Search results
Results from the WOW.Com Content Network
An important aspect in the study of elliptic curves is devising effective ways of counting points on the curve.There have been several approaches to do so, and the algorithms devised have proved to be useful tools in the study of various fields such as number theory, and more recently in cryptography and Digital Signature Authentication (See elliptic curve cryptography and elliptic curve DSA).
Schoof's algorithm is an efficient algorithm to count points on elliptic curves over finite fields.The algorithm has applications in elliptic curve cryptography where it is important to know the number of points to judge the difficulty of solving the discrete logarithm problem in the group of points on an elliptic curve.
The Schoof–Elkies–Atkin algorithm (SEA) is an algorithm used for finding the order of or calculating the number of points on an elliptic curve over a finite field.Its primary application is in elliptic curve cryptography.
Set of affine points of elliptic curve y 2 = x 3 − x over finite field F 61. Let K = F q be the finite field with q elements and E an elliptic curve defined over K. While the precise number of rational points of an elliptic curve E over K is in general difficult to compute, Hasse's theorem on elliptic curves gives the following inequality:
In mathematics the division polynomials provide a way to calculate multiples of points on elliptic curves and to study the fields generated by torsion points. They play a central role in the study of counting points on elliptic curves in Schoof's algorithm .
A sample elliptical routine for weight loss: Here's an elliptical workout routine designed to help you achieve your weight-loss goals. The entire routine should take 30 minutes. 1. Warm Up (5 minutes)
What you need: An elliptical machine and 25–30 minutes.This workout combines increasing and decreasing intensity to maximize calorie burn. The Routine: Warm-up (5 minutes) 1-minute low intensity
Next we need an algorithm to count the number of points on E. Applied to E, this algorithm (Koblitz and others suggest Schoof's algorithm) produces a number m which is the number of points on curve E over F N, provided N is prime. If the point-counting algorithm stops at an undefined expression this allows to determine a non-trivial factor of N.