[PDF] Top 20 Efficient Arithmetic on Elliptic Curves over Fields of Characteristic Three
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Efficient Arithmetic on Elliptic Curves over Fields of Characteristic Three
... Weierstraß elliptic curves with a point of order 3 and their equivalent Hessian curves over finite fields of characteristic ...ordinary elliptic curves in ... See full document
14
Analogue of Vélu's Formulas for Computing Isogenies over Hessian Model of Elliptic Curves
... 8. Christophe Doche, Thomas Icart, and David R. Kohel. Efficient scalar multiplication by isogeny decom- positions. In Public Key Cryptography - PKC 2006, 9th International Conference on Theory and Practice of ... See full document
23
Implementing efficient 384-Bit NIST elliptic curves over prime fields on an ARM946E
... An elliptic curve over real numbers can be described by a set of points (x,y) satisfying the equation y 2 = x 3 + ax + b where x, y, a, and b are real ...the elliptic curve y 2 = x 3 + ax + b can be ... See full document
88
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
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 ...in characteristic two, among common ... See full document
18
Heights on elliptic curves over number fields, period lattices, and complex elliptic logarithms
... and elliptic logarithms is an important computation in its own right, and also has a number of applications towards certain algorithms, in- cluding one for determining a lower bound for the canonical height on ... See full document
233
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
Study of Finite Field over Elliptic Curve: Arithmetic Means
... of elliptic curves defined over finite fields, has found applications in ...that elliptic curves over finite fields provide an inexhaustible supply of finite ... See full document
7
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
Efficient Arithmetic In (Pseudo-)Mersenne Prime Order Fields
... requires efficient arithmetic over the underlying ...squaring over the finite field is required for efficient pro- jective coordinate based scalar multiplication as well as for ... See full document
37
Efficient Pairings Computation on Jacobi Quartic Elliptic Curves
... the elliptic curve. Pairing computation on the Edwards model of elliptic curves has been done successively in [9, 10] and ...using elliptic curves of Weierstrass form can be found in ... See full document
23
Faster Cryptographic Hash Function From Supersingular Isogeny Graphs
... supersingular elliptic curves over finite ...of characteristic p, the algorithm requires roughly 2 log p modular multiplications per bit of the ...less efficient than other provably ... See full document
20
Arithmetic deformation theory via arithmetic fundamental groups and nonarchimedean theta functions, notes on the work of Shinichi Mochizuki
... stated over an arbitrary algebraic number field and is established over an arbitrary algebraic number field, and the methods of the proofs do not depend on the specific features of the number field under ... See full document
28
Efficient Arithmetic for the Implementation of Elliptic Curve Cryptography
... of elliptic curve scalar multiplication ...in three as- pects, namely, the finite field arithmetic cost, the critical path delay, and the protection strength from side-channel attacks (SCAs) based on ... See full document
153
Regular Ternary Algorithm for Scalar Multiplication on Elliptic Curves over Finite Fields of Characteristic Three
... that elliptic curves in characteristic three could be applied in cryptographic ...supersingular elliptic curves in characteristic three with great efficiency [12] ... See full document
7
On Efficient Pairings on Elliptic Curves over Extension Fields
... suitable elliptic curves for pairings, namely pairing-friendly curves, which contain the large prime subgroup and the small embedding ...strong elliptic curves used in ECC can be ... See full document
17
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
... IFP ) over finite fields such as RSA [23], DSA [18] and ElGamal [9]. Because of this singularity (requires a shorter key sizes are translated to less power and storage requirements, and reduced computing ... See full document
10
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
On the Torsion Subgroups of Certain Elliptic Curves over Q
... is nonzero, is a nonsingular curve. By Mordell’s theorem, is a finitely generated abelian group and its torsion subgroup is a finite abelian group. Mazur proved that of an elliptic curve over the ... See full document
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