Public key cryptography and error correcting codes as Ising models

We employ the methods of statistical physics to study the performance of Gallager type error-correcting codes. In this approach, the transmitted codeword comprises Boolean sums of the original message bits selected by two randomly-constructed sparse matrices. We show that a broad range of these codes potentially saturate Shannon's bound but are limited due to the decoding dynamics used. Other codes show sub-optimal performance but are not restricted by the decoding dynamics. We show how these codes may also be employed as a practical public-key cryptosystem and are of competitive performance to modern cyptographical methods.Comment: 6 page

Statistical Mechanical Approach to Lossy Data Compression:Theory and Practice

The encoder and decoder for lossy data compression of binary memoryless sources are developed on the basis of a specific-type nonmonotonic perceptron. Statistical mechanical analysis indicates that the potential ability of the perceptron-based code saturates the theoretically achievable limit in most cases although exactly performing the compression is computationally difficult. To resolve this difficulty, we provide a computationally tractable approximation algorithm using belief propagation (BP), which is a current standard algorithm of probabilistic inference. Introducing several approximations and heuristics, the BP-based algorithm exhibits performance that is close to the achievable limit in a practical time scale in optimal cases.Comment: 10 pages, 2 figures, REVTEX preprin

Typical Performance of Gallager-type Error-Correcting Codes

The performance of Gallager's error-correcting code is investigated via methods of statistical physics. In this approach, the transmitted codeword comprises products of the original message bits selected by two randomly-constructed sparse matrices; the number of non-zero row/column elements in these matrices constitutes a family of codes. We show that Shannon's channel capacity is saturated for many of the codes while slightly lower performance is obtained for others which may be of higher practical relevance. Decoding aspects are considered by employing the TAP approach which is identical to the commonly used belief-propagation-based decoding.Comment: 6 pages, latex, 1 figur

Statistical mechanics of lossy data compression using a non-monotonic perceptron

The performance of a lossy data compression scheme for uniformly biased Boolean messages is investigated via methods of statistical mechanics. Inspired by a formal similarity to the storage capacity problem in the research of neural networks, we utilize a perceptron of which the transfer function is appropriately designed in order to compress and decode the messages. Employing the replica method, we analytically show that our scheme can achieve the optimal performance known in the framework of lossy compression in most cases when the code length becomes infinity. The validity of the obtained results is numerically confirmed.Comment: 9 pages, 5 figures, Physical Review

Cryptographical Properties of Ising Spin Systems

The relation between Ising spin systems and public-key cryptography is investigated using methods of statistical physics. The insight gained from the analysis is used for devising a matrix-based cryptosystem whereby the ciphertext comprises products of the original message bits; these are selected by employing two predetermined randomly-constructed sparse matrices. The ciphertext is decrypted using methods of belief-propagation. The analyzed properties of the suggested cryptosystem show robustness against various attacks and competitive performance to modern cyptographical methods.Comment: 4 pages, 2 figure

Statistical mechanics of typical set decoding

The performance of ``typical set (pairs) decoding'' for ensembles of Gallager's linear code is investigated using statistical physics. In this decoding, error happens when the information transmission is corrupted by an untypical noise or two or more typical sequences satisfy the parity check equation provided by the received codeword for which a typical noise is added. We show that the average error rate for the latter case over a given code ensemble can be tightly evaluated using the replica method, including the sensitivity to the message length. Our approach generally improves the existing analysis known in information theory community, which was reintroduced by MacKay (1999) and believed as most accurate to date.Comment: 7 page

Fast algorithm for calculating two-photon absorption spectra

We report a numerical calculation of the two-photon absorption coefficient of electrons in a binding potential using the real-time real-space higher-order difference method. By introducing random vector averaging for the intermediate state, the task of evaluating the two-dimensional time integral is reduced to calculating two one-dimensional integrals. This allows the reduction of the computation load down to the same order as that for the linear response function. The relative advantage of the method compared to the straightforward multi-dimensional time integration is greater for the calculation of non-linear response functions of higher order at higher energy resolution.Comment: 4 pages, 2 figures. It will be published in Phys. Rev. E on 1, March, 199

Enhanced GATA4 expression in senescent systemic lupus erythematosus monocytes promotes high levels of IFNα production

Enhanced interferon α (IFNα) production has been implicated in the pathogenesis of systemic lupus erythematosus (SLE). We previously reported IFNα production by monocytes upon activation of the stimulator of IFN genes (STING) pathway was enhanced in patients with SLE. We investigated the mechanism of enhanced IFNα production in SLE monocytes. Monocytes enriched from the peripheral blood of SLE patients and healthy controls (HC) were stimulated with 2′3′-cyclic GAMP (2′3′-cGAMP), a ligand of STING. IFNα positive/negative cells were FACS-sorted for RNA-sequencing analysis. Gene expression in untreated and 2′3′-cGAMP-stimulated SLE and HC monocytes was quantified by real-time PCR. The effect of GATA binding protein 4 (GATA4) on IFNα production was investigated by overexpressing GATA4 in monocytic U937 cells by vector transfection. Chromatin immunoprecipitation was performed to identify GATA4 binding target genes in U937 cells stimulated with 2′3′-cGAMP. Differentially expressed gene analysis of cGAS-STING stimulated SLE and HC monocytes revealed the enrichment of gene sets related to cellular senescence in SLE. CDKN2A, a marker gene of cellular senescence, was upregulated in SLE monocytes at steady state, and its expression was further enhanced upon STING stimulation. GATA4 expression was upregulated in IFNα-positive SLE monocytes. Overexpression of GATA4 enhanced IFNα production in U937 cells. GATA4 bound to the enhancer region of IFIT family genes and promoted the expressions of IFIT1, IFIT2, and IFIT3, which promote type I IFN induction. SLE monocytes with accelerated cellular senescence produced high levels of IFNα related to GATA4 expression upon activation of the cGAS-STING pathway

The Statistical Physics of Regular Low-Density Parity-Check Error-Correcting Codes

A variation of Gallager error-correcting codes is investigated using statistical mechanics. In codes of this type, a given message is encoded into a codeword which comprises Boolean sums of message bits selected by two randomly constructed sparse matrices. The similarity of these codes to Ising spin systems with random interaction makes it possible to assess their typical performance by analytical methods developed in the study of disordered systems. The typical case solutions obtained via the replica method are consistent with those obtained in simulations using belief propagation (BP) decoding. We discuss the practical implications of the results obtained and suggest a computationally efficient construction for one of the more practical configurations.Comment: 35 pages, 4 figure