David Freeman Department of Mathematics   University of California Berkeley, CA 94720, USA

Office: 941 Evans Hall email:

Current Research

I am interested in number theory and arithmetic geometry with applications to cryptography. Specific interests include elliptic and hyperelliptic curve cryptography, pairing-based systems, and multi-party computation.

Amongst my current research projects are:

• Constructing pairing-friendly abelian varieties. New preprint now available, as well as additional examples.
• Public-key cryptosystems based on pairings (joint with Dan Boneh and Edward Schaefer).
• Constructing genus 2 curves useful for cryptography (joint with Kristin Lauter and Marco Streng).

My academic advisors are Ken Ribet (UC Berkeley) and Ed Schaefer (Santa Clara University). I am currently supported by the Department of Defense.

Starting in June 2008 I will be a postdoctoral fellow in the Applied Cryptography Group at Stanford University under the supervision of Dan Boneh. From July 2008 I will be supported by a National Science Foundation Mathematical Sciences Postdoctoral Research Fellowship.

From December 2008 to December 2009 I will be a postdoctoral fellow at CWI, Amsterdam and Leiden University under the supervision of Ronald Cramer. I will be supported by a National Science Foundation International Research Fellowship.

Here are my curriculum vitae and travel schedule.

Publications, Presentations, and Preprints

Papers Published or Submitted

• A generalized Brezing-Weng method for constructing pairing-friendly ordinary abelian varieties. Preprint, 2008. Additional examples.
• Abelian varieties with prescribed embedding degree (with P. Stevenhagen and M. Streng). To appear in ANTS-VIII, Banff, Canada, May 2008.
• Constructing pairing-friendly genus 2 curves with ordinary Jacobians. In Pairing-Based Cryptography - Pairing 2007, Springer LNCS 4575, 2007, 152-176.
• Computing endomorphism rings of Jacobians of genus 2 curves over finite fields (with K. Lauter). Symposium on Algebraic Geometry and its Applications, Tahiti, May 2007.
• A taxonomy of pairing-friendly elliptic curves (with M. Scott and E. Teske), preprint, 2006.
• Constructing pairing-friendly elliptic curves with embedding degree 10. ANTS-VII, Springer LNCS 4076, 2006, 452-465.
• The isoperimetric problem on singular surfaces (with A. Cotton, A. Gnepp, T. Ng, J. Spivack, C. Yoder).   Journal of the Australian Mathematical Society 78:2 (April 2005) 167-199.
• The double bubble problem in spherical and hyperbolic space (with A. Cotton).   International Journal of Mathematics and Mathematical Sciences 32:11 (15 Dec 2002), 641-699.

Conference Presentations

• Implementing the genus 2 CM method. Invited talk at AMS Special Session on Low Genus Curves and Applications, AMS-MAA Joint Mathematics Meetings, San Diego, CA, January 2008.
• Constructing pairing-friendly genus 2 curves with ordinary Jacobians. Paring 2007, Tokyo, Japan, July 2007.
• Constructing Pairing-Friendly Elliptic Curves for Cryptography (Part 1, Part 2). Invited talk at the 2nd KIAS-KMS Summer Workshop on Cryptography, Seoul, Korea, June 2007.
• Methods for constructing pairing-friendly elliptic curves. Invited talk at the 10th Workshop on Elliptic Curves in Cryptography (ECC 2006), Toronto, Canada, September 2006.
• Constructing pairing-friendly elliptic curves with embedding degree 10. ANTS-VII, Berlin, Germany, July 2006.

Other Papers

• Pairing-based identification schemes. Hewlett-Packard Laboratories technical report HPL-2005-154, August 2005.
• Fast arithmetic and pairing evaluation on genus 2 curves. Preprint, March 2005.
• Applications of modular forms. Cambridge University Part III Essay, May 2003.

Courses and Teaching

In Fall 2007 I was a Graduate Student Instructor for Math 16a, taught by Jack Wagoner. Section web page.
In Fall 2005 I was a Graduate Student Instructor for Math 1a, taught by Vaughan Jones. Section web page.

I took (and passed) my qualifying exam on May 12, 2005. Here is my syllabus. In theory I know everything on it.

J'ai réussi à l'examen français du département des maths en 2003. Ich habe die Deutsche Prüfung der mathematischen Abteilung in 2006 bestanden.

Other activities

• UC Berkeley University Chorus.
• University of California Alumni Chorus.
• Cal Cycling.
• Harvard Radio Broadcasting (WHRB).
• See what I'm doing in my spare time.
• Fact Tree Enterprises web sites:
  • ClassicalCDGuide.com: This site recommends classical music CDs, with lists of the Top 10 CDs and Top 20 CDs, and recommendations by composer, era, and genre. The site is very extensive, and the reviews are extremely detailed. Great for a beginner or someone looking to expand his or her collection!
  • SailingCourseGuide.com: This guide provides general advice for anyone in the U.S. who wants to sign up for a sailing course, including tips on how to choose between schools and warning signs of problematic programs.
  • SpainAdventure.com: This site guides prospective study abroad students through the wonderful possibilities of studying Spanish in Spain and provides tips on choosing a destination, finding a school, and having a good time.