• Distribution of points on algebraic sets and varieties
• Exponential and character sums
• Curve based cryptography
• Efficient implementation of arithmetic of cryptographic systems
• Algebraic graph theory
• Sparse polynomials over finite fields

Submitted papers:

1. "Difference sets and three-weight linear codes from trinomials",(with M. Shafaeiabr), August 2021.

Published or accepted papers:

1. A note on the stability of trinomials over finite fields, (with K. M. Shokri),
   Finite Fields and Their Applications, Vol. 63, 13 pp, 2020.

2. "On isogeny graphs of supersingular elliptic curves over finite fields", (with G. Adj and A. Menezes), February 2018.
   Finite Fields and Their Applications, Vol. 55, pp 268--283, 2019.

3. "Fibre Products of Supersingular Curves and the Enumeration of Irreducible Polynomials with Prescribed Coefficients", (with Faruk Gologlu, Robert Granger, Gary McGuire and Emrah Yilmaz).
   Finite Fields and Their Applications, Vol. 42, pp 128--164, 2016.

4. "Sets with many pairs of orthogonal vectors over finite fields", (with A. Mohammadian).
   Finite Fields and Their Applications, Vol. 37, pp 179--192, 2016.

5. "Decomposing jacobians of curves over finite fields in the absence of algebraic structure", (with G. McGuire and A. Rojas Leon).
   Journal of Number Theory, Vol. 156, pp 414--431, 2015.

6. "Curves over finite fiels and linear recurring sequences"(with G. McGuire).
   Surveys in Combinatorics, pp 195--220, 2015.

7. "Exponential sums over points of elliptic curves", (with Igor Shparlinski).
   Journal of Number Theory, Vol. 140, pp 299--313, 2014.

8. "An efficient deterministic test for Kloosterman sum zeros", (with Robert Granger).
   Mathematics of Computation, Vol. 83, pp 347--363, 2014.

9. "Weight Distribution of Irreducible Polynomials over Finite Fields".
   in Handbook of Finite Fields and their Applications, edited by G. Mullen and D. Panario, CRC Press, 2013.

10. "On Isogeny Classes of Edwards Curves over Finite Fields", (with Robert Granger).
    Journal of Number Theory, Vol. 132, Issue 6, pp 1337--1358, 2012.

11. "On Stable Quadratic Polynomials", (with Florian Luca, Alina Ostafe and Igor Shparlinski).
    Glasgow Mathematical Journal, Vol. 54, no. 2, pp 359--369, 2012.

12. "Generalization of a Theorem of Carlitz".
    Finite Fields and their Applications, Vol.17, Issue 5, pp 473--480, 2011.

13. "Low Complexity Cubing and Cube Root Computation over $\F_{3^m}$ in Polynomial Basis", (with Francisco Rodriguez-Henriquez).
    IEEE Transactions on Computers, Vol. 59, Issue 10, pp 1297--1308, 2010.

14. "On the Distribution of the Number of Points on Algebraic Curves in Extensions of Finite Fields ",(with Igor Shparlinski).
    Mathematical Research Letters, Vol. 17, Issue 4, pp 689--699, 2010.

15. "On Multiplicative order of Gauss periods", (with Igor Shparlinski and Jose Felipe Voloch).
    International Journal of Number Theory, Vol. 6, Issue 4, pp 887--882, 2010.

16. Bilinear Exponential Sums and Sum-Product Problem on Elliptic Curves", (with Igor Shparlinski).
    Proceedings of the Edinburgh Mathematical Society, Vol. 53, Isuue 01, pp 1--12, 2010.

17. "Graphs with integral spectrum", (with N. Alon, I. Blake, and I. Shparlinski).
    Linear Algebra and Its Applications, Vol. 430, Issue 1, pp 547-552, 2009.

18. "On the parity of the number of irreducible factors of self-Reciprocal polynomials over finite fields", (with Gerardo Vega).
    Finite Fields and Their Applications, Vol. 14, Issue 1, pp 124-131, 2008.

19. "On parallel formulations of scalar multiplications on Koblitz curves ", (with D. Hankerson and F. Rodriguez- Henriquez).
    JUCS, Special Issue on Cryptography in Computer System Security, Springer, vol 14, Issue 3, pp 481-504, 2008.

20. "Software implementation of arithmetic in GF(3^m)", (with D. Hankerson and A. Menezes).
    Proceedings of WAIFI 2007, LNCS, vol. 4547 Springer-Verlag, Berlin, pp 85-102, 2007.

21. "Distribution of matrices with restricted entries over finite fields", (with Igor Shparlinski).
    Indagationes Mathematicae, vol. 18, Issue 3, pp 327-337, 2007.

22. "Geometric progressions in sum-sets over finite fields", (with Igor Shparlinski).
    Monatshefte fur Mathematik, 152, pp 177-185, 2007.

23. "The trace spectra of polynomial bases for GF(2^n)",.
    Applicable Algebra in Engineering, Communication and Computing, 18, pp 391-396, 2007.

24. "Formulas for cube roots in GF(3^m)",(with D. Hankerson and A. Menezes).
    Discrete Applied Mathematics, Volume 155, Issue 3, pp 260-270, 2007.

25. On the distribution of irreducible trinomials over F3".
    Finite Fields and Their Applications, Volume 13, Issue 3, pp 659-664, 2007.

26. "Irreducible polynomials of maximum weight",(with A. Menezes).
    Utilitas Mathematica, 72, 111-123, 2007.

27. Self-reciprocal irreducible pentanomials over F2".
    Designs, Codes and Cryptography, 38, 395-397, 2006.

28. On the number of trace-one elements in polynomial bases for GF(2^n)"(with A. Menezes).
    Designs, Codes and Cryptography, 37, 493-507,2005.

Papers in preparation:

1. BCH codes, m-sequences and intersection of Fermat's hypersurfaces, (with K. M. Shokri).

2. "Sparse Polynomials Over Finite Fields".

3. "On the Quadratic Transformations of Irreducible Polynomials over Finite Fields".

4. "Graphs with Interal Spectrum II".

5. "On the Number of Solutions of some Equations over Finite Fields". (with Rod Gow and Igor Shparlinski)

Theses:

• "Distribution of irreducible polynomials over finite fields", Ph.D. Thesis, Supervisor: Professor A. Menezes.

• " Growth rate of the number of the generators of the direct product of finite groups", MSc. Thesis (in Persian), Supervisor: Professor M. Darafsheh.