Analyzing the spontaneous activity of the human brain using dynamic approaches can reveal functional organizations. The co-activation pattern (CAP) analysis of signals from different brain regions is used to characterize brain neural networks that may serve specialized functions. However, CAP is based on spatial information but ignores temporal reproducible transition patterns, and lacks robustness to low signal-to-noise rate (SNR) data. To address these issues, this study proposes a new CAP framework based on hidden semi-Markov model (HSMM) called HSMM-CAP analysis, which can be performed to investigate spatiotemporal CAPs (stCAPs) of the brain. HSMM-CAP uses empirical spatial distributions of stCAPs as emission models, and assumes that the state sequence of stCAPs follows a semi-Markov process. Based on the assumptions of sparsity, heterogeneity, and semi-Markov property of stCAPs, the HSMM-CAP-K-means method is constructed to infer the state sequence and transition parameters of stCAPs. In addition, HSMM-CAP provides the inverse relationship between the number of states and sparsity. Simulation studies verify the performance of HSMM-CAP at different levels of SNR. The spatiotemporal dynamics of stCAPs are also revealed by the proposed method on real-world resting-state fMRI data. Our method provides a new data-driven computational framework for revealing the brain spatiotemporal dynamics of resting-state fMRI data.

Abstract We present an overview of quantum-safe cryptography (QSC) with a focus on post-quantum cryptography (PQC) and information-theoretic security. From a cryptographic point of view, lattice and code-based schemes are among the most promising PQC solutions. Both approaches are based on the hardness of decoding problems of linear codes with different metrics. From an information-theoretic point of view, lattices and linear codes can be constructed to achieve certain secrecy quantities for wiretap channels as is intrinsically classical- and quantum-safe. Historically, coding theory and cryptography are intimately connected since Shannon’s pioneering studies but have somehow diverged later. QSC offers an opportunity to rebuild the synergy of the two areas, hopefully leading to further development beyond the NIST PQC standardization process. In this paper, we provide a survey of lattice and code designs that are believed to be quantum-safe in the area of cryptography or coding theory. The interplay and similarities between the two areas are discussed. We also conclude our understandings and prospects of future research after NIST PQC standardisation.

Shamir's celebrated secret sharing scheme provides an efficient method for encoding a secret of arbitrary length $\ell$ among any $N \leq 2^\ell$ players such that for a threshold parameter $t$, (i) the knowledge of any $t$ shares does not reveal any information about the secret and, (ii) any choice of $t+1$ shares fully reveals the secret. It is known that any such threshold secret sharing scheme necessarily requires shares of length $\ell$, and in this sense Shamir's scheme is optimal. The more general notion of ramp schemes requires the reconstruction of secret from any $t+g$ shares, for a positive integer gap parameter $g$. Ramp secret sharing scheme necessarily requires shares of length $\ell/g$. Other than the bound related to secret length $\ell$, the share lengths of ramp schemes can not go below a quantity that depends only on the gap ratio $g/N$. In this work, we study secret sharing in the extremal case of bit-long shares and arbitrarily small gap ratio $g/N$, where standard ramp secret sharing becomes impossible. We show, however, that a slightly relaxed but equally effective notion of semantic security for the secret, and negligible reconstruction error probability, eliminate the impossibility. Moreover, we provide explicit constructions of such schemes. One of the consequences of our relaxation is that, unlike standard ramp schemes with perfect secrecy, adaptive and non-adaptive adversaries need different analysis and construction. For non-adaptive adversaries, we explicitly construct secret sharing schemes that provide secrecy against any $τ$ fraction of observed shares, and reconstruction from any $ρ$ fraction of shares, for any choices of $0 \leq τ< ρ\leq 1$. Our construction achieves secret length $N(ρ-τ-o(1))$, which we show to be optimal. For adaptive adversaries, we construct explicit schemes attaining a secret length $Ω(N(ρ-τ))$.

Non-malleable codes are randomized codes that protect coded messages against modification by functions in a tampering function class. These codes are motivated by providing tamper resilience in applications where a cryptographic secret is stored in a tamperable storage device and the protection goal is to ensure that the adversary cannot benefit from their physical tampering with the device. In this paper we consider nonmalleable codes for protection of secure communication against active physical layer adversaries. We define a class of functions that closely model tampering of communication by adversaries who can eavesdrop on a constant fraction of the transmitted codeword, and use this information to select a vector of tampering functions that will be applied to a second constant fraction of codeword components (possibly overlapping with the first set). We derive rate bounds for non-malleable codes for this function class and give a modular construction that adapts and provides new analysis for an existing construction in the new setting. We discuss our results and directions for future work.

Non-malleable codes protect against an adversary who can tamper with the coded message by using a tampering function in a specified function family, guaranteeing that the tampering result will only depend on the chosen function and not the coded message. The codes have been motivated for providing protection against tampering with hardware that stores the secret cryptographic keys, and have found significant attention in cryptography. Traditional Shannon model of communication systems assumes the communication channel is perfectly known to the transmitter and the receiver. Arbitrary Varying Channels (AVCs) remove this assumption and have been used to model adversarially controlled channels. Transmission over these channels has been originally studied with the goal of recovering the sent message, and more recently with the goal of detecting tampering with the sent messages. In this paper we introduce non-malleability as the protection goal of message transmission over these channels, and study binary (discrete memoryless) AVCs where possible tampering is modelled by the set of channel states. Our main result is that non-malleability for these channels is achievable at a rate asymptotically approaching 1. We also consider the setting of an AVC with a special state s*, and the additional requirement that the message must be recoverable if s* is applied to all the transmitted bits. We give the outline of a message encoding scheme that in addition to non-malleability, can provide recovery for all s* channel.

Post-quantum secure communication has attracted much interest in recent years. Known computationally secure post-quantum key agreement protocols are resource intensive for small devices. These devices may need to securely send frequent short messages, for example to report the measurement of a sensor. Secure communication using physical assumptions provides information-theoretic security (and so quantum-safe) with small computational over-head. Security and efficiency analysis of these systems however is asymptotic. In this poster we consider two secure message communication systems, and derive and compare their security and efficiency for finite length messages. Our results show that these systems indeed provide an attractive alternative for post-quantum security.

Key agreement using physical layer properties of communication channels is a well studied problem. iJam is a physical layer key agreement protocol that achieves security by creating a “virtual” wiretap channel for the adversary through a subprotocol between the sender and the receiver that uses self-jamming by the receiver. The protocol was implemented and its security was shown through extensive experiments. The self-jamming subprotocol of iJam was later modelled as a wiretap channel and used for designing a secure message transmission protocol with provable security. We use the same wiretap model of the subprotocol to design secret key agreement protocols with provable security. We propose two protocols that use the wiretap channel once from Alice to Bob, and a protocol that uses two wiretap channels, one from Alice to Bob, and one in the opposite direction. We provide security proof and efficiency analysis for the protocols. The protocols effectively give physical layer security protocols that can be implemented and have provable security. We discuss our results and propose directions for future research.

Nested lattices Ae⊂ Abhave previously been studied for coding in the Gaussian wiretap channel and two design criteria, namely, the secrecy gain and flatness factor, have been proposed to study how the coarse lattice Aeshould be chosen so as to maximally conceal the message against the eavesdropper. In this paper, we study the connection between these two criteria and show the secrecy-goodness of even unimodular lattices, which means exponentially vanishing flatness factor as the dimension grows.

The secrecy gain of a lattice is a lattice invariant used to characterize wiretap lattice codes for Gaussian channels. The secrecy gain has been classified for unimodular lattices up to dimension 23, and so far, a few sparse examples are known for l-modular lattices, with l = 2, 3. We propose some constructions of 5-modular lattices via the Construction A of lattices from linear codes, and study the secrecy gain of the resulting lattices.

Lattice coding over a Gaussian wiretap channel, where an eavesdropper listens to transmissions between a transmitter and a legitimate receiver, is considered. A new lattice invariant called the secrecy gain is used as a code design criterion for wiretap lattice codes since it was shown to characterize the confusion that a chosen lattice can cause at the eavesdropper: the higher the secrecy gain of the lattice, the more confusion. In this paper, secrecy gains of extremal odd unimodular lattices as well as unimodular lattices in dimensionn, 16 ≤n≤ 23, are computed, covering the four extremal odd unimodular lattices and all the 111 nonextremal unimodular lattices (both odd and even), providing thus a classification of the best wiretap lattice codes coming from unimodular lattices in dimensionn, 8n≤ 23. Finally, to permit lattice encoding via Construction A, the corresponding error correction codes of the best lattices are determined.

Lattice coding over a Gaussian wiretap channel is considered with respect to a lattice invariant called the secrecy gain, which was introduced in [1] to characterize the confusion that a chosen lattice can cause at the eavesdropper: the higher the secrecy gain of the lattice, the more confusion. In this paper, secrecy gains of several 2- and 3-modular lattices are computed. Most are shown to have a secrecy gain larger than the best unimodular lattices can achieve.

We consider lattice coding over a Gaussian wiretap channel with respect to the secrecy gain, a lattice invariant introduced in [1] to characterize the confusion that a chosen lattice can cause at the eavesdropper. The secrecy gain of the best unimodular lattices constructed from binary self-dual codes in dimension n, 24 ≤ n ≤ 32 are calculated. Numerical upper bounds on the secrecy gain of unimodular lattices in general and of unimodular lattices constructed from binary self-dual codes in particular are derived for all even dimensions up to 168.

We consider lattice coding over a Gaussian wiretap channel, where an eavesdropper listens to the transmissions between a transmitter and a legitimate receiver. In [1], a new lattice invariant called the secrecy gain was introduced as a code design criterion for wiretap lattice codes, shown to characterize the confusion that a chosen lattice code can cause at the eavesdropper: the higher the secrecy gain of the lattice, the more confusion. In this paper, a formula for the secrecy gain of unimodular lattices is derived. Secrecy gains of extremal odd unimodular lattices as well as unimodular lattices in dimension 16 are computed and compared. Finally, best wiretap lattice codes coming from unimodular lattices in dimension n, 8 ≤ n ≤ 16 are classified.