Computing the order of points on an elliptic curve modulo N is as difficult as factoring N
نویسندگان
چکیده
K e y w o r d s P u b l i c k e y cryptography, Elliptic curves, Costly computational problems.
منابع مشابه
Equivalence of Counting the Number of Points on Elliptic Curve over the Ring Zn and Factoring n
1 I n t r o d u c t i o n Elliptic curves can be applied to public-key cryptosystems, and as such several schemes have been proposed [3, 4, 5, 6, 9, 11]. There are two typical elliptic curve cryptosystems: E1Gamal-type scheme [4, 11] and RSA-type schemes [3, 5, 6]. The security of the EIGamal-type elliptic curve cryptosystem is based on the difficulty of solving a discrete logarithm over ellipt...
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Let $E$ be an elliptic curve over $Bbb{Q}$ with the given Weierstrass equation $ y^2=x^3+ax+b$. If $D$ is a squarefree integer, then let $E^{(D)}$ denote the $D$-quadratic twist of $E$ that is given by $E^{(D)}: y^2=x^3+aD^2x+bD^3$. Let $E^{(D)}(Bbb{Q})$ be the group of $Bbb{Q}$-rational points of $E^{(D)}$. It is conjectured by J. Silverman that there are infinitely many primes $p$ for which $...
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متن کاملThe distribution of the number of points modulo an integer on elliptic curves over finite fields
Let Fq be a finite field and let b and N be integers. We study the probability that the number of points on a randomly chosen elliptic curve E over Fq equals b modulo N . We prove explicit formulas for the cases gcd(N, q) = 1 and N = char(Fq). In the former case, these formulas follow from a random matrix theorem for Frobenius acting on the Ntorsion part of E, obtained by applying density resul...
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ورودعنوان ژورنال:
- Appl. Math. Lett.
دوره 14 شماره
صفحات -
تاریخ انتشار 2001