[PDF] Top 20 A New Family of Pairing-Friendly elliptic curves
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A New Family of Pairing-Friendly elliptic curves
... of pairing-friendly elliptic ...supersingular curves of small characteristic, and to the reconsid- eration of the field sizes required for implementation based on non- supersingular ... See full document
16
A short-list of pairing-friendly curves resistant to Special TNFS at the 128-bit security level
... on elliptic curves, where the characteristic is special ...alternative pairing- friendly curves can be ...for pairing-friendly ...a new practical trade-off between ... See full document
30
Constructing Pairing-Friendly Genus 2 Curves with Split Jacobian
... constructing pairing-friendly elliptic curves and simple abelian varieties which are isoge- nous over some extension to a product of elliptic ...generate pairing-friendly ... See full document
22
Optimal TNFS-secure pairings on elliptic curves with even embedding degree
... of elliptic curves com- puted by Fotiadis and Konstantinou [14]; we compute the optimal choice for each family together with the fastest curve shape/pairing combina- ...of elliptic ... See full document
30
Self-pairings on supersingular elliptic curves with embedding degree $three$
... supersingular elliptic curves with even embedding degrees ...supersingular elliptic curves with k = 3 is not an automorphism of the ...of curves in [28]. In this paper, we tackle this ... See full document
15
Parametrizations for Families of ECM-friendly curves
... five new elliptic parametrizations that enable fast generation of curves for all families of curves from ...the family of curves that are, based on their Galois properties, most ... See full document
11
Hashing to elliptic curves of $j$-invariant $1728$
... pairing-friendly curves are Kachisa–Schaefer–Scott (KSS) curves of embedding degree 16 [25, Exam. 4.2], which have become (according to [3], [4], [17]) a popular alternative for those of j = ... See full document
17
On Efficient Pairings on Elliptic Curves over Extension Fields
... that pairing-friendly curves over extension fields could be more suitable for the pairing implementation not relying on a fast field arithmetic of certain extension ...a ... See full document
17
TNFS Resistant Families of Pairing-Friendly Elliptic Curves
... These new variants of the TNFS attacks have a major impact on pairing-based cryptography and particularly on the selection of the underlying elliptic curve groups and extension ...selecting ... See full document
23
Pairing-Friendly Twisted Hessian Curves
... of elliptic curve was being studied, most of the previous articles on this topic were considering even embedding ...the pairing com- putation (avoiding a field inversion) which does not directly apply to ... See full document
24
Scalable Zero Knowledge via Cycles of Elliptic Curves
... and elliptic curves, there is also an engineering ...composing pairing-based zk-SNARKs. Do there exist any other PCD-friendly 2-cycles, not based on MNT curves? Or cycles of length ... See full document
49
An Algebraic Proof of the Associative Law of Elliptic Curves
... Problem For given P and Q is it possible to find n in polynomial time? This is called the discrete logarithm problem and it is known as a very hard one to solve [9]. The security of the elliptic curve cryptography ... See full document
11
Elliptic and Hyperelliptic Curves: a Practical Security Analysis
... Even if the probability of a fruitless cycle is lowered using the look-ahead strategy in Sec- tion 3.1, the walks will still eventually enter a fruitless cycle, which clearly must be dealt with. The first step towards a ... See full document
16
How To Know The Limit Set Of A Fuchsian Group On A Boundary Of A Hyperbolic Plane
... M¨ ob( H ). We consider three cases: γ is parabolic, hyperbolic or elliptic. Let γ ∈ M¨ ob( H ) be a parabolic M¨ obius transformation. By replacing γ with a conjugate transformation, we may assume that γ has its ... See full document
39
Analogue of Vélu's Formulas for Computing Isogenies over Hessian Model of Elliptic Curves
... liptic curves isogenies (SIDH) ...These curves are almost all birationally equivalent to the Weierstrass model but depending on the properties of each curve such as arithmetic of points, a careful choice of ... See full document
23
Pairing computation on Edwards curves with high-degree twists
... Edwards curves which are seen as the intersection of quadric surfaces in ...Tate pairing computation on twisted Edwards ...for pairing computation on twisted Edwards ...of pairing computation ... See full document
14
On Isogeny Graphs of Supersingular Elliptic Curves over Finite Fields
... cessitates a careful treatment of the vertices corresponding to supersingular elliptic curves having j-invariant equal to 0 and 1728. We note that the security of the aforementioned cryptographic schemes ... See full document
14
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
... [14] N. Shylashree, V. Sridhar. "Hardware Realization of Fast Multi-Scalar El- liptic Curve Point Multiplication by Reducing the Hamming Weights Over GF(p)", I.J.Computer Network and Information Security, volume ... See full document
22
Ed3363 (HighFive) -- An alternative Elliptic Curve
... If a non-cryptographer were asked to guess how much stronger TOP SE- CRET cryptography is compared with commercial strength cryptography, I would imagine that most would suggest a hundred times, maybe a thousand times, ... See full document
7
Efficient Arithmetic on Elliptic Curves over Fields of Characteristic Three
... implementing elliptic curve cryptosystems ...a new tripling formulae for Hessian curve in characteristic ...Hessian curves has been presented by Farashahi, Joye, Bernstein, Lange and Kohel [6, ... See full document
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