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Constructing Supersingular Elliptic Curves Depending on the Coefficients of Weierstrass Equation | ||
| journal of the college of basic education | ||
| Article 1, Volume 15, Issue 65, 2010, Pages 169-174 | ||
| Author | ||
| Samaa Fuad Ibraheem | ||
| Abstract | ||
| In the use of elliptic curves in its applications (especially in cryptography), one often needs to construct elliptic curves with a known type (number of points) over a given finite field Fp, where some types are more secure than others. So we introduce a simple way to construct a supersingular elliptic curve by computing the coefficient of xp-1 in f(x)(p-1)/2 wheref(x)= x3+ax+b. And we give an algorithm that compute that coefficient and construct the required curve.Keywords: Weierstrass equation, supersingular elliptic curve, cryptography, algorithm. | ||
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