165 research outputs found
On a new generalization of Huff curves
Recently two kinds of Huff curves were introduced as elliptic curves models and their arithmetic was studied. It was also shown that they are suitable for cryptographic use such as Montgomery curves or Koblitz curves (in Weierstrass form) and Edwards curves.
In this work, we introduce the new generalized Huff curves with , which contains the generalized Huff\u27s model with of Joye-Tibouchi-Vergnaud and the generalized Huff curves with of Wu-Feng as a special case.
The addition law in projective coordinates is as fast as in the previous particular cases. More generally all good properties of the previous particular Huff curves, including completeness and independence of two of the four curve parameters, extend to the new generalized Huff curves. We verified that the method of Joye-Tibouchi-Vergnaud for computing of pairings can be generalized over the new curve
Migration and Elastic Labour in Economic Development: Southeast Asia before World War II
Between 1880 and 1939, Burma, Malaya and Thailand received inflows of migrants from India and China comparable in size to European immigration in the New World. This article examines the forces that lay behind this migration to Southeast Asia and asks if experience there bears out Lewis' unlimited labor supply hypothesis. We find that it does and, furthermore, that immigration created a highly integrated labor market stretching from South India to Southeastern China. Emigration from India and China and elastic labor supply are identified as important components of Asian globalization before the Second World War.
Analogue of Vélu\u27s Formulas for Computing Isogenies over Hessian Model of Elliptic Curves
Vélu\u27s formulas for computing isogenies over Weierstrass model of elliptic curves has been extended to other models of elliptic curves such as the Huff model, the Edwards model and the Jacobi model of elliptic curves. This work continues this line of research by providing efficient formulas for computing isogenies over elliptic curves of Hessian form. We provide explicit formulas for computing isogenies of degree 3 and isogenies of degree l not divisible by 3. The theoretical cost of computing these maps in this case is slightly faster than the case with other curves. We also extend the formulas to obtain isogenies over twisted and generalized Hessian forms of elliptic curves. The formulas in this work have been verified with the Sage software and are faster than previous results on the same curve
Side Channel Attacks against Pairing over Theta Functions
In \cite{LuRo2010}, Lubicz and Robert generalized the Tate pairing over any abelian variety and more precisely over Theta functions. The security of the new algorithms is an important issue for the use of practical cryptography. Side channel attacks are powerful attacks, using the leakage of information to reveal sensitive data. The pairings over elliptic curves were sensitive to side channel attacks. In this article, we study the weaknesses of the Tate pairing over Theta functions when submitted to side channel attacks
Elliptic Curve Arithmetic for Cryptography
The advantages of using public key cryptography over secret key
cryptography include the convenience of better key management and
increased security. However, due to the complexity of the
underlying number theoretic algorithms, public key cryptography
is slower than conventional secret key cryptography, thus
motivating the need to speed up public key cryptosystems.
A mathematical object called an elliptic curve can be used in the
construction of public key cryptosystems. This thesis focuses on
speeding up elliptic curve cryptography which is an attractive
alternative to traditional public key cryptosystems such as RSA.
Speeding up elliptic curve cryptography can be done by speeding
up point arithmetic algorithms and by improving scalar
multiplication algorithms. This thesis provides a speed up of
some point arithmetic algorithms. The study of addition chains
has been shown to be useful in improving scalar multiplication
algorithms, when the scalar is fixed. A special form of an
addition chain called a Lucas chain or a differential addition
chain is useful to compute scalar multiplication on some elliptic
curves, such as Montgomery curves for which differential addition
formulae are available. While single scalar multiplication may
suffice in some systems, there are others where a double or a
triple scalar multiplication algorithm may be desired. This
thesis provides triple scalar multiplication algorithms in the
context of differential addition chains. Precomputations are
useful in speeding up scalar multiplication algorithms, when the
elliptic curve point is fixed. This thesis focuses on both
speeding up point arithmetic and improving scalar multiplication
in the context of precomputations toward double scalar
multiplication. Further, this thesis revisits pairing
computations which use elliptic curve groups to compute pairings
such as the Tate pairing. More specifically, the thesis looks at
Stange's algorithm to compute pairings and also pairings on
Selmer curves. The thesis also looks at some aspects of the
underlying finite field arithmetic
Chaos synchronization in generalized Lorenz systems and an application to image encryption
Examples of synchronization, pervasive throughout the natural world, are often awe-inspiring because they tend to transcend our intuition. Synchronization in chaotic dynamical systems, of which the Lorenz system is a quintessential example, is even more surprising because the very defining features of chaos include sensitive dependence on initial conditions. It is worth pursuing, then, the question of whether high-dimensional extensions of such a system also exhibit synchronization. This study investigates synchronization in a set of high-dimensional generalizations of the Lorenz system obtained from the inclusion of additional Fourier modes. Numerical evidence supports that these systems exhibit self-synchronization. An example application of this phenomenon to image encryption is also provided. Numerical experiments also suggest that there is much more to synchronization in these generalized Lorenz systems than self-synchronization; while setting the dimension of the driver system higher than that of the receiver system does not result in perfect synchrony, the smaller the dimensional difference between the two, the more closely the receiver system tends to follow the driver, leading to self-synchronization when their dimensions are equal. © 2021 The Author
Range, Endurance, and Optimal Speed Estimates for Multicopters
Multicopters are among the most versatile mobile robots. Their applications range from inspection and mapping tasks to providing vital reconnaissance in disaster zones and to package delivery. The range, endurance, and speed a multirotor vehicle can achieve while performing its task is a decisive factor not only for vehicle design and mission planning, but also for policy makers deciding on the rules and regulations for aerial robots. To the best of the authors’ knowledge, this work proposes the first approach to estimate the range, endurance, and optimal flight speed for a wide variety of multicopters. This advance is made possible by combining a state-of-the-art first-principles aerodynamic multicopter model based on blade-element-momentum theory with an electric-motor model and a graybox battery model. This model predicts the cell voltage with only 1.3% relative error ( 43.1mV ), even if the battery is subjected to non-constant discharge rates. Our approach is validated with real-world experiments on a test bench as well as with flights at speeds up to 65km/h in one of the world’s largest motion-capture systems. We also present an accurate pen-and-paper algorithm to estimate the range, endurance and optimal speed of multicopters to help future researchers build drones with maximal range and endurance, ensuring that future multirotor vehicles are even more versatile
Angular Power Spectra with Finite Counts
Angular anisotropy techniques for cosmic diffuse radiation maps are powerful
probes, even for quite small data sets. A popular observable is the angular
power spectrum; we present a detailed study applicable to any unbinned source
skymap S(n) from which N random, independent events are observed. Its exact
variance, which is due to the finite statistics, depends only on S(n) and N; we
also derive an unbiased estimator of the variance from the data. First-order
effects agree with previous analytic estimates. Importantly, heretofore
unidentified higher-order effects are found to contribute to the variance and
may cause the uncertainty to be significantly larger than previous analytic
estimates---potentially orders of magnitude larger. Neglect of these
higher-order terms, when significant, may result in a spurious detection of the
power spectrum. On the other hand, this would indicate the presence of
higher-order spatial correlations, such as a large bispectrum, providing new
clues about the sources. Numerical simulations are shown to support these
conclusions. Applying the formalism to an ensemble of Gaussian-distributed
skymaps, the noise-dominated part of the power spectrum uncertainty is
significantly increased at high multipoles by the new, higher-order effects.
This work is important for harmonic analyses of the distributions of diffuse
high-energy gamma-rays, neutrinos, and charged cosmic rays, as well as for
populations of sparse point sources such as active galactic nuclei.Comment: 27 pages, 8 figure
Impact of Point Spread Function Higher Moments Error on Weak Gravitational Lensing II: A Comprehensive Study
Weak gravitational lensing, or weak lensing, is one of the most powerful
probes for dark matter and dark energy science, although it faces increasing
challenges in controlling systematic uncertainties as \edit{the statistical
errors become smaller}. The Point Spread Function (PSF) needs to be precisely
modeled to avoid systematic error on the weak lensing measurements. The weak
lensing biases induced by errors in the PSF model second moments, i.e., its
size and shape, are well-studied. However, Zhang et al. (2021) showed that
errors in the higher moments of the PSF may also be a significant source of
systematics for upcoming weak lensing surveys. Therefore, the goal of this work
is to comprehensively investigate the modeling quality of PSF moments from the
to order, and estimate their impact on
cosmological parameter inference. We propagate the \textsc{PSFEx} higher
moments modeling error in the HSC survey dataset to the weak lensing
\edit{shear-shear correlation functions} and their cosmological analyses. We
find that the overall multiplicative shear bias associated with errors in PSF
higher moments can cause a shift on the cosmological
parameters for LSST Y10. PSF higher moment errors also cause additive biases in
the weak lensing shear, which, if not accounted for in the cosmological
parameter analysis, can induce cosmological parameter biases comparable to
their uncertainties for LSST Y10. We compare the \textsc{PSFEx} model
with PSF in Full FOV (\textsc{Piff}), and find similar performance in modeling
the PSF higher moments. We conclude that PSF higher moment errors of the future
PSF models should be reduced from those in current methods to avoid a need to
explicitly model these effects in the weak lensing analysis.Comment: 24 pages, 17 figures, 3 tables; Submitted to MNRAS; Comments welcome
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