Yuriy S. Polyakov

Anomalous diffusion as a stochastic component in the dynamics of complex processes

Anomalous diffusion, process in which the mean-squared displacement of system states is a non-linear function of time, is usually identified in real stochastic processes by comparing experimental and theoretical displacements at relatively small time intervals. This paper proposes an interpolation expression for the identification of anomalous diffusion in complex signals for the cases when the dynamics of the system under study reaches a steady state (large time intervals). This interpolation expression uses the chaotic difference moment (transient structural function) of the second order as an average characteristic of displacements. A general procedure for identifying anomalous diffusion and calculating its parameters in real stochastic signals, which includes the removal of the regular (low-frequency) components from the source signal and the fitting of the chaotic part of the experimental difference moment of the second order to the interpolation expression, is presented. The procedure was applied to the analysis of the dynamics of magnetoencephalograms, blinking fluorescence of quantum dots, and X-ray emission from accreting objects. For all three applications, the interpolation was able to adequately describe the chaotic part of the experimental difference moment, which implies that anomalous diffusion manifests itself in these natural signals. The results of this study make it possible to broaden the range of complex natural processes in which anomalous diffusion can be identified. The relation between the interpolation expression and a diffusion model, which is derived in the paper, allows one to simulate the chaotic processes in the open complex systems with anomalous diffusion.

Analysis of cross-correlations in electroencephalogram signals as an approach to proactive diagnosis of schizophrenia

We apply flicker-noise spectroscopy (FNS), a time series analysis method operating on structure functions and power spectrum estimates, to study the clinical electroencephalogram (EEG) signals recorded in children/adolescents (11 to 14 years of age) with diagnosed schizophrenia-spectrum symptoms at the National Center for Psychiatric Health (NCPH) of the Russian Academy of Medical Sciences. The EEG signals for these subjects were compared with the signals for a control sample of chronically depressed children/adolescents. The purpose of the study is to look for diagnostic signs of subjects’ susceptibility to schizophrenia in the FNS parameters for specific electrodes and cross-correlations between the signals simultaneously measured at different points on the scalp. Our analysis of EEG signals from scalp-mounted electrodes at locations F3 and F4, which are symmetrically positioned in the left and right frontal areas of cerebral cortex, respectively, demonstrates an essential role of frequency–phase synchronization, a phenomenon representing specific correlations between the characteristic frequencies and phases of excitations in the brain. We introduce quantitative measures of frequency–phase synchronization and systematize the values of FNS parameters for the EEG data. The comparison of our results with the medical diagnoses for 84 subjects performed at NCPH makes it possible to group the EEG signals into 4 categories corresponding to different risk levels of subjects’ susceptibility to schizophrenia. We suggest that the introduced quantitative characteristics and classification of cross-correlations may be used for the diagnosis of schizophrenia at the early stages of its development.

Stochastic Variability in X-Ray Emission from the Black Hole Binary GRS 1915+105

We examine stochastic variability in the dynamics of X-ray emission from the black hole system GRS 1915+105, a strongly variable microquasar commonly used for studying relativistic jets and the physics of black hole accretion. The analysis of sample observations for 13 different states in both soft (low) and hard (high) energy bands is performed by flicker-noise spectroscopy (FNS), a phenomenological time series analysis method operating on structure functions and power spectrum estimates. We find the values of FNS parameters, including the Hurst exponent, flicker-noise parameter, and characteristic timescales, for each observation based on multiple 2500 s continuous data segments. We identify four modes of stochastic variability driven by dissipative processes that may be related to viscosity fluctuations in the accretion disk around the black hole: random (RN), power-law (1F), one-scale (1S), and two-scale (2S). The variability modes are generally the same in soft and hard energy bands of the same observation. We discuss the potential for future FNS studies of accreting black holes.

Dynamics of stainless steel turning: Analysis by flicker-noise spectroscopy

We use flicker-noise spectroscopy (FNS), a phenomenological method for the analysis of time and spatial series operating on structure functions and power spectrum estimates, to identify and study harmful chatter vibrations in a regenerative turning process. The 3D cutting force components experimentally measured during stainless steel turning are analyzed, and the parameters of their stochastic dynamics are estimated. Our analysis shows that the system initially exhibiting regular vibrations associated with spindle rotation becomes unstable to high-frequency noisy oscillations (chatter) at larger cutting depths. We suggest that the chatter may be attributed to frictional stick-and-slip interactions between the contact surfaces of cutting tool and workpiece. We compare our findings with previously reported results obtained by statistical, recurrence, multifractal, and wavelet methods. We discuss the potential of FNS in monitoring the turning process in manufacturing practice.

Cross-correlation earthquake precursors in the hydrogeochemical and geoacoustic signals for the Kamchatka peninsula

We propose a new type of earthquake precursor based on the analysis of correlation dynamics between geophysical signals of different nature. The precursor is found using a two-parameter cross-correlation function introduced within the framework of flicker-noise spectroscopy, a general statistical physics approach to the analysis of time series. We consider an example of cross-correlation analysis for water salinity time series, an integral characteristic of the chemical composition of groundwater, and geoacoustic emissions recorded at the G-1 borehole on the Kamchatka peninsula in the time frame from 2001 to 2003, which is characterized by a sequence of three groups of significant seismic events. We found that cross-correlation precursors took place 27, 31, and 35 days ahead of the strongest earthquakes for each group of seismic events, respectively. At the same time, precursory anomalies in the signals themselves were observed only in the geoacoustic emissions for one group of earthquakes.

PICADOR: End-to-end encrypted Publish–Subscribe information distribution with proxy re-encryption

Abstract This article presents PICADOR, a system for end-to-end encrypted Publish–Subscribe information distribution with proxy re-encryption. PICADOR is designed for topic-based Pub/Sub systems and provides end-to-end payload confidentiality. The main novelty of PICADOR is that it provides an information distribution service with end-to-end encryption where publishers and subscribers do not need to establish shared encryption and decryption keys. Multiple publishers post encrypted information to a Pub/Sub broker which uses Proxy Re-Encryption (PRE) to convert this information into a representation that can only be decrypted by approved subscribers. The broker is unable to decrypt the information. To support PICADOR, we design and implement a novel PRE scheme that leverages a general lattice encryption software library. We prototype our system using a scalable Java-based information substrate that supports topic-based Pub/Sub operations. We experimentally evaluate performance and scalability tradeoffs in the context of enterprise and mobile applications. We discuss design tradeoffs and application-specific customizations.

Implementation and Evaluation of Improved Gaussian Sampling for Lattice Trapdoors

We report on our implementation of a new Gaussian sampling algorithm for lattice trapdoors. Lattice trapdoors are used in a wide array of lattice-based cryptographic schemes including digital signatures, attributed-based encryption, program obfuscation and others. Our implementation provides Gaussian sampling for trapdoor lattices with prime moduli, and supports both single- and multi-threaded execution. We experimentally evaluate our implementation through its use in the GPV hash-and-sign digital signature scheme as a benchmark. We compare our design and implementation with prior work reported in the literature. The evaluation shows that our implementation 1) has smaller space requirements and faster runtime, 2) does not require multi-precision floating-point arithmetic, and 3) can be used for a broader range of cryptographic primitives than previous implementations.

Fast Proxy Re-Encryption for Publish/Subscribe Systems

We develop two IND-CPA-secure multihop unidirectional Proxy Re-Encryption (PRE) schemes by applying the Ring-LWE (RLWE) key switching approach from the homomorphic encryption literature. Unidirectional PRE is ideal for secure publish-subscribe operations where a publisher encrypts information using a public key without knowing upfront who the subscriber will be and what private key will be used for decryption. The proposed PRE schemes provide a multihop capability, meaning that when PRE-encrypted information is published onto a PRE-enabled server, the server can either delegate access to specific clients or enable other servers the right to delegate access. Our first scheme (which we call NTRU-ABD-PRE) is based on a variant of the NTRU-RLWE homomorphic encryption scheme. Our second and main PRE scheme (which we call BV-PRE) is built on top of the Brakerski-Vaikuntanathan (BV) homomorphic encryption scheme and relies solely on the RLWE assumption. We present an open-source C++ implementation of both schemes and discuss several algorithmic and software optimizations. We examine parameter selection tradeoffs in the context of security, runtime/latency, throughput, ciphertext expansion, memory usage, and multihop capabilities. Our experimental analysis demonstrates that BV-PRE outperforms NTRU-ABD-PRE in both single-hop and multihop settings. The BV-PRE scheme has a lower time and space complexity than existing IND-CPA-secure lattice-based PRE schemes and requires small concrete parameters, making the scheme computationally efficient for use on low-resource embedded systems while still providing 100 bits of security. We present practical recommendations for applying the PRE schemes to several use cases of ad hoc information sharing for publish-subscribe operations.

Practical implementations of program obfuscators for point functions

Point function obfuscators have recently been shown to be the first examples of program obfuscators provable under hardness assumptions commonly used in cryptography. This is remarkable, in light of early results in this area, showing impossibility of a single obfuscation solution for all programs. Point functions can be seen as functions that return 1 if the input value is equal to a secret value stored in the program, and 0 otherwise. In this paper, we select representative point function obfuscators from the literature, state their theoretical guarantees, and report on their (slightly) optimized implementations. We show that implementations of point function obfuscators, satisfying different obfuscation notions, can be used with practical performance guarantees. Notable implementation results due to our design and coding optimizations are: (a) very fast obfuscators based on group theory, and (b) obfuscators based on lattice theory with running time <; 8s, using inexpensive computing resources.

Practical Implementation of Lattice-Based Program Obfuscators for Point Functions

Lattice-based cryptography has recently produced several time-efficient cryptosystems that are provably secure under assumptions that are not known to be more easily solvable by quantum computers. An interesting research direction is improving their storage complexity, as current solutions are far from practical with respect to this metric. In this paper we show that program obfuscators for point functions based on lattice theory which are time-efficient, storage-efficient, and provably secure under studied modifications of assumptions commonly studied in lattice-based cryptography (i.e., LWE and LWR assumptions). Point function obfuscators have recently been shown to be the first examples of program obfuscators provable under hardness assumptions commonly used in cryptography. Point functions can be seen as functions that return 1 if the input value is equal to a secret value stored in the program, and 0 otherwise. Notable implementation results due to our design and coding optimizations are: (a) a point function obfuscator based on a modified LWR assumption with running time 0.01s and storage less than 100B, and (b) a point function obfuscator based on modified LWE assumption with running time 0.2s and storage less than 35KB, both using commodity computing resources.