[PDF] Top 20 On Efficient Pairings on Elliptic Curves over Extension Fields
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On Efficient Pairings on Elliptic Curves over Extension Fields
... of elliptic curve cryptography, three kinds of finite fields have been widely studied, ...friendly curves are usually chosen among ordinary curves over prime fields and ... See full document
17
On Elliptic Curves with Everywhere Good Reduction over Certain Number Fields
... more efficient way (re- ducing the number of Mordell-Weil groups that we have to determine) to achieve this project and also easy-to- read sorted tables of such curves, including information (with ... See full document
8
Darmon points on elliptic curves over number fields of arbitrary signature
... quadratic extension, some standard conjectures concerning the functional equations of twisted L-functions ...defined over ring class fields of ...to curves defined over imaginary ... See full document
36
Self-pairings on supersingular elliptic curves with embedding degree $three$
... supersingular elliptic curves over large different prime fields at AES 80-bit security level since discrete loga- rithms in small characteristic are more vulnerable than that in large ... See full document
15
Regular Ternary Algorithm for Scalar Multiplication on Elliptic Curves over Finite Fields of Characteristic Three
... an efficient and regular ternary algorithm for scalar multiplication on elliptic curves over finite fields of characteristic ... See full document
7
Computing Optimal Ate Pairings on Elliptic Curves with Embedding Degree $9,15$ and $27$
... to efficient computation of pairings on elliptic curves with even embedding degree since the advent of pairing-based ...ate pairings on elliptic curves of embedding ... See full document
27
On Isogeny Graphs of Supersingular Elliptic Curves over Finite Fields
... Two elliptic curves E/k : Y 2 = X 3 +aX + b and E 0 /k : Y 2 = X 3 + a 0 X + b 0 are isomorphic over the extension field K/k if there exists u ∈ K ∗ such that a 0 = u 4 a and b 0 = u 6 ... See full document
14
An Efficient Many-Core Architecture for Elliptic Curve Cryptography Security Assessment
... We present a novel pipelined many-core architecture implementing the parallel version of Pollard rho for elliptic curves over generic prime fields using the negation map speed-up and fruitless ... See full document
18
Implementing efficient 384-Bit NIST elliptic curves over prime fields on an ARM946E
... data. Elliptic Curve Cryptosystems (ECCs) have quickly become the cryptography of choice because of the reduced overhead required in comparison to other cryptosystems to achieve the same level of security, ... See full document
88
Edwards model of elliptic curves defined over any fields
... of elliptic curves dened over elds of all char- ...of elliptic curve called level 4 theta model, comming from theta functions of level 4 ...common curves such as Weierstrass, Edwards, ... See full document
18
Efficient Implementation of Finite Field Multipliers over Binary Extension Fields
... of digital circuits, as the technology node scales down less delay and power is expected. The reason lies in the fact that the smaller the dimensions of transistors become, the less capacitance has to be charged and ... See full document
150
Faster Cryptographic Hash Function From Supersingular Isogeny Graphs
... A class of provably secure hash functions are based on expander graphs. An expander graph is, informally, a graph with low degree and high connectivity. The use of expander graphs for hashing started with the works of ... See full document
20
On the Bit Security of Elliptic Curve Diffie--Hellman
... the elliptic curve Diffie–Hellman key exchange protocol has known even fewer results, mainly because of the inherent nonlinearity of the ...For elliptic curves over prime fields there ... See full document
31
Efficient Arithmetic on Elliptic Curves over Fields of Characteristic Three
... Hessian curves over fields of characteristic ...Weierstraß elliptic curves in characteristic three. The efficient basic group operations are provided for the Weierstraß ... See full document
14
Efficient Pairings Computation on Jacobi Quartic Elliptic Curves
... Ate pairings in a full loop of Miller’s algorithm, based on the fastest operations counts summarized in Tables 3, 4, 5 and ...For elliptic curves with embedding degrees k = 8, we consider the ... See full document
23
On elliptic curves of prime power conductor over imaginary quadratic fields with class number one
... all curves with complex multiplication over K are isogenous to a quadratic twist of E, we are led to determine which quadratic twists have bad reduction at exactly one odd ...quadratic extension K( √ ... See full document
34
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
... computable endomorphism. Presented solution is faster than classic solutions with similar level of security from …ve to nine times. We present method for generation of such curves. We also propose to use this ... See full document
22
Elliptic Curves
... go over the problems that would have caused me insomnia if they were left ...about elliptic curves, but about how to write mathematics and about ... See full document
87
Universal adelic groups for imaginary quadratic number fields and elliptic curves
... an elliptic curve E/Q which gives rise to a different topo- logical group is a non-trivial problem that one can solve in a simple way using the extensive database [RZB14] that was compiled by Rouse and ... See full document
114
Self-pairings on Hyperelliptic Curves
... Abstract. A self-pairing is a pairing computation where both inputs are the same group element. Self-pairings are used in some cryptographic schemes and protocols. In this paper, we show how to compute the ... See full document
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