Principal Researcher
Manager, Cryptography group

Kristin Lauter is Principal Researcher and the head of the Cryptography Group at Microsoft Research.  She directs the group's research activities in theoretical and applied cryptography and in the related math fields of number theory and algebraic geometry. Group members publish basic research in prestigious journals and conferences and collaborate with academia through joint publications, and by helping to organize conferences and serve on program committees. The group also works closely with product groups, providing consulting services and technology transfer.  The group maintains an active program of post-docs, interns, and visiting scholars. Her personal research interests include algorithmic number theory, elliptic curve cryptography, hash functions, and security protocols.

See the recent article in Science magazine on her work on hash functions.

Conferences organized:

• WIN: Women in Numbers
• AMS Special Session on Low Genus Curves
• 10th Annual Pacific Northwest Number Theory Conference
• IPAM Workshop on Number Theory and Cryptography - Open Problems
• AMS Special Session on Computational Arithmetic Geometry

Program committees: Crypto 2007, ICISC 2007, ANTS 2008, Pairings 2008, Crypto 2008, SAC 2008

Recent talks

Elliptic Curve Cryptography

• The Advantages of Elliptic Curve Cryptography for Wireless Security, IEEE Wireless Comm. Magazine, Feb. 2004
• UCSD Graduate CS course on Elliptic Curve Cryptography, Winter 2005

Recent publications:

Computational Arithmetic Geometry, co-edited with Ken Ribet, AMS Contemporary Mathematics, volume 463.

Cryptography

• Full Cryptanalysis of LPS and Morgenstern Hash Function, by Christophe Petit, Kristin Lauter, Jean-Jacques Quisquater, in Security and Cryptography of Networks 2008
• The Elliptic Curve Discrete Logarithm Problem and Equivalent Hard Problems for Elliptic Divisibility Sequences   by Kristin E. Lauter and Katherine E. Stange, in Selected Areas in Cryptography 2008
• Evaluating large degree isogenies and applications to pairing based cryptography, by Reinier Broker, Denis Charles, Kristin Lauter, in Pairing 2008.
• Stronger Security of Authenticated Key Exchange, by Brian LaMacchia, Kristin Lauter, Anton Mityagin, in ProvSec2007, submitted version, published version.
• Signatures for Network Coding, by Denis Charles, Kamal Jain, Kristin Lauter, Invited paper for CISS06, to appear in Int. J. Information and Coding Theory (IJICoT)
• Security Analysis of KEA Authenticated Key Exchange, by Kristin Lauter and Anton Mityagin, In PKC2006
• Cryptographic hash functions from expander graphs, by Denis Charles, Eyal Goren, Kristin Lauter, Second NIST Hash Function Workshop to appear in Journal of Cryptology.

Arithmetic Geometry

• The distance between superspecial abelian varieties with real multiplication, by Eyal Goren, Kristin Lauter, to appear in Journal of Number Theory.
• Explicit Heegner Points: Kolyvagin's Conjecture and Non-trivial Elements in the Shafarevich-Tate Group. by Dimitar Jetchev, Kristin Lauter, William Stein, to appear in Journal of Number Theory
• Families of Ramanujan graphs and quaternion algebras, by Denis Charles, Eyal Goren, Kristin Lauter, to appear in AMS-CRM volume "Groups and Symmetries" in honor of John McKay.
• Computing the Cassels pairing on Kolyvagin classes in the Shafarevich-Tate group, by Kirsten Eisentraeger, Dimitar Jetchev, Kristin Lauter, in Pairing 2008.
• Evil Primes and Superspecial Moduli, by Eyal Goren, Kristin Lauter, International Mathematics Research Notices, volume 2006, Article ID 53864, pages 1–19. (http://arxiv.org/abs/math/0512472)
• Class invariants of quartic CM fields,by Eyal Goren, Kristin Lauter, Annales de l'Institut Fourier, Vol. 57 no. 2 (2007), p. 457-480. (http://www.arxiv.org/math.NT/0404378)
• Primes in the denominators of Igusa class polynomials, by Kristin Lauter. (http://www.arxiv.org/math.NT/0301240)

Cryptographic implementation improvements

• Improved Weil and Tate pairings for elliptic and hyperelliptic curves, by K. Eisentraeger, K<. Lauter, P.L. Montgomery, In: Algorithmic Number Theory - ANTS-VI, Buell (Ed.), LNCS 3076, 169--183. Published version. http://www.arxiv.org/ math.NT/0311391
• Trading Inversions for Multiplications in Elliptic Curve Cryptography, by Mathieu Ciet, Marc Joye, Kristin Lauter and Peter L. Montgomery, In Designs, Codes, and Cryptography. Published version. http://eprint.iacr.org/2003/257/
• Fast Elliptic Curve Arithmetic and Improved Weil Pairing Evaluation, by K. Eisentraeger, K. Lauter, P.L. Montgomery, In: Topics in Cryptology - CT-RSA 2003, M. Joye (Ed.): LNCS 2612, 343-354, Springer, Berlin 2003.
• The equivalence of the geometric and algebraic group laws for Jacobians of genus 2 curves, by K. Lauter, Topics in Algebraic and Noncommutative Geometry, AMS Contemporary Mathematics Series 324 (2003) 165--171.

Algorithmic number theory

• Modular polynomials for genus 2, by Reinier Broker and Kristin Lauter, submitted to London Math Society Journal of Mathematics and Computation.
• Computing Hilbert class polynomials, by Juliana Belding, Reinier Broker, Andreas Enge, Kristin Lauter, in ANTS 2008, Selfridge Prize for best paper.
• Computing endomorphism rings of Jacobians of genus 2 curves over finite fields, by David Freeman, Kristin Lauter, in Proceedings of SAGA 2007, Number Theory and its applications, World Scientific. (http://www.arxiv.org/math.NT/0701305)
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• Computing Modular Polynomials, by Denis Charles, Kristin Lauter, London Math Society Journal of Computation and Mathematics,  The LMS JCM, (8) 195-204.
• A CRT algorithm for constructing genus 2 curves over finite fields, by Kirsten Eisentraeger, Kristin Lauter, to appear in Proceedings of AGCT 2005. (http://www.arxiv.org/math.NT/0405305)
• Constructing elliptic curves with a known number of points over a prime field, by A. Agashe, K. Lauter, R. Venkatesan, High Primes and Misdemeanours: lectures in honour of the 60th birthday of Hugh Cowie Williams, Fields Institute Communications Series, Volume 42, pp. 1-17.

Number of points on curves over finite fields

• Pointless curves of genus 3 and 4, by Everett W. Howe, Kristin E. Lauter, Jaap Top, inArithmetic, geometry and coding theory, Yves Aubry - Gilles Lachaud (Éd.) Séminaires et Congrès 11 (2005), xviii+216 pages, pp. 125--141.
• Improved upper bounds for the number of points on curves over finite fields, by Everett W. Howe, Kristin E. Lauter, Annales de l'Institut Fourier, volume 53, 6 (2003), 1677--1737.
• The maximum number of points on a curve of genus 4 over F₈ is 25, by David Savitt, with an Appendix by K. Lauter, Canad. J. Math., 55 (2003), 331--352.
• The maximum or minimum number of rational points on genus three curves over finite fields, by Kristin Lauter with an Appendix by J-P. Serre, Compositio Math. 134 (2002) 87--111.

• Publications and preprints
• Biographical sketch