Pairing based cryptography is one of the best security solution that devote a lot of attention. So, to make pairing practical, secure and computationally effcient, we choose to work with extension finite field of the form 𝔽
p
k
with k ≥ 12. In this paper, we focus on the case of curves with embedding degree 18. We use the tower building technique, and study the case of degree 2 or 3 twist to carry out most arithmetics operations in 𝔽
p
2 , 𝔽
p
3, 𝔽
p
6, 𝔽
p
9 and 𝔽
p
18, thus we speed up the computation in optimal ate pairing.
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.
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.
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