Deterministic Randomness Research Articles

Pairgoth: A Modern and Flexible Software for Efficient Go Tournament Organization

Pairing players during a Go tournament is a complex task. One must register the players, pair them using a pairing system, gather the results and display the information to the players. Several standalone programs offer these functionalities, however they are often game-specific and maintained and developed by a single person. The pairing itself is non-trivial, because of different pairing systems and of many parameters influencing them. This creates challenges for an intuitive user interface which can be used by non-experts tournament organizers. In this article, Pairgoth is presented, a new pairing software inspired from Opengotha, a mainstream Go pairing software heavily used in Europe. Several improvements have been added to the pairing algorithm, which has also been made more generic. New pairing systems can easily be implemented in Pairgoth. Although initially designed for Go, it can easily be used for other games such as Chess, Shogi or Scrabble. Pairgoth consists of a pairing engine coupled with a web-based user interface. This allows management of the tournament from several machines, including smartphones. It already supports Swiss and MacMahon pairing systems, while more options are currently under development (Round-Robin, accelerated Swiss, Amalfi, …). Pairgoth was tested in real conditions at the international Grenoble tournament (TIGGRE 2024, 5 rounds Mac-Mahon tournament with top group and super top-group, 158 players from 29k to 7d) and at international Paris tournament (51st TIP, 6 rounds Mac-Mahon tournament with top-group, 160 players from 30k to 8d). Pairgoth was also successfully used during the 2024 European Go Congress in Toulouse, where nearly a thousand players participated. It was used for the prestigious main tournament as well as the majority of the side tournaments. It was recently used in the 2024 KPMC edition, making Pairgoth used in several countries. On top of presenting Pairgoth, this article also tackles challenges encountered in pairing engines such as deterministic randomness, non-uniqueness of pairings, and the computation of fair standing criteria.

Homodyne detection in quantum optics: deterministic extractors and quantum random number generators on ‘vacuum fluctuations’

Quantum random number generators with a continuous variable are considered based on a primary randomness of the outcomes of homodyne measurements of a coherent state. A deterministic method of extraction of truly random 0 and 1 from the primary sequence of measurements of the quadrature of the field in homodyne detection is considered. The method, in the case of independence of successive measurement outcomes, in the asymptotic limit of long sequences, allows us to extract with a polynomial complexity all the true randomness contained in the primary sequence. The method does not require knowledge of the probability distribution function of the primary random sequence, and also does not require additional randomness in the extraction of random 0 and 1. The approach with deterministic randomness extractors, unlike other methods, contains fewer assumptions and conditions that need to be satisfied in the experimental implementation of such generators, and is significantly more effective and simple in experimental implementation. The fundamental limitations dictated by nature for achieving statistical independence of successive measurement outcomes are also considered. The statistical independence of the measurement outcomes is the equivalent of true randomness, in the sense that is possible in the case of the independence of the measurement outcomes, provably, with deterministic extractor, to extract a ‘truly random sequence of 0 and 1’. It is shown that in the asymptotic limit it is possible to extract all the true randomness contained in the outcomes of physical measurements.

Network-Compatible Unconditionally Secured Classical Key Distribution via Quantum Superposition-Induced Deterministic Randomness

Based on the addressability of quantum superposition and its unitary transformation, a network-compatible, unconditionally secured key distribution protocol is presented for arbitrary networking in a classical regime with potential applications of one-time-pad cryptography. The network capability is due to the addressable unitary transformation between arbitrary point-to-point connections in a network through commonly shared double transmission channels. The unconditional security is due to address-sensitive eavesdropping randomness via network authentication. The proposed protocol may offer a solid platform of unconditionally secured classical cryptography for mass-data communications in a conventional network, which would be otherwise impossible.

Grating Theory Approach to Optics of Nanocomposites.

Nanocomposites, i.e., materials comprising nano-sized entities embedded in a host matrix, can have tailored optical properties with applications in diverse fields such as photovoltaics, bio-sensing, and nonlinear optics. Effective medium approaches such as Maxwell-Garnett and Bruggemann theories, which are conventionally used for modeling the optical properties of nanocomposites, have limitations in terms of the shapes, volume fill fractions, sizes, and types of the nanoentities embedded in the host medium. We demonstrate that grating theory, in particular the Fourier Eigenmode Method, offers a viable alternative. The proposed technique based on grating theory presents nanocomposites as periodic structures composed of unit-cells containing a large and random collection of nanoentities. This approach allows us to include the effects of the finite wavelength of light and calculate the nanocomposite characteristics regardless of the morphology and volume fill fraction of the nano-inclusions. We demonstrate the performance of our approach by calculating the birefringence of porous silicon, linear absorption spectra of silver nanospheres arranged on a glass substrate, and nonlinear absorption spectra for a layer of silver nanorods embedded in a host polymer material having Kerr-type nonlinearity. The developed approach can also be applied to quasi-periodic structures with deterministic randomness or metasurfaces containing a large collection of elements with random arrangements inside their unit cells.

Experimental demonstrations of unconditional security in a purely classical regime

So far, unconditional security in key distribution processes has been confined to quantum key distribution (QKD) protocols based on the no-cloning theorem of nonorthogonal bases. Recently, a completely different approach, the unconditionally secured classical key distribution (USCKD), has been proposed for unconditional security in the purely classical regime. Unlike QKD, both classical channels and orthogonal bases are key ingredients in USCKD, where unconditional security is provided by deterministic randomness via path superposition-based reversible unitary transformations in a coupled Mach–Zehnder interferometer. Here, the first experimental demonstration of the USCKD protocol is presented.

Unconditionally secured classical cryptography using quantum superposition and unitary transformation

Over decades quantum cryptography has been intensively studied for unconditionally secured key distribution in a quantum regime. Due to the quantum loopholes caused by imperfect single photon detectors and/or lossy quantum channels, however, the quantum cryptography is practically inefficient and even vulnerable to eavesdropping. Here, a method of unconditionally secured key distribution potentially compatible with current fiber-optic communications networks is proposed in a classical regime for high-speed optical backbone networks. The unconditional security is due to the quantum superposition-caused measurement indistinguishability between paired transmission channels and its unitary transformation resulting in deterministic randomness corresponding to the no-cloning theorem in a quantum key distribution protocol.

BER performance analysis of compound chaotic sequence (CCS)-based NR-DCSK system under multipath fading channel

This paper presents the performance analysis of compound chaotic sequence (CCS)-based noise reduction differential chaos shift keying (NR-DCSK) system under multipath Rayleigh fading channel conditions. The special characteristics of chaotic sequences are their deterministic randomness behaviour that adds security and multipath immunity to the data when used as a carrier in communication systems. In this paper, the chaotic sequences are generated by combining the outputs of chaotic maps, such as logistic map, Chebyshev map, Bernoulli shift map, tent map, etc., leading to new complex sequences known as CCSs. This sequence possesses more randomness, overcomes severe interference levels encountered during transmission and provides higher multipath immunity compared with those of pseudo-noise (PN) codes. Since NR-DCSK is a spread spectrum technique, its performance in wireless multipath fading channels has important considerations. The CCS is used as a carrier in NR-DCSK systems, which leads to improved bit error rate (BER) performance. Comparisons of simulation results to theoretical BER expressions of additive white Gaussian noise (AWGN) and Rayleigh fading channels have been carried out to test the efficiency of the proposed CCS-based NR-DCSK system.

Chaos Theories by Elizabeth Hazen

Reviewed by: Chaos Theories by Elizabeth Hazen Kevin Holton Elizabeth Hazen. Chaos Theories. Alan Squire Publishing, 2016. Chaos theory, a mathematical field studying deterministic randomness, is built on the notion that even without new variables, a tiny change in a given system can have massive effects on the outcome. Chaos Theories, by Elizabeth Hazen, puts the every day minutia of human existence into such terms, analyzing the consequence of a single missed alarm, one missing person out of billions in a time of massive population growth, or a moon that never formed. All these grand ideas are balanced against the narrative of her son's birth, the tiny variable that throws her vast cosmos into turmoil with outcomes as great as they are terrible. With poems appearing in Best American Poetry 2013 and Southwest Review, among other markets, and a style that blends science with song, similar to Kimiko Hahn, Hazen has clearly identified her literary niche. [End Page 37] The opening poem, "Chaos Theory," is this theory in motion, overviewing the idea without slogging through math. "All it takes for things to turn / is a blip, a shift minute as the flutter of wings, / the opening of a door, a telephone / unanswered," Hazen writes. Focusing on these tiny details, she goes on to say, "I wake each day to an alarm," but the poem ends with, "Even this sorry heart, / a periodic after all, pounds wildly / at entrances, exits, the memory of his touch, / try as it will to keep a steady beat." "Ghost Story" focuses more on these anxieties and phantom sensations. The open lines read, "What you heard / is not the same as what was said." Hazen describes the "catastrophe" of a crying child, and how "ghosts / can move through walls, inhabit your skin, reflect / like wavelengths, echoing light or sound, the idea / but not the thing." After several couplets describing the fear that comes with facing an illusionary figure, the narrator chastising herself to be braver because specters like this are not real, the final couplet reads, "The voice you hear is in your head. Over / and over she asks, Then why are you afraid?" Other poems are more rooted in the concrete science for which the collection is named. "Ceres" begins with a quote from NASA describing "gravitational perturbations from Jupiter" that kept Ceres from becoming a full planet. She describes the myth of Jupiter being able to limit Ceres due to her "lesser form," but reminds the reader of "her domain: growth, harvest, motherly love, / and like all mothers she is volatile." After ruminating on Ceres, Hazen writes of her own experience giving birth. "When he pushed through me, / gagging for that first breath, no equation could / contain his need, my relief, the bleeding." In the end, she praises Ceres's strength, writing, "however / the universe has failed you, you endure. […] You are exactly where you want to be." Section two opens with "Strange Attractors," in which Hazen describes how "chaos breeds patterns" in a bar late at night, where "I am strange and turbulent," reminding that "Movement / is a theory too." This more fluid application of science to the quotidian resurfaces in "Thanatosis," where she says "the alternative to fight or flight is tonic immobility," with the narrator reliving the time she hid in her mother's closet, in the pitch black behind her dresses. "While I'm inside this darkness I can see / no difference between death and immobility." This scene plays out again in "Closet," except set from a second-person perspective, addressing an unknown "you" who this time hides in the father's closet, where the narrator finds adult magazines. This discovery of adulthood within her childhood self culminates in the lines, "a word takes shape / like the answer to a question no one has asked you yet." Ghosts likewise return in "When I was a Girl" which begins, "My memory is a haunted house that will / not let me leave." The poem goes on about how this house watches her from every angle, observing her actions, trying "to prove I'm nothing but a neatly folded lie." However, the final two couplets reverse the overbearing tone, embracing a more...

A Novel Digital Image Encryption Algorithm Based on Orbit Variation of Phase Diagram

Chaotic systems have been widely used in digital image encryption algorithms because of their characteristics of deterministic randomness, extreme sensitivity to initial values, etc. Although these chaos-based algorithms are good at performance in general, most of them are ineffective when confronting attacks such as the chosen plain image attack. So, this paper proposes a new digital image encryption algorithm based on orbit variation of phase diagram (AOVPD), which modifies the iterative sequence of chaotic system with the pixel values of plain image. Theoretical analysis proves that the proposed AOVPD has the ability to resist chosen plain image attack within two rounds of operation, while the existing algorithms could be cracked in the same situation. To be specific, AOVPD is effective when confronting various attacks including chosen plain image attack. Also, simulation results show that the proposed algorithm has an outstanding safety performance.

Deterministic Randomness Extraction from Generalized and Distributed Santha--Vazirani Sources

A Santha--Vazirani (SV) source is a sequence of random bits where the conditional distribution of each bit, given the previous bits, can be partially controlled by an adversary. Santha and Vazirani show that deterministic randomness extraction from these sources is impossible. In this paper, we study the generalization of SV sources for nonbinary sequences. We show that unlike the binary setup of Santha and Vazirani, deterministic randomness extraction in the generalized case is sometimes possible. In particular, if the adversary has access to $s$ “nondegenerate” dice that are $c$-sided and can choose one die to throw based on the previous realizations of the dice, then deterministic randomness extraction is possible if $s<c$. We present a necessary condition and a sufficient condition for the possibility of deterministic randomness extraction. These two conditions complement each other in the nondegenerate cases. Next, we turn to a distributed setting. In this setting the SV source consists of a random sequence of pairs $(a_1, b_1), (a_2, b_2), \ldots$ distributed between two parties, where the first party receives $a_i$'s and the second one receives $b_i$'s. The goal of the two parties is to extract common randomness without communication. Using the notion of maximal correlation, we prove a necessary condition and a sufficient condition for the possibility of common randomness extraction from these sources. Based on these two conditions, the problem of common randomness extraction essentially reduces to the problem of randomness extraction from (nondistributed) SV sources. This result generalizes results of Gács and Körner, and Witsenhausen about common randomness extraction from independently and identically distributed sources to adversarial sources.

Minimalist design of a robust real-time quantum random number generator

We present a simple and robust construction of a real-time quantum random number generator (QRNG). Our minimalist approach ensures stable operation of the device as well as its simple and straightforward hardware implementation as a stand-alone module. As a source of randomness the device uses measurements of time intervals between clicks of a single-photon detector. The obtained raw sequence is then filtered and processed by a deterministic randomness extractor, which is realized as a look-up table. This enables high speed on-the-fly processing without the need of extensive computations. The overall performance of the device is around 1 random bit per detector click, resulting in 1.2 Mbit/s generation rate in our implementation.

The variable-interval arithmetic coding using asymptotic deterministic randomness for data compression and encryption

Different from the traditional way which compresses the data first and then encrypts the compressed bit-stream later, a novel compression and encryption scheme using variable model arithmetic coding and coupled chaotic system can encrypt and compress the input plaintext synchronously. However, there will be a compromise between the amount of compression achieved and the amount of security incorporated, because the compression efficiency is determined by the key bit-stream. In this paper, an improved scheme using variable-interval arithmetic coding and asymptotic deterministic randomness has been proposed. The improved scheme is secure because the key bit-stream generated by the asymptotic deterministic randomness can resist previous attacks against chaotic encryption. In addition, the compression efficiency will not change with the key bit-stream, because the statistical model will no longer be changed. The results show that the new scheme can achieve high security and compression efficiency.

Spectral analysis and generation of certain highly oscillatory curves related to chaos

Highly oscillatory phenomena are omnipresent in applications. Two important underlying sources are stochastic fluctuations and deterministic randomness. In this paper, we will present heuristics, theorems, and a few illustrations on the Fourier spectrum and deterministic random time series, based upon our understanding of certain rapid oscillations in chaos.

Distribution of periodic orbits for the Casati–Prosen map on rational lattices

We study numerically the periodic orbits of the Casati–Prosen map, a two-parameter reversible map of the torus, with zero entropy. For rational parameter values, this map preserves rational lattices, and each lattice decomposes into periodic orbits. We consider the distribution function of the periods over prime lattices, and its dependence on the parameters of the map. Based on extensive numerical evidence, we conjecture that, asymptotically, almost all orbits are symmetric, and that for a set of rational parameters having full density, the distribution function approaches the gamma-distribution R ( x ) = 1 − e − x ( 1 + x ) . These properties, which have been proved to hold for random reversible maps, were previously thought to require a stronger form of deterministic randomness, such as that displayed by rational automorphisms over finite fields. Furthermore, we show that the gamma-distribution is the limit of a sequence of singular distributions which are observed on certain lines in parameter space. Our experiments reveal that the convergence rate to R is highly non-uniform in parameter space, being slowest in sharply-defined regions reminiscent of resonant zones in Hamiltonian perturbation theory.

Deterministic extractors for small-space sources

We give polynomial-time, deterministic randomness extractors for sources generated in small space, where we model space s sources on { 0 , 1 } n as sources generated by width 2 s branching programs. Specifically, there is a constant η > 0 such that for any ζ > n − η , our algorithm extracts m = ( δ − ζ ) n bits that are exponentially close to uniform (in variation distance) from space s sources with min-entropy δn, where s = Ω ( ζ 3 n ) . Previously, nothing was known for δ ⩽ 1 / 2 , even for space 0. Our results are obtained by a reduction to the class of total-entropy independent sources. This model generalizes both the well-studied models of independent sources and symbol-fixing sources. These sources consist of a set of r independent smaller sources over { 0 , 1 } ℓ , where the total min-entropy over all the smaller sources is k. We give deterministic extractors for such sources when k is as small as polylog ( r ) , for small enough ℓ.

Symbolic dynamics approach to parameter estimation without initial value

Symbolic dynamics, which partitions the infinite number of finite length trajectories into a finite number of trajectory sets, allows a simplified and “coarse-grained” description of the dynamics of a system with a limited number of symbols. In this Letter, we will show that control parameters affect dynamical characters of symbolic sequences. To be more specific, we will analyze how control parameters affect statistical property of Skewed Tent map symbolic sequences. Besides, we will also analyze how control parameters affect ergodic property of both Logistic map and Tent map symbolic sequences. Both theoretical and experimental results show that the above mentioned effects of control parameters discourage the use of chaotic symbolic sequences in cryptography. Furthermore, we will propose an improved scheme utilizing asymptotic deterministic randomness to avoid the undesirable effects.

Deterministic randomness in a model of finance and growth

Following the literature on growth, cycles and financial development, this paper develops an economic growth model in which the source of endogenous business cycles relates to the allocation of credit between productive investment and consumption. An important role is given to consumer sentiment, because this determines the demand of households for credit; in particular, optimistic beliefs about the economy’s macro performance divert financial resources from investment in favor of consumption. The dynamic analysis indicates that Neimark–Sacker and flip bifurcations eventually separate stable and unstable manifolds and, as a result, a region of nonlinear motion is generated: cycles of various periodicities and chaotic motion characterize the behavior of the long run time paths of accumulated wealth, output and consumption.

Discrete asymptotic deterministic randomness for the generation of pseudorandom bits

The deterministic randomness not only can become a dominant approach in exploring the relationship between chaos and randomness, but also can be associated with some famous number theoretical concepts and open problems in number theory. Compared with chaotic sequences, asymptotic deterministic randomness sequences have the characteristic of multi-value correspondence, which makes those sequences unpredictable in short steps. In this Letter, we will propose the definition of the discrete asymptotic deterministic randomness, and then analyze the dynamical characteristics such as maximum-period and multi-value correspondence. Referring to the NIST800-22 statistical test suite, we will present and discuss two examples of PRBGs based on DADR, from the point of view of FPGA design and randomness quality.

Pseudo-random number generator based on asymptotic deterministic randomness

A novel approach to generate the pseudorandom-bit sequence from the asymptotic deterministic randomness system is proposed in this Letter. We study the characteristic of multi-value correspondence of the asymptotic deterministic randomness constructed by the piecewise linear map and the noninvertible nonlinearity transform, and then give the discretized systems in the finite digitized state space. The statistic characteristics of the asymptotic deterministic randomness are investigated numerically, such as stationary probability density function and random-like behavior. Furthermore, we analyze the dynamics of the symbolic sequence. Both theoretical and experimental results show that the symbolic sequence of the asymptotic deterministic randomness possesses very good cryptographic properties, which improve the security of chaos based PRBGs and increase the resistance against entropy attacks and symbolic dynamics attacks.

How to get more mileage from randomness extractors

AbstractLet 𝒞 be a class of distributions over Bn. A deterministic randomness extractor for 𝒞 is a function E : BnarBm such that for any X in 𝒞 the distribution E(X) is statistically close to the uniform distribution. A long line of research deals with explicit constructions of such extractors for various classes 𝒞 while trying to maximize m.In this paper we give a general transformation that transforms a deterministic extractor E which extracts “few” bits into an extractor E′ that extracts “almost all the bits present in the source distribution.” More precisely, we prove a general theorem saying that if E and 𝒞 satisfy certain properties, then we can transform E into an extractor E′.Our methods build on (and generalize) a technique of Gabizon et al. [FOCS (2004) 394–403] that presents such a transformation for the very restricted class 𝒞 of “oblivious bit‐fixing sources.” The high level idea is to find properties of E and 𝒞 which allow “recycling” the output of E so that it can be “reused” to operate on the source distribution. An obvious obstacle is that the output of E is correlated with the source distribution.Using our transformation we give an explicit construction of a two‐source extractor E : Bn × BnarBm such that for every two independent distributions X1 and X2 over Bn with min‐entropy at least k = (1/2 + δ)n and eps ≤ 2, E(X1,X2) is eps‐close to the uniform distribution on m = 2k ‐ Cδ log(1/eps) bits. This result is optimal except for the precise constant Cδ and improves previous results by Chor and Goldreich [SICOMP 17 (1988) 230–261], Vazirani [Combinatorica 7 (1987) 375–392], and Dodis et al. [RANDOM (2004) 334–344].We also give explicit constructions of extractors for samplable distributions that extract many bits even out of “low‐entropy” samplable distributions. These constructions rely on average case hardness assumptions and extend some previous results by Trevisan and Vadhan [FOCS (2000) 32–42] which give such extractors only for distributions with “high entropy.” © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2008