##### Department of Mathematics,

University of California San Diego

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### Math 295 - Mathematics Colloquium

## Peter Stevenhagen

#### Leiden University, Netherlands

## Efficient construction of elliptic curves

##### Abstract:

Over the last 20 years, efficient algorithms have been developed to count the number of points of a given elliptic curve over a finite field. We discuss the inverse problem of constructing elliptic curves with a given number of points over a finite field. The difficulty of the problem depends on its exact wording. We present a solution to the problem that easily handles curves of the size occurring in cryptographic practice, and explain why it should be expected to do so.

Host: J. Buhler

### October 7, 2004

### 4:00 PM

### AP&M 6438

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