Research Interests
Arithmetic algebraic geometry, Number theory, Cryptography and Combinatorics; more specifically: Distribution of points on algebraic sets and varieties, Exponential and character sums, Arithmetic of finite fields, Curve based cryptography, Algebraic graph theory, Sparse polynomials over finite fields, Extremal combinatorics.
Professional Service
- Editorial Board Member, Designs, Codes and Cryptography (2017 – present).
- Section Editor for Number Theory, Cryptography and Combinatorics, Bulletin of the Iranian Mathematical Society (2022 - present).
- Chair of Combinatorics and Computing Group, School of Mathematics, IPM (2020-present).
- Hiring Committee Member, School of Mathematics, IPM (2013–present).
- Conference Organizer for multiple IPM Combinatorics and Computing Conferences (IPMCCC).
Academic Appointments
- Associate Professor of Mathematics (with Tenure), Institute for Research in Fundamental Sciences (IPM), Tehran, Iran (June 2016 – present)
- Senior Research Fellow (tenure track), Institute for Research in Fundamental Sciences (IPM), Tehran, Iran (Jun. 2012 – Jul. 2016)
- Postdoctoral Research Fellow, University College Dublin, Dublin, Ireland (Sep. 2008 – May. 2012)
- Postdoctoral Research Fellow, University of Waterloo, Waterloo, Canada (Sep. 2007 - Aug. 2008)
- Postdoctoral Research Fellow, University of Toronto and Fields Institute, Toronto, Canada (Sep. 2006 - Aug. 2007)
Selected Publications
Journal Papers & Book Chapters
For a full list, please see my CV
- (with H. Norouzi) Triangular slice-rank method and set-intesection problems. arXiv:2508.13809.
- (with M. Shafaeiabr) Difference sets and three-weight linear codes from trinomials. Finite Fields and their Applications, Vol. 89, August 2023.
- (with G. Adj, and A. Menezes) On isogeny graphs of supersingular elliptic curves over finite fields. Finite Fields and their Application, Vol. 55, January 2019.
- (with G. McGuire and A. Rojas Leon)Decomposing jacobians of curves over finite fields in the absence of algebraic structure Journal of Number Theory, Vol. 156, pp 414--431, 2015.
- (with G. McGuire) Curves over finite fields and linear recurring sequences. Surveys in Combinatorics 2015, Cambridge University Press, 2015.
- (with R. Granger) An efficient deterministic test for Kloosterman zeros. Mathematics of Computation, Vol. 83, 2014.
- Weight distribution of irreducible polynomials over finite fields. Handbook of Finite Fields and Their Applications, CRC Press, 2013.
- (with R. Granger)On Isogeny Classes of Edwards Curves over Finite Fields Journal of Number Theory, Vol. 132, Issue 6, pp 1337--1358, 2012.
- (with I. Shparlinski) On the distribution of the number of points on algebraic curves in extensions of finite fields. Mathematical Research Letters, Vol. 17, No 4, 2010.
Teaching Experience
- Instructor at IPM, Tehran: Post-quantum Cryptography, Lattice-based Cryptography, Code-based Cryptography, Algebraic Curves, Finite Fields, Elliptic Curves, Introduction to Public Key Cryptography.
- Instructor at University of Waterloo: Introduction to Combinatorics, Linear Algebra II.
- High School Instructor (Iran, 1999-2001): Elementary number theory, Geometry, Combinatorics, Real analysis. Prepared students for national and international mathematical Olympiads.
Education
- Ph.D. in Mathematics, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Canada (Jan 2002 – Aug 2006)
Dissertation: "Distribution of Irreducible Polynomial over Finite Fields". Advisor: Alfred Menezes. - M.Sc. in Mathematics, University of Tehran, Tehran, Iran (Sep 1997 – Aug 1999)
Dissertation: “Growth Sequences in Groups". Advisor: Mohammad Reza Darafsheh. - B.Sc. in Electronics Engineering, University of Tehran, Tehran, Iran (Sep 1993 – Aug 1997)
Honors and Awards
- Outstanding Teaching Assistant Award, University of Waterloo, Canada, Spring 2006.
- Silver Medal, International Mathematical Olympiad, Istanbul, Turkey, 1993.
- Gold Medal, National Olympiad in Mathematics, Iran, 1993.