Profile picture
Administrative data

Dimitar Jetchev

dimitar.jetchev@epfl.ch

EPFL SB MATH TAN
MA C3 604 (Bâtiment MA)
Station 8
1015 Lausanne

Office: MA C3 604
EPFL › SB › MATH › TAN

Website: https://tan.epfl.ch

Expertise

number theory, arithmetic geometry, mathematical cryptology

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).
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.

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

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)

Selected publications

Isogeny Graphs of Ordinary Abelian Varieties

E. H. Brooks, D. Jetchev, B. Wesolowski
Published in submitted, (2016) in

The Birch and Swinnerton-Dyer Formula for Elliptic Curves of Analytic Rank One

D. Jetchev, C. Skinner, X. Wan
Published in submitted, (2016) in

Vertical Distribution Relations for Special Cycles on Unitary Shimura Varieties

R. Boumasmoud, E. H. Brooks, D. Jetchev
Published in submitted, (2016) in

Cyclic Isogenies for Abelian Varieties with Real Multiplication

A. Dudeanu, D. Jetchev, D. Robert
Published in preprint, (2016), (available upon request) in

Hecke and Galois Properties of Special Cycles on Unitary Shimura Varieties

D. Jetchev
Published in submitted, (2015) in

Random Self-Reducibility of the Discrete Logarithm Problem in Genus 2

D. Jetchev, B. Wesolowski
Published in preprint, (2015) in

Collision bounds for the additive Pollard rho algorithm for solving discrete logarithms

J. Bos, A. Dudeanu, D. Jetchev
Published in J. Math. Cryptology, Vol. 8, No. 1, (2014), pp.71-92 in

How to Fake Auxiliary Input

D. Jetchev, K. Pietrzak
Published in Theory of Cryptography, TCC 2014, Lecture Notes in Computer Science Vol. 8349, (2014), pp 566-590 in

Liftings of Reduction Maps for Quaternion Algebras

C. Cornut, D. Jetchev
Published in Bull. Lond. Math. Soc., Vol 35, 2, (2013), pp. 370-386 in

Understanding Adaptivity: Random Systems Revisited.

D. Jetchev, O. Oezen, M. Stam
Published in Advances in Cryptology, ASIACRYPT 2012, (2012), pp. 313-330 in

Hardness of Computing Individual Bits for One-Way Functions on Elliptic Curves.

A. Duc, D. Jetchev
Published in Advances in Cryptology, CRYPTO 2012, LNCS, (2012), pp. 832-849 in

Collisions Are Not Incidental: A Compression Function Exploiting Discrete Geometry.

D. Jetchev, O. Oezen, M. Stam
Published in Theory of Cryptography, TCC 2012, (2012), pp.303-320 in

Equidistribution of Heegner points and ternary quadratic forms

D. Jetchev, B. Kane
Published in Math. Ann., Vol. 350, Issue 3, (2011), pp.501-531 in

Explicit Heegner Points: Kolyvagin's Conjecture and Non-trivial Elements in the Shafarevich-Tate Group

D. Jetchev, K. Lauter, W. Stein
Published in J. of Number Theory, Vol. 129, Issue 2, (2009), pp. 284-302 in

Global Divisibility of Heegner Points and Tamagawa Numbers

D. Jetchev
Published in Compositio Math., Vol. 144, Issue 04, (2008), pp. 811-826 in

Bit Security of the Elliptic Curve Diffie-Hellman Secret Keys

D. Jetchev, R. Venkatesan
Published in Advances in Cryptology, CRYPTO 2008, LNCS, (2008), Vol. 5157/2008, 75-92 in

Computing the Cassels Pairing on Kolyvagin Classes in the Shafarevich-Tate Group

K. Eisentraeger, D. Jetchev, K. Lauter
Published in Pairing-based Cryptography, PAIRING 2008, LNCS, (2008), Vol. 5209/2008, 113-125 in

Visibility of the Shafarevich-Tate Group at Higher Level

D. Jetchev, W. Stein
Published in Documenta Math. 12, (2007), 673--696 in

Teaching & PhD

Past EPFL PhD Students

Réda Boumasmoud, Marius Lorenz Vuille

Past EPFL PhD Students as codirector

Alina Dudeanu