Elliptic Curve Cryptography
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.
Publications
2012
- Joppe W. Bos, Marcelo E. Kaihara, Thorsten Kleinjung, Arjen K. Lenstra, and Peter L. Montgomery, Solving a 112-bit Prime Elliptic Curve Discrete Logarithm Problem on Game Consoles using Sloppy Reduction, in International Journal of Applied Cryptography, vol. 2, no. 3, pp. 212–228, Inderscience Enterprises Ltd., 2012
- Kristin Lauter and Damien Robert, Improved CRT Algorithm for Class Polynomials in Genus 2, in Algorithmic Number Theory Symposium, vol. 2012, Mathematical Science Publishers, 2012
- Razvan Barbulescu, Joppe W. Bos, Cyril Bouvier, Thorsten Kleinjung, and Peter L. Montgomery, Finding ECM-Friendly Curves through a Study of Galois Properties, in Algorithmic Number Theory – ANTS-X, Mathematical Science Publishers, 2012
- Reinier Bröker, Kristin Lauter, and Andrew V. Sutherland, Modular polynomials via isogeny volcanoes, in Mathematics of Computation, vol. 81, no. 278, American Mathematical Society, 2012
- Tolga Acar, Dan Shumow, Kristin Lauter, and Michael Naehrig, Affine Pairings on ARM, in Pairing 2012, Springer Verlag, 17 May 2012
2011
- Craig Costello and Kristin Lauter, Group Law Computations on Jacobians of Hyperelliptic Curves, in Selected Areas in Cryptography, Springer, 2011
- Craig Costello, Kristin Lauter, and Michael Naehrig, Attractive Subfamilies of BLS Curves for Implementing High-Security Pairings, in Progress in Cryptology -- INDOCRYPT 2011, Lecture Notes in Computer Science 7107, Springer Verlag, 2011
- Geovandro C. C. F. Pereira, Marcos A. Simplício Jr, Michael Naehrig, and Paulo S.L.M. Barreto, A Family of Implementation-Friendly BN Elliptic Curves, in Journal of Systems and Software, Elsevier, 2011
2010
- Kristin Lauter, Peter L. Montgomery, and Michael Naehrig, An Analysis of Affine Coordinates for Pairing Computation, in Pairing 2010, Springer Verlag, 2010
- Laura Hitt O'Connor, Gary McGuire, Michael Naehrig, and Marco Streng, A CM construction for curves of genus 2 and p-rank 1, in Journal of Number Theory, Elsevier , 2010
- Christophe Arene, Tanja Lange, Michael Naehrig, and Christophe Ritzenthaler, Faster Computation of the Tate Pairing, in Journal of Number Theory, Elsevier , 2010
- Craig Costello, Tanja Lange, and Michael Naehrig, Faster Pairing Computations on Curves with High-Degree Twists, in Public Key Cryptography -- PKC 2010, Springer Verlag, 2010
- Michael Naehrig, Ruben Niederhagen, and Peter Schwabe, New Software Speed Records for Cryptographic Pairings, in LATINCRYPT 2010, Springer Verlag, 2010
2009
- Joppe W. Bos, Marcelo E. Kaihara, Thorsten Kleinjung, Arjen K. Lenstra, and Peter L. Montgomery, On the Security of 1024-bit RSA and 160-bit Elliptic Curve Cryptography, August 2009
- Joppe W. Bos, Marcelo E. Kaihara, and Peter L. Montgomery, Pollard Rho on the PlayStation 3, September 2009
2008
- Michael Naehrig, Paulo S. L. M. Barreto, and Peter Schwabe, On compressible pairings and their computation, in Progress in Cryptology - AFRICACRYPT 2008, Springer, 2008
- Kristin Lauter and Katherine Stange, The Elliptic Curve Discrete Logarithm Problem and Equivalent Hard Problems for Elliptic Divisibility Sequences, in Selected Areas in Cryptography 2008 , Springer Verlag, 2008
2007
- David Freeman and Kristin Lauter, Computing endomorphism rings of Jacobians of genus 2 curves over finite fields, in Proceedings of SAGA 2007, vol. 2007, pp. 10, World Scientific Publishing, 2007
2006
- Denis Xavier Charles, Kamal Jain, and Kristin Lauter, Signatures for Network Coding, in Invited paper: CISS 2006, appeared in: Int. J. Information and Coding Theory (IJICoT), vol. 2006, Inderscience Enterprises Ltd., 2006
- Paulo S. L. M. Barreto and Michael Naehrig, Pairing-friendly elliptic curves of prime order, in Selected Areas in Cryptography - SAC 2005, Springer, 2006
2004
- Kristin Lauter and Denis Charles, Computing Modular Polynomials, no. MSR-TR-2004-75, August 2004
2003
- Kirsten Eisenträger, Kristin Lauter, and Peter L. Montgomery, Improved Weil and Tate pairings for elliptic and hyperelliptic curves, in Algorithmic Number Theory - ANTS-VI, vol. 2003, Springer Verlag, 2003
- Kirsten Eisenträger, Kristin Lauter, and Peter L. Montgomery, Fast Elliptic Curve Arithmetic and Improved Weil Pairing Evaluation, in LNCS 2612, vol. 2002, pp. 112, Springer Verlag, 2003
- Mathieu Ciet, Marc Joye, Kristin Lauter, and Peter L. Montgomery, Trading Inversions for Multiplications in Elliptic Curve Cryptography, in Designs, Codes, and Cryptography, vol. 2003, pp. 257, Springer, 2003
2001
- Amod Agashe, Kristin Lauter, and Ramarathnam Venkatesan, Constructing elliptic curves with a given number of points over a finite field, in Fields Insitute Communications Series, Volume 42, vol. 2001, pp. 96, American Mathematical Society, 2001
Resources
- UCSD Graduate CS course on Elliptic Curve Cryptography, given by Kristin Lauter, Winter 2005
- The Advantages of Elliptic Curve Cryptography for Wireless Security, IEEE Wireless Comm. Magazine, February 2004
Videos
Conferences and Workshops
- Elliptic Curve Cryptography (ECC) Workshops
- Pairing-Based Cryptography (Pairing) Conferences
- The fifth International Conference on Pairing-Based Cryptography - Pairing 2012 in Cologne, Germany, May 2012
- The 25th Anniversary Conference for Elliptic Curve Cryptography in Redmond, October 2010
