scholarly journals Supersingular curves with small noninteger endomorphisms

2020 ◽  
Vol 4 (1) ◽  
pp. 7-22
Author(s):  
Jonathan Love ◽  
Dan Boneh
Keyword(s):  
Supersingular Curves

scholarly journals Families of supersingular curves in characteristic 2

2002 ◽  
Vol 9 (5) ◽  
pp. 639-650 ◽  
Author(s):  
Jasper Scholten ◽  
Hui June Zhu
Keyword(s):  
Characteristic 2 ◽  
Supersingular Curves

A comparison of MNT curves and supersingular curves

2006 ◽  
Vol 17 (5) ◽  
pp. 379-392 ◽  
Author(s):  
D. Page ◽  
N. P. Smart ◽  
F. Vercauteren
Keyword(s):  
Supersingular Curves

scholarly journals SUPERSINGULAR EDWARDS CURVES AND EDWARDS CURVE POINTS COUNTING METHOD OVER FINITE FIELD

2020 ◽  
pp. 68-88
Author(s):  
Ruslan Skuratovskii
Keyword(s):  
Finite Field ◽  
Elliptic Curves ◽  
Algebraic Curves ◽  
Discrete Logarithm ◽  
Edwards Curves ◽  
Projective Curves ◽  
Birational Equivalence ◽  
Supersingular Curves ◽  
Edwards Curve ◽  
Embedding Degree

We consider problem of order counting of algebraic affine and projective curves of Edwards [2, 8] over the finite field $F_{p^n}$. The complexity of the discrete logarithm problem in the group of points of an elliptic curve depends on the order of this curve (ECDLP) [4, 20] depends on the order of this curve [10]. We research Edwards algebraic curves over a finite field, which are one of the most promising supports of sets of points which are used for fast group operations [1]. We construct a new method for counting the order of an Edwards curve over a finite field. It should be noted that this method can be applied to the order of elliptic curves due to the birational equivalence between elliptic curves and Edwards curves. We not only find a specific set of coefficients with corresponding field characteristics for which these curves are supersingular, but we additionally find a general formula by which one can determine whether a curve $E_d [F_p]$ is supersingular over this field or not. The embedding degree of the supersingular curve of Edwards over $F_{p^n}$ in a finite field is investigated and the field characteristic, where this degree is minimal, is found. A birational isomorphism between the Montgomery curve and the Edwards curve is also constructed. A one-to-one correspondence between the Edwards supersingular curves and Montgomery supersingular curves is established. The criterion of supersingularity for Edwards curves is found over $F_{p^n}$.

scholarly journals Supersingular Curves in Cryptography

2001 ◽  
pp. 495-513 ◽  
Author(s):  
Steven D. Galbraith
Keyword(s):  
Supersingular Curves

Hyperelliptic supersingular curves

1991 ◽  
pp. 247-284 ◽  
Author(s):  
Frans Oort
Keyword(s):  
Supersingular Curves

scholarly journals Supersingular curves over finite fields and weight divisibility of codes

2014 ◽  
Vol 259 ◽  
pp. 474-484 ◽  
Author(s):  
Cem Güneri ◽  
Gary McGuire
Keyword(s):  
Finite Fields ◽  
Curves Over Finite Fields ◽  
Supersingular Curves

scholarly journals Fibre products of supersingular curves and the enumeration of irreducible polynomials with prescribed coefficients

2016 ◽  
Vol 42 ◽  
pp. 128-164 ◽  
Author(s):  
Omran Ahmadi ◽  
Faruk Göloğlu ◽  
Robert Granger ◽  
Gary McGuire ◽  
Emrah Sercan Yilmaz
Keyword(s):  
Irreducible Polynomials ◽  
Fibre Products ◽  
Supersingular Curves

scholarly journals FPGA Implementation of Various Elliptic Curve Pairings over Odd Characteristic Field with Non Supersingular Curves

2016 ◽  
Vol E99.D (4) ◽  
pp. 805-815
Author(s):  
Yasuyuki NOGAMI ◽  
Hiroto KAGOTANI ◽  
Kengo IOKIBE ◽  
Hiroyuki MIYATAKE ◽  
Takashi NARITA
Keyword(s):  
Elliptic Curve ◽  
Fpga Implementation ◽  
Supersingular Curves ◽  
Characteristic Field

Supersingular Curves of Genus 2 over Finite Fields of Characteristic 2

1992 ◽  
Vol 159 (1) ◽  
pp. 73-81 ◽  
Author(s):  
Gerard Van Der Geer ◽  
Marcel Van Der Vlugt
Keyword(s):  
Finite Fields ◽  
Genus 2 ◽  
Characteristic 2 ◽  
Supersingular Curves
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