Kristin Lauter is a Principal Researcher and Research Manager for 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. Her personal research interests include algorithmic number theory, elliptic curve, pairing-based,  and lattice-based cryptography, homomorphic encryption, and cloud security and privacy, including privacy for healthcare.

Lauter is currently serving as President of the Association for Women in Mathematics, and on the Council of the American Mathematical Society.  She was selected to be a Fellow of the American Mathematical Society in 2014.  She is on the Editorial Board for the SIAM Journal on Applied Algebra and Geometry (SIAGA),  Journal of Mathematical Cryptology, and International Journal of Information and Coding Theory. She was a co-founder of the Women In Numbers Network, a research collaboration community for women in number theory, and she serves on the Scientific Advisory Board for BIRS, the Banff International Research Station.  Lauter is also an Affiliate Professor in the Department of Mathematics at the University of Washington. She received her BA, MS, and PhD, all in mathematics, from the University of Chicago, in 1990, 1991, and 1996, respectively. She was T.H. Hildebrandt Assistant Professor of Mathematics at the University of Michigan (1996-1999), and a Visiting Scholar at Max Planck Institut fur Mathematik in Bonn, Germany (1997), and at Institut de Mathematiques Luminy in France (1999). In 2008, Lauter, together with her coauthors, was awarded the Selfridge Prize in Computational Number Theory.

Here is my CV: Kristin Lauter Curriculum Vitae2016.



Homomorphic Encryption

Established: March 27, 2016

Homomorphic encryption (HE) refers to a special type of encryption technique that allows for computations to be done on encrypted data, without requiring access to a decryption key. While traditional encryption schemes can be used to privately outsource data storage to third parties, the data can not be used for computations without first decrypting it, resulting in a huge loss of utility. Homomorphic encryption allows computations to be performed without first decrypting the data. The results…

Research Collaboration Conferences for Women

Established: November 5, 2012

A new initiative to build networks of female researchers in many areas of mathematics, through Research Collaboration Conferences at math institutes, which focus on building collaboration groups consisting of senior and junior women in a given area. RCCW: The research collaboration networks for women in mathematics linked to this effort so far are WIN, WiSh, WIT, WhAM!, WIG, WINART.  Microsoft Research is proud to have co-funded the WIN, WhAM! and WiSh conferences and the AWM Symposia. WIN: Women…

Elliptic Curve Cryptography (ECC)

Established: January 9, 2012

In the last 25 years, Elliptic Curve Cryptography (ECC) has become a mainstream primitive for cryptographic protocols and applications. ECC has been standardized for use in key exchange and digital signatures. This project focuses on efficient generation of parameters and implementation of ECC and pairing-based crypto primitives, across architectures and platforms.

Secure Multi-Party Computation

Established: June 10, 2011

It is often the case that mutually distrustful parties need to perform a joint computation but cannot afford to reveal their inputs to each other. This can occur, for example, during auctions, data mining, voting, negotiations and business analytics. Secure multi-party computation (MPC) allows a set of parties, each with a private input, to securely and jointly perform any computation over their inputs.

Health and Genomic Privacy

Established: October 1, 2010

Electronic health records make patients' medical information more accessible and mobile, and have the potential to vastly improve health care; however, they also introduce new security and privacy concerns. Emerging technology for sequencing the human genome can help unlock secrets of human health, but making genomic data available also poses important privacy and security challenges. We explore the challenge of preserving patients’ privacy in electronic health record systems and genomics. Privacy for Electronic Medical Records…

Lattice-based Cryptography

Established: July 3, 2010

Lattices are geometric objects that have recently emerged as a powerful tool in cryptography. Lattice-based schemes have also proven to be remarkably resistant to sub-exponential and quantum attacks (in sharp contrast to their number-theoretic friends). Our goal is to use lattices to construct cryptographic primitives that are simultaneously highly efficient and highly functional. Our Techfest Poster on Lattice-based Cryptography

Cloud Security & Cryptography

Established: August 27, 2009

Cloud computing provides clients with a virtual computing infrastructure on top of which they can store data and run applications.  While the benefits of cloud computing are clear, it introduces new security challenges since cloud operators are expected to manipulate client data without necessarily being fully trusted. We are designing cryptographic primitives and protocols tailored to the setting of cloud computing, attempting to strike a balance between security, efficiency and functionality. Projects The current generation of cloud computing infrastructures do not provide any…

Number Theory and Arithmetic Geometry

Established: August 27, 2009

Research on number theory and arithmetic geometry Related Links Cryptography group Events Computer Security and Cryptography (April 12-16, 2010)


Link description

Cloud Security and Privacy


July 18, 2011


Kristin Lauter, Carl Gunter, and Radu Sion


Microsoft Research, University of Illinois at Urbana-Champaign, Stony Brook University


by Google Scholar


Progress in Cryptology — LATINCRYPT 2015, 4th International Conference on Cryptology and Information Security in Latin America, Guadalajara, Mexico, August 23-26, 2015. Lecture Notes in Computer Science 9230, Springer. Co-edited with Francisco Rodriguez-Henriquez.

Selected Areas in Cryptography 2013, Lecture Notes in Computer Science, Springer 2014. Co-edited with Tanja Lange and Petr Lisonek.

WIN–Women in Numbers: Research Directions in Number Theory, Fields Institute Communications Series, Volume 60 (2011). Co-edited with Alina-Carmen Cojocaru, Rachel Pries, Renate Scheidler.

Computational Arithmetic Geometry. AMS Contemporary Mathematics Series, volume 463 (2008). Co-edited with Ken Ribet.

Topics in Algebraic and Noncommutative Geometry, Proceedings of the Conferences in memory of Ruth Michler. AMS Contemporary Mathematics Series, volume 324 (2003) . Co-edited with Caroline Grant Melles, Jean-Paul Brasselet, Gary Kennedy, Lee McEwan.

Articles by area



  • 2015/971 ( PDF ) Attacks on Search RLWE Hao Chen, Kristin Lauter, and Katherine E. Stange
  • 2015/965 ( PDF ) Private Genome Analysis through Homomorphic Encryption Miran Kim and Kristin Lauter,  BioMed Central, Journal of Medical Informatics and Decision Making
  • 2015/758 ( PDF ) Ring-LWE Cryptography for the Number Theorist Yara Elias and Kristin E. Lauter and Ekin Ozman and Katherine E. Stange, Proceedings of WIN3
  • 2015/386 ( PDF ) Privately Evaluating Decision Trees and Random Forests David J. Wu and Tony Feng and Michael Naehrig and Kristin Lauter
  • 2015/176 ( PDF ) Key Recovery for LWE in Polynomial Time Kim Laine and Kristin Lauter
  • 2015/133 ( PDF ) Private Computation on Encrypted Genomic Data Kristin Lauter and Adriana Lopez-Alt and Michael Naehrig, LatinCrypt 2014 (GenoPri 2014).
  • 2015/132 ( PDF ) Homomorphic Computation of Edit Distance Jung Hee Cheon and Miran Kim and Kristin Lauter, Workshop on Applied Homomorphic Cryptography 2015
  • 2015/106 ( PDF ) Provably weak instances of Ring-LWE Yara Elias and Kristin E. Lauter and Ekin Ozman and Katherine E. Stange, CRYPTO 2015
  • 10.1093/bioinformatics/btv563 HEALER: Homomorphic computation of ExAct Logistic rEgRession for secure rare disease variants analysis in GWAS. BioinformaticsShuang Wang, Yuchen Zhang, Wenrui Dai, Kristin Lauter, Miran Kim, Yuzhe Tang, Hongkai Xiong, Xiaoquian Jiang.


Arithmetic geometry

Cryptographic implementation improvements

Algorithmic number theory

Number of points on curves over finite fields

  • Genus-2 curves and Jacobians with a given number of points. LMS Journal of Computation and Mathematics, With Reinier Bröker, Everett W. Howe, Peter Stevenhagen. http://arxiv.org/pdf/1403.6911.pdf
  • New methods for bounding the number of points on curves over finite fields, by Everett W. Howe, Kristin E. Lauter, in Geometry and Arithmetic, Editors: C. Faber, G.Farkas, R. de Jong, European Mathematical Society 2012, pp. 173–212.
  • Pointless curves of genus 3 and 4, by Everett W. Howe, Kristin E. Lauter, Jaap Top, in Arithmetic, 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.
  • Geometric methods for improving the upper bounds on the number of rational points on algebraic curves over finite fields. Lauter, Kristin, with an appendix in French by J.-P. Serre. J. Algebraic Geom. 10 (2001), no. 1, 19–36.
  • Zeta functions of curves over finite fields with many rational points. Kristin Lauter, Coding theory, cryptography and related areas (Guanajuato, 1998), 167–174, Springer, Berlin, 2000.
  • Non-existence of a curve over F3 of genus 5 with 14 rational points. Kristin Lauter, Proc. Amer. Math. Soc. 128 (2000), no. 2, 369–374. MR 1664414.Abstract, references, and article information View Article: PDF
  • Improved upper bounds for the number of rational points on algebraic curves over finite fields. Kristin Lauter, C. R. Acad. Sci. Paris Sér. I Math. 328 (1999), no. 12, 1181–1185.
  • A Formula for Constructing Curves over Finite Fields with Many Rational Points Kristin Lauter, Journal of Number Theory, Volume 74, Issue 1, January 1999, Pages 56-72.
  • Deligne-Lusztig curves as ray class fields. Kristin Lauter, Manuscripta Math. 98 (1999), no. 1, 87–96.
  • Ray Class Field Constructions of Curves over Finite Fields with Many Rational Points, K. Lauter, Algorithmic Number Theory Symposium (ed. by H. Cohen), Lecture Notes in Computer Science 1122, 187-195 Springer, Berlin 1996.

Talks and conferences

Invited talks

Selected past invited talks

Older talks…to be completed:

ANTS II: Algorithmic Number Theory Symposium, Universite de Bordeaux, May 20, 1996.

Oberwolfach Meeting on Finite Fields, Oberwolfach, Germany, January 20, 1997.

Connecticut Valley Undergraduate Colloquium Series, UMass, Amherst, April 23, 1997.

AGCT-6: Arithmetic, Geometry, and Coding Theory, C.I.R.M. Luminy, France, June 24, 1997.

AMS Summer Research Conference, Applications of Curves over Finite Fields, Seattle, 1997.

European Research Conference, Number Theory and Arithmetical Geometry, Spain, Oct 1997.

ICCC: 2nd International Conference on Coding Theory and Cryptography, Mexico, April, 1998.

AMS Fall Western Section Meeting, Tucson, Arizona, November 14-15, 1998

Oberwolfach Meeting on Explicit Methods in Number Theory, Oberwolfach, July, 1999.

AGCT-7: Arithmetic, Geometry, and Coding Theory, October, 1999, C.I.R.M., Luminy, France

Workshop on Unusual Applications of Number Theory, 10-14 January 2000, DIMACS

AMS Western Section Regional Meeting, Invited Address, October, 2000, San Francisco

MSRI Workshop on Number Theory, Genus three curves over finite fields October, 2000

Sixth Pacific North West Number Theory Conference Vancouver, March 2002.

IPAM New Trends in Cryptography, April 2002

University of Michigan Undergraduate Colloquium, April 2002

High Primes and Misdemeanours, Lectures in honour of Hugh Williams, Banff 2003

Pacific Northwest Number Theory Conference, Vancouver, April 2004

BIRS Workshop: Explicit Methods in Number Theory, November, 2004

BIRS Workshop Number Theory Inspired by Cryptography November, 2005.

Steering committees

Program co-chair

Conferences co-organized

Program committees



Homomorphic encryption

Genomic privacy

Cryptographic hash functions

Cryptographic cloud storage

Practical somewhat homomorphic encryption

Women in math