# A Computational Study of Icart's Function

## Submission Type

Event

## Expected Graduation Date

2015

## Location

Room E102, Center for Natural Sciences, Illinois Wesleyan University

## Start Date

4-18-2015 11:00 AM

## End Date

4-18-2015 12:00 PM

## Disciplines

Number Theory

## Abstract

A hash function maps elements of a larger, initial set into a smaller, resultant set. Sometimes, not all elements in the smaller set will be mapped to as a result; in general it is useful to know the size of this image. Here our target set is the points on an elliptic curve, which has an equation of the form y^2 = x^3 + ax + b. A hash function is useful here in offering a deterministic way to map an input to a pair of x and y values that satisfy such an equation. One such hash function was created by Thomas Icart. The researchers Fouque and Tibouchi provided a bound on the size of the image of Icart's output for curves defined over fields larger than 2^19. This research confirms their result for all fields and for many curves.

A Computational Study of Icart's Function

Room E102, Center for Natural Sciences, Illinois Wesleyan University

A hash function maps elements of a larger, initial set into a smaller, resultant set. Sometimes, not all elements in the smaller set will be mapped to as a result; in general it is useful to know the size of this image. Here our target set is the points on an elliptic curve, which has an equation of the form y^2 = x^3 + ax + b. A hash function is useful here in offering a deterministic way to map an input to a pair of x and y values that satisfy such an equation. One such hash function was created by Thomas Icart. The researchers Fouque and Tibouchi provided a bound on the size of the image of Icart's output for curves defined over fields larger than 2^19. This research confirms their result for all fields and for many curves.