##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Kristin Lauter

#### Microsoft

## Generating curves over finite fields with a known number of points

##### Abstract:

It is often useful in cryptography to be able to generate an elliptic curve over a finite field with a given number of points. This talk will explain the complex multiplication (CM) method for constructing suitable elliptic curves and explain a variant which is joint work with A. Agashe and R. Venkatesan. I will also explain the CM method for generating genus 2 curves and some interesting problems which arise.

Host: Cristian Popescu

### February 26, 2004

### 1:00 PM

### AP&M 7321

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