validate our design.
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Private information retrieval (PIR) is a database query protocol that provides user privacy in that the user can learn a particular entry of the database of his interest but his query would be hidden from the data centre. Symmetric private information retrieval (SPIR) takes PIR further by additionally offering database privacy, where the user cannot learn any additional entries of the database. Unconditionally secure SPIR solutions with multiple databases are known classically, but are unrealistic because they require long shared secret keys between the parties for secure communication and shared randomness in the protocol. Here, we propose using quantum key distribution (QKD) instead for a practical implementation, which can realise both the secure communication and shared randomness requirements. We prove that QKD maintains the security of the SPIR protocol and that it is also secure against any external eavesdropper. We also show how such a classical-quantum system could be implemented practically, using the example of a two-database SPIR protocol with keys generated by measurement device-independent QKD. Through key rate calculations, we show that such an implementation is feasible at the metropolitan level with current QKD technology.
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In this paper, we propose a new theoretical security model for Shannon cipher systems under side-channel attacks, where the adversary is not only allowed to collect ciphertexts by eavesdropping the public communication channel but is also allowed to collect the physical information leaked by the devices where the cipher system is implemented on, such as running time, power consumption, electromagnetic radiation, etc. Our model is very robust as it does not depend on the kind of physical information leaked by the devices. We also prove that in the case of one-time pad encryption, we can strengthen the secrecy/security of the cipher system by using an appropriate affine encoder. More precisely, we prove that for any distribution of the secret keys and any measurement device used for collecting the physical information, we can derive an achievable rate region for reliability and security such that if we compress the ciphertext using an affine encoder with a rate within the achievable rate region, then: (1) anyone with a 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 region. We derive our result by adapting the framework of the one helper source coding problem posed and investigated by Ahlswede and Körner (1975) and Wyner (1975). For reliability and security, we obtain our result by combining the result of Csizár (1982) on universal coding for a single source using linear codes and the exponential strong converse theorem of Oohama (2015) for the one helper source coding problem.
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This paper investigates the problem of secret key generation over a wiretap channel when the terminals observe correlated sources. These sources are independent of the main channel and the users overhear them before the transmission takes place. A novel outer bound is proposed and, employing a previously reported inner bound, the secret key capacity is derived under certain less-noisy conditions on the channel or source components. This result improves upon the existing literature where the more stringent condition of degradedness is required. Furthermore, numerical evaluation of the achievable scheme and previously reported results for a binary model are presented; a comparison of the numerical bounds provides insights on the benefit of the chosen scheme.
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In this paper, we propose a theoretical framework to analyze the secure communication problem for broadcasting two encrypted sources in the presence of an adversary which launches side-channel attacks. The adversary is not only allowed to eavesdrop the ciphertexts in the public communication channel, but is also allowed to gather additional information on the secret keys via the side-channels, physical phenomenon leaked by the encryption devices during the encryption process, such as the fluctuations of power consumption, heat, or electromagnetic radiation generated by the encryption devices. Based on our framework, we propose a countermeasure against such adversary by using the post-encryption-compression (PEC) paradigm, in the case of one-time-pad encryption. We implement the PEC paradigm using affine encoders constructed from linear encoders and derive the explicit the sufficient conditions to attain the exponential decay of the information leakage as the block lengths of encrypted sources become large. One interesting feature of the proposed countermeasure is that its performance is independent from the type of side information leaked by the encryption devices.
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Asymptotic secrecy-capacity achieving polar coding schemes are proposed for the memoryless degraded broadcast channel under different reliability and secrecy requirements: layered decoding or layered secrecy. In these settings, the transmitter wishes to send multiple messages to a set of legitimate receivers keeping them masked from a set of eavesdroppers. The layered decoding structure requires receivers with better channel quality to reliably decode more messages, while the layered secrecy structure requires eavesdroppers with worse channel quality to be kept ignorant of more messages. Practical constructions for the proposed polar coding schemes are discussed and their performance evaluated by means of simulations.
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The problem of multilevel diversity coding with secure regeneration (MDC-SR) is considered, which includes the problems of multilevel diversity coding with regeneration (MDC-R) and secure regenerating code (SRC) as special cases. Two outer bounds are established, showing that separate coding can achieve the minimum-bandwidth-regeneration (MBR) point of the achievable normalized storage-capacity repair-bandwidth trade-off regions for the general MDC-SR problem. The core of the new converse results is an exchange lemma, which can be established using Han's subset inequality.