[PDF] Top 20 Elliptic Curves in Generalized Huff's Model
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Analogue of Vélu's Formulas for Computing Isogenies over Hessian Model of Elliptic Curves
... liptic curves isogenies (SIDH) ...Weierstrass model of an elliptic ...Hessian model, the Edward model, the Jacobi model, the Huff ...These curves are almost all ... See full document
23
Modular elliptic curves over real abelian fields and the generalized Fermat equation $x^{2\ell}+y^{2m}=z^p$
... condition (a) of Theorem 1.2 is satisfied. It is known [Miller 2014] that the class number h + n of K is 1 for all n < 100. Thus condition (b) is also satisfied. Write E n + for the group of units of K and C n + for ... See full document
30
2-Selmer groups and Heegner points on elliptic curves
... Shimura curves with non-maximal level at a prime p ramified in the quaternion algebra (in the special case when p = ...These curves have a p-adic uniformization by a tame étale covering of Drinfeld’s p-adic ... See full document
104
On Indifferentiable Deterministic Hashing into Elliptic Curves
... Abstract. In this paper, we give new deterministic encodings based on Elligator’s model, for some families of elliptic curves. These encodings are almost -injective and easily invertible. This allows ... See full document
29
Periods of Tribonacci sequences and elliptic curves
... order s is not an easy thing. So, for showing that it can be generalized and have a first step towards a broader program, we will do the work at first for Tribonacci sequences, that is, the linear ... See full document
17
Short Signcryption Scheme for the Internet of Things
... scheme S-ECSC for the Internet of things based on elliptic curves cryptosystem; and prove the provable security of S-ECSC under the Random Oracle model, including confidentiality in ... See full document
10
On the Implementation of Unified Arithmetic on Binary Huff Curves
... new model of elliptic curves ...Huff model was revisited in 2010 [14], which fully described and formulated the case of odd char- acteristic fields and provided an outline for binary ...Huff ... See full document
16
Congruence formulas for Legendre modular polynomials
... of generalized elliptic curves E/S, endowed with a locally free subgroup A of rank p such that A +E[2] meets each irreducible component of any geometric fiber of E (E[2] is the subgroup of ... See full document
18
Pairings on Generalized Huff Curves
... on elliptic curves were introduced in 1948 by Weil [21], but their utilization in cryptography is actually quite ...some elliptic curves to a discrete logarithm in some extension of the base ... See full document
9
An Improved Model for Predicting the Scattered S-N Curves
... the S-N ...the S-N curve. In the latter case, the width of the scatter band of the S-N curve in the very-high-cycle domain is much larger than in the high-cycle domain, see ...to model the ... See full document
11
An Algebraic Proof of the Associative Law of Elliptic Curves
... universal polynomials of elliptic curves which are independent of the parameters a and b . More than 10 pages are required to write down the outputs. As we will see their explicit forms are irrelevant for ... See full document
11
Point Decomposition Problem in Binary Elliptic Curves
... We implemented the methods proposed in Section 3 on a desktop computer (Intel(R) Xeon(R) CPU E31240 3.30GHz) using Groebner basis algorithms in Magma [1]. For each parameter set (n, m, n 0 ), we solved 5 random instances ... See full document
13
A New Family of Pairing-Friendly elliptic curves
... friendly curves with an embedding degree of k = 54, which fills a gap that might be useful in the event of a deeper un- derstanding emerging of the true difficulty of the discrete logarithm problem as it applies ... See full document
16
Fixed Argument Pairing Inversion on Elliptic Curves
... is composed of the Miller step which evaluates the Miller function f at two rational points P and Q (or divisors) on the elliptic curve and the final exponentiation step which raises the result value f (P, Q) of ... See full document
10
Hashing to elliptic curves of $j$-invariant $1728$
... However in pairing-based cryptography ordinary elliptic curves of j (E) = 0, 1728 are only interesting [13, Ch. 4]. This is due to the existence of high-degree twists for them, leading to faster pairing ... See full document
17
Elliptic and Hyperelliptic Curves: a Practical Security Analysis
... the curves with m > ...NIST curves, and the addition of two residues might result in a carry occupying an additional word, which slows down the ... See full document
16
Faster arithmetic on elliptic curves using Fp2. Application to GLV-GLS and NIST elliptic curves over Fp isomorphic to twisted Hessian curves over fields extension
... Z=549 768 396874Z. Because number 549 768 396874 is not prime, then we need to …nd generator G 0 of order equal to 274 884 198 437, because it is the biggest prime order of any point on this curve. We can to do this ... See full document
22
Improved Arithmetic on Elliptic Curves over Prime Field
... Using Jacobian coordinates system offer a faster point doubling than projective coordinates system. On other hand, it offer a slower point addition than projective coordinates system, which is usually the most frequent ... See full document
10
Binary quadratic forms, elliptic curves and Schoof's algorithm
... [26], [57, p.111]. These capital results were proved by Gauss [26, art. 171 and art. 183] by means of two constructive demonstrations with the same structure: successive transforma- tions of a starting form f(x, y) ... See full document
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