Hyperelliptic curves
Self-pairings on Hyperelliptic Curves
... There has been a lot of work on efficient implementations of the general bilinear pairing e(P, Q). Motivated by the idea of Miller loop shortening [2], many optimizations have been proposed [6, 9, 14, 7]. On the other ...
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Elliptic and Hyperelliptic Curves: a Practical Security Analysis
... elliptic curves for discrete logarithm-based public-key cryptography, there is an active research area investigating the potential of using hyperelliptic curves of genus ...of curves, the best ...
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Infinite-dimensional Lie algebras determined by the space of symmetric squares of hyperelliptic curves
... We construct Lie algebras of vector fields on universal bundles of symmetric squares of hyperelliptic curves of genus g = 1, 2, . . . . For each of these Lie algebras, the Lie subalge- bra of vertical ...
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Néron Tate heights on the Jacobians of high genus hyperelliptic curves
... The first significant new results appear in the fifth chapter, which is essen- tially devoted to the effective computation of arithmetic intersection pairings on hyperelliptic curves, utilising a formula of ...
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Bit Security of the Hyperelliptic Curves Diffie-Hellman Problem
... elliptic curves isogeny theory. The hyperelliptic Ja- cobians also have explicit isogenies, there are some research work on ...of hyperelliptic curve Diffie- Hellman secret keys using ...
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Dickson polynomials, hyperelliptic curves and hyper-bent functions
... and hyperelliptic curves, in a setting as general as possible, in order to make them suitable for use in the study of new families of Boolean ...of hyperelliptic curves is crucial for the ...
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Parity of ranks of Jacobians of hyperelliptic curves of genus 2
... part of the Galois representation 4 . The Weil-Deligne representation for semistable Jacobians of hyperelliptic curves of genus g at odd places are computed in [14]. Remark 3.4.31. The cluster picture ...
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Explicit Mumford isomorphism for hyperelliptic curves
... with hyperelliptic Riemann surfaces, we need to consider for the proof hyperelliptic curves over arbitrary base ...a hyperelliptic curve of genus g over S any smooth, proper curve p : X → S of ...
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Sieving for rational points on hyperelliptic curves
... on our original elliptic curve. By contrast, a program written by Cremona based on more usual sieving ideas (as described in Section 3.6 of of [Cre1]) and running on the same machine, took roughly 95 minutes to find the ...
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A Simple Method for Obtaining Relations Among Factor Basis Elements for Special Hyperelliptic Curves
... For small genus curves, the algorithm is no longer a sub-exponential time algorithm. It can still, however, be faster than the generic Pollard rho algorithm. This was described by Gaudry [6] which led to an ...
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A New Method for Decomposition in the Jacobian of Small Genus Hyperelliptic Curves
... a hyperelliptic curve is a crucial step in an index calculus algorithm for the discrete log problem in the ...genus curves, in the year 2000, Gaudry had proposed a suitable factor basis and a decomposition ...
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An Arakelov-theoretic approach to naïve heights on hyperelliptic Jacobians
... The technique used by all these authors was to work with a projective embedding of the Jacobian or a quotient (usually the Kummer variety), to- gether with equations for the duplication maps, and thereby obtain results ...
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Increasing the Security of SCADA Systems using Key Management and Hyperelliptic Curve Cryptography
... propose Hyperelliptic curves over finite fields key management architecture for a robust SCADA system which supports the replace protocol for availability and reduces the length of keys to be stored in a ...
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Explicit endomorphism of the Jacobian of a hyperelliptic function field of genus 2 using base field operations
... 2 hyperelliptic curves, there are algorithms for arbitrary genus [11], we will present a method to calculate the group operation using only arithmetic in the base field without polynomial pseudo inversion ...
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EdDSA for more curves
... Choosing ` sufficiently large is important for security: standard “rho” attacks use approximately 0.886 √ ` additions on average to determine an EdDSA secret key from an EdDSA public key[r] ...
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STRESS-STRAIN CURVES
... Stress-strain curves are an extremely important graphical measure of a material’s mechanical properties, and all students of Mechanics of Materials will encounter them ...these curves, and in doing so will ...
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Preparation of Calibration Curves
... If, after plotting the data and examining the regression statistics, the calibration data are judged to be satisfactory the calibration equation ( i.e. , the gradient and the intercept) [r] ...
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Tzitzeica Curves and Surfaces »
... asymptotic curves must have nonpositive ...totic curves. To see an example of nontrivial asymptotic/Tzitzeica curves on a Tzitzeica surface, consider the surface z = 1 ë Ix 2 + y 2 M, which is indeed ...
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Twisted Hessian curves
... Completeness relies on two further tools. First, we use a rotated addition law. Unlike the standard (Sylvester) addition law, the rotated addition law is strongly unified. In fact, the rotated addition law works in every ...
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Dynamic Laffer Curves
... Some quali1cations need to be made on the previous results: (a) under our parameterization, tailored to the US economy, feasible tax cuts exist only for values of the intertemporal elast[r] ...
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