Publication list 2012
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:
- ML Confidential: Machine Learning on Encrypted Data Thore Graepel, Kristin Lauter, Michael Naehrig 2012/323 ( PDF )
- Can Homomorphic Encryption Be Practical? with Michael Naehrig, Vinod Vaikuntanathan, in CCSW 2011, ACM Cloud Computing Security Workshop 2011.
- Cryptographic Cloud Storage, with Seny Kamara, in Proceedings of Financial Cryptography FC 2010: Workshop on Real-Life Cryptographic Protocols and Standardization.
- Patient Controlled Encryption: patient privacy in electronic medical records, with Josh Benaloh, Melissa Chase, Eric Horvitz, in CCSW'09 ACM Cloud Computing Security Workshop.
- 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
- 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, 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, in Journal of Cryptology.
- The Advantages of Elliptic Curve Cryptography for Wireless Security, IEEE Wireless Comm. Magazine, February 2004
Comparing arithmetic intersection formulas for denominators of Igusa class polynomials, arXiv:1211.0788. by J. Anderson, J. Balakrishnan, K. Lauter, J. Park, B. Viray.
A Gross-Zagier formula for quaternion algebras over totally real fields, by Eyal Z. Goren and Kristin E. Lauter, to appear in Algebra and Number Theory. 2011/666
Igusa class polynomials, embeddings of quartic CM fields, and arithmetic intersection theory, by Helen Grundman, Jennifer Johnson-Leung, Kristin Lauter, Adriana Salerno, Bianca Viray, Erika Wittenborn, in WIN--Women in Numbers: Research Directions in Number Theory, Fields Institute Communications Series, Volume 60 (2011). arXiv:1006.0208 [pdf]
- Genus 2 Curves with Complex Multiplication, Eyal Z. Goren and Kristin E. Lauter, Int Math Res Notices, published online April 12, 2011 doi:10.1093/imrn/rnr052 2010/156
The distance between superspecial abelian varieties with real multiplication, by Eyal Goren, Kristin Lauter, Journal of Number Theory, Volume 129, Issue 6, June 2009, Pages 1562-1578 doi:10.1016/j.jnt.2008.07.005
Explicit Heegner points: Kolyvagin's conjecture and non-trivial elements in the Shafarevich–Tate group by Dimitar Jetchev, Kristin Lauter, William Stein, Journal of Number Theory, Volume 129, Issue 2, February 2009, Pages 284-302
- Families of Ramanujan graphs and quaternion algebras, by Denis Charles, Eyal Goren, Kristin Lauter, in Groups and Symmetries: From Neolithic Scots to John McKay, AMS/CRM, 2009.
- 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
Two is Greater than One, by Joppe W. Bos, Craig Costello, Huseyin Hisil, and Kristin Lauterno. MSR-TR-2012-117, November 2012
Attractive Subfamilies of BLS Curves for Implementing High-Security Pairings, by Craig Costello, Kristin Lauter, and Michael Naehrig, Progress in Cryptology – INDOCRYPT 2011, Lecture Notes in Computer Science 7107, Springer-Verlag (2011), pp 320–342.
Group Law Computations on Jacobians of Hyperelliptic Curves, by Craig Costello and Kristin Lauter, in Selected Areas in Cryptography SAC 2011, Lecture Notes in Computer Science Volume 7118, Springer-Verlag (2012), pp 92-117. 2011/306 (PDF)
An Analysis of Affine Coordinates for Pairing Computation, by Kristin Lauter, Peter L. Montgomery, Michael Naehrig, Pairing-Based Cryptography – Pairing 2010, Lecture Notes in Computer Science 6487, Springer-Verlag (2010), pp 1–20.
- 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
Improved CRT Algorithm for Class Polynomials in Genus 2, by Kristin Lauter and Damien Robert, In ANTS-X: Algorithmic Number Theory Symposium 2012, 2012/443
Explicit CM-theory for level 2-structures on abelian surfaces, by Reinier Broker, David Gruenewald, Kristin Lauter, Algebra and Number Theory, Vol. 5 (2011), No. 4, 495-528. DOI: 10.2140/ant.2011.5.495, arXiv:0910.1848
Computing genus 2 curves from invariants on the Hilbert moduli space, by Kristin Lauter and Tonghai Yang, Journal of Number Theory, Elliptic Curve Cryptography Volume 131, Issue 5 (2011) 2010/294 ( PDF )
- Modular polynomials via isogeny volcanoes Reinier Broker, Kristin Lauter, Andrew V. Sutherland, Mathematics of Computation 2011. DOI:http://dx.doi.org/10.1090/S0025-5718-2011-02508-1 arXiv:1001.0402 [pdf, ps, other]
- Evaluating large degree isogenies and applications to pairing based cryptography, by Reinier Broker, Denis Charles, Kristin Lauter, in Pairing 2008.
- Modular polynomials for genus 2, by Reinier Broker and Kristin Lauter, 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).
- 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, in Proceedings of AGCT 2005: Arithmetics, Geometry, and Coding Theory - Société Mathématique de France, 2011. 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
New methods for bounding the number of points on curves over finite fields, by Everett W. Howe, Kristin E. Lauter, Preprint, 2012. (35 pages)
- 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.