Point Compression and Coordinate Recovery for Edwards Curves over Finite Field

Justus, Benjamin

doi:10.2478/awutm-2014-0014

Cited by 2 publications

(2 citation statements)

References 8 publications

(9 reference statements)

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“…Harold M. Edwards introduced a new formula for elliptic curves over fields of characteristic = 2 ( [14]). Edwards curve have played a big roles in recent elliptic curve method applications ( [15]), technically, it's not an elliptic curve due to its singularities. Even so, we will work with these kind of curve because every Edwards curve is bi-rationally equivalent to an elliptic curve in Weierstrass form, due to symmetry of the Edwards curve.…”

Section: New Compression Points In Edwards Curvesmentioning

confidence: 99%

New Compression Point Reducing Memory Size in Field of Characteristic ≠ 2,3

Assoujaa

Ezzouak

Mouanis

2022

Preprint

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Compression point is a new method to compress the space memory and still have the same data. In this paper, we will present a new method of compression points work well with addition operation in elliptic curve, so instead of storing the value of two points P = (xP,yP ), Q = (xQ,yQ), we will store the addition of the x-coordinates i,e ( α = xP + xQ,yP,yQ) or the y-coordinates i,e (xP,xQ,β = yP + yQ). In this article, we show a new technique for compressing two points in elliptic curve with different coordinate system: Affine, Projective and Jacobian in a field of characteristic ≠ 2 & 3, and show the cost of theses operations. This method can save if we work with affine, Projective or Jacobian coordinates, at least 25%, 17%, 17% of memory size respectively, and also see what happens in case if we take Edwards curve and Montgomery curve cases.

show abstract

Section: New Compression Points In Edwards Curvesmentioning

confidence: 99%

New Compression Point Reducing Memory Size in Field of Characteristic ≠ 2,3

Assoujaa

Ezzouak

Mouanis

2022

Preprint

View full text Add to dashboard Cite

show abstract

Section: New Compression Points In Edwards Curvesmentioning

confidence: 99%

New compression point reducing memory size in field of characteristic different from 2 and 3

Assoujaa

Ezzouak

Mouanis

2022

Preprint

View full text Add to dashboard Cite

Compression point is a new method to compress the space memory and still havethe same data. In this paper, we will present a new method of compression points workwell with addition operation in elliptic curve, so instead of storing the value of two pointsP = (xP;yP), Q = (xQ;yQ), we will store the addition of the x-coordinates i,e(a = xP+xQ;yP;yQ) or the y-coordinates i,e (xP;xQ;b = yP+yQ).In this article, we show a new technique for compressing two points in elliptic curve withdifferent coordinate system: Affine, Projective and Jacobian in a field of characteristic different from 2& 3 , and show the cost of theses operations. This method can save if we work with affine,Projective or Jacobian coordinates, at least 25%, 17%, 17% of memory size respectively,and also see what happens in case if we take Edwards curve and Montgomery curve cases.

show abstract

Point Compression and Coordinate Recovery for Edwards Curves over Finite Field

Cited by 2 publications

References 8 publications

New Compression Point Reducing Memory Size in Field of Characteristic ≠ 2,3

New Compression Point Reducing Memory Size in Field of Characteristic ≠ 2,3

New compression point reducing memory size in field of characteristic different from 2 and 3

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