Dimitar Jetchev
EPFL SB MATH GR-JET
MA C3 605 (Bâtiment MA)
Station 8
CH-1015 Lausanne
Unité: SMA-ENS
Current work
I am currently an SNSF-funded professor and the head of the research group GR-JET in SMA/FSB. Some of my recent research projects include the following:
- Constructing an Euler system from higher dimensional cycles on unitary groups and using it to study the Bloch-Kato conjecture for automorphic representations for unitary groups.
- Constructing universal norms from special cycles in unitary Shimura varieties, proving non-triviality of these norms and Iwasawa theoretic applications (joint with Hunter Brooks and Reda Boumasmoud).
- Birch and Swinnerton-Dyer conjectural formula for elliptic curves of analytic rank 1 (joint with Christopher Skinner and Xin Wan).
- Computing cyclic isogenies for abelian varieties with real multiplication (joint with Alina Dudeanu and Damien Robert).
- Random self-reducibility of the discrete logarithm problem in genus 2 (joint with Benjamin Wesolowski).
- Structure of isogeny graphs of abelian surfaces and threefolds over finite fields (joint with H. Brooks and B. Wesolowski).
Biography
Currently, I am a Swiss National Science Foundation Professor in number theory, arithmetic algebraic geometry and mathematical cryptology at SMA, EPFL. I completed my PhD in number theory and arithmetic geometry at the University of California, Berkeley in 2008 under the supervision of Prof. Ken Ribet. I was then a post-doc at IHES, Bures-sur-Yvette as well as the Laboratory for Cryptologic Algorithms, LACAL at EPFL.
Teaching
- Spring 2017 - Anneaux et Corps
- Fall 2016 - Algebraic Curves and Cryptography
- String 2016 - Number Theory in Cryptography
- Fall 2015 - Algèbre Linéaire : IN/SC - Math 111-(e)
- Spring 2015 - Introduction to Bruhat-Tits theory
- Fall 2014 - Algèbre Linéaire : IN/SC - Math 111-(e)
- Spring 2014 - Introduction to Shimura Varieties
- Fall 2013 - Algèbre Linéaire : IN/SC - Math 111-(e)
- Fall 2011 - Advanced Topics in Cryptology (a course at IC with Prof. Arjen Lenstra)
- Fall 2010 - Algorithms in Public Key Cryptography (a course at IC with Prof. Arjen Lenstra)
EDUCATION
University of California at Berkeley, Ph.D., M.A. in mathematics, May 2008
Ph.D. Thesis: Heegner Points, Component groups, Kolyvagin systems and Selmer groups
Advisor: Prof. Kenneth A. Ribet
Harvard University, B.A. in mathematics, June 2004
RESEARCH INTERESTS
Elliptic curves, Selmer groups, Euler systems, special points, equidistribution, analytic and ergodic methods, mathematical foundations of cryptology, ECC, symmetric key cryptography, complexity analysis of cryptologic algorithms
Publications
MAIN PUBLICATIONS
| E. H. Brooks, D. Jetchev, B. Wesolowski submitted, (2016) |
Isogeny Graphs of Ordinary Abelian Varieties |
| D. Jetchev, C. Skinner, X. Wan submitted, (2016) |
The Birch and Swinnerton-Dyer Formula for Elliptic Curves of Analytic Rank One |
| R. Boumasmoud, E. H. Brooks, D. Jetchev submitted, (2016) |
Vertical Distribution Relations for Special Cycles on Unitary Shimura Varieties |
| A. Dudeanu, D. Jetchev, D. Robert preprint, (2016), (available upon request) |
Cyclic Isogenies for Abelian Varieties with Real Multiplication |
| D. Jetchev submitted, (2015) |
Hecke and Galois Properties of Special Cycles on Unitary Shimura Varieties |
| D. Jetchev, B. Wesolowski preprint, (2015) |
Random Self-Reducibility of the Discrete Logarithm Problem in Genus 2 |
| J. Bos, A. Dudeanu, D. Jetchev J. Math. Cryptology, Vol. 8, No. 1, (2014), pp.71-92 |
Collision bounds for the additive Pollard rho algorithm for solving discrete logarithms |
| D. Jetchev, K. Pietrzak Theory of Cryptography, TCC 2014, Lecture Notes in Computer Science Vol. 8349, (2014), pp 566-590 |
How to Fake Auxiliary Input |
| C. Cornut, D. Jetchev Bull. Lond. Math. Soc., Vol 35, 2, (2013), pp. 370-386 |
Liftings of Reduction Maps for Quaternion Algebras |
| D. Jetchev, O. Oezen, M. Stam Advances in Cryptology, ASIACRYPT 2012, (2012), pp. 313-330 |
Understanding Adaptivity: Random Systems Revisited. |
| A. Duc, D. Jetchev Advances in Cryptology, CRYPTO 2012, LNCS, (2012), pp. 832-849 |
Hardness of Computing Individual Bits for One-Way Functions on Elliptic Curves. |
| D. Jetchev, O. Oezen, M. Stam Theory of Cryptography, TCC 2012, (2012), pp.303-320 |
Collisions Are Not Incidental: A Compression Function Exploiting Discrete Geometry. |
| D. Jetchev, B. Kane Math. Ann., Vol. 350, Issue 3, (2011), pp.501-531 |
Equidistribution of Heegner points and ternary quadratic forms |
| D. Jetchev, K. Lauter, W. Stein J. of Number Theory, Vol. 129, Issue 2, (2009), pp. 284-302 |
Explicit Heegner Points: Kolyvagin's Conjecture and Non-trivial Elements in the Shafarevich-Tate Group |
| D. Jetchev Compositio Math., Vol. 144, Issue 04, (2008), pp. 811-826 |
Global Divisibility of Heegner Points and Tamagawa Numbers |
| D. Jetchev, R. Venkatesan Advances in Cryptology, CRYPTO 2008, LNCS, (2008), Vol. 5157/2008, 75-92 |
Bit Security of the Elliptic Curve Diffie-Hellman Secret Keys |
| K. Eisentraeger, D. Jetchev, K. Lauter Pairing-based Cryptography, PAIRING 2008, LNCS, (2008), Vol. 5209/2008, 113-125 |
Computing the Cassels Pairing on Kolyvagin Classes in the Shafarevich-Tate Group |
| D. Jetchev, W. Stein Documenta Math. 12, (2007), 673--696 |
Visibility of the Shafarevich-Tate Group at Higher Level |
Enseignement & Phd
Enseignement
- Mathematics,
Programmes doctoraux
- Doctoral Program in Mathematics
Doctorants
Cours
Algebraic curves and cryptography
Le but de ce cours est d'introduire les notions fondamentales de la cryptographie à clés publiques basée sur la théorie des courbes algébriques sur les corps finis. On va introduire les schémas basiques ainsi qu'étudier le problème du logarithme discret s... 