Name: Dr Umar Hayat
Designation: Associate Professor(Tenured)
Department: Mathematics

Qualifications: PhD  University of Warwick, UK
Supervisor: Prof. Miles Reid, FRS

Post-doc.University College Dublin, Ireland
Mentor:  Dr. Miguel Bustamante

Phone: +92-51 9064-2192
Status: On Job
Other Weblink:

Research Interests Publications Conferences Research Projects

Algebraic/Arithmetic Geometry, Cryptography, Discrete Mathematics, Machine Learning, Commutative Algebra

 25. Azam, N. A., Ullah, I., and Hayat, U. (2021). A fast and secure public-key image encryption scheme based on Mordell elliptic curves. Optics and Lasers in Engineering137, 106371. Impact factor: 4.273

24. Haider, T., Barkat, A., Hayat, U., Ali, A., Awais, M., Alam, A., and Shah, M. A. (2021). Identification of radon anomalies induced by earthquake activity using intelligent systems. Journal of Geochemical Exploration222, 106709. Impact factor: 3.352

23. Ullah, Ikram, Naveed Ahmed Azam, and Umar Hayat. "Efficient and secure substitution box and random number generators over Mordell elliptic curves." Journal of Information Security and Applications 56 (2021): 102619. Impact factor: 2.327

22. Ullah, I., Hayat, U., and Bustamante, M. D. (2020). Image Encryption Using Elliptic Curves and Rossby/Drift Wave Triads. Entropy22(4), 454. Impact factor: 2.494

21. Umer, M., Hayat, U., Abbas, F., Agarwal, A., and Kitanov, P. (2020). An Efficient Algorithm for Eigenvalue Problem of Latin Squares in a Bipartite Min-Max-Plus System. Symmetry12(2), 311. Impact factor: 2.645

20. U. Hayat, M. UmerB. Davvaz, I. Gutman, A. Nolla de Celis  A novel method to construct NSSD molecular graphs. Open Math. (Poland)  2019; 17:1526–1537. Impact factor: 0.726

19. U. Hayat, A. Ali, G. Murtaza, M. Ullah, I. Ullah, A. Nolla de Celis, N. Rajpoot, Classification of well log data using vanishing component analysis. Pure Appl. Geophys. (2019).  Impact factor: 1.466

18.  Umar Hayat, Adnan Barkat, Aamir Ali, Khaista Rehman, Shazia Sifat, Talat Iqbal, Fractal analysis of shallow and intermediate-depth seismicity of Hindu Kush,  Chaos solitons & fractals, (United Kingdom), Vol. 128 (2019) 71-82. Impact factor: 3.064

17.  Umar Hayat, Shahid Amanullah, Shane Walsh, Mamoon Abdullah, Miguel D. Bustamante ,Discrete resonant Rossby/drift wave triads: explicit parameterisations and a fast direct numerical search algorithm,  Communications in Nonlinear Science and Numerical Simulation, (Netherlands),  Volume 79, December 2019, 104896. Impact factor: 3.967


16.  Mubasher Umer, Umar Hayat, Fazal Abbas, An efficient algorithm for nontrivial eigenvectors in max-plus algebra,  Symmetry, (Switzerland) , 2019, 11, 738; doi:10.3390/sym11060738. Impact factor: 2.143


15. Naveed Ahmad Azam, Umar Hayat, Ikram Ullah, Efficient construction of a substitution box based on a Mordell elliptic curve over a finite field,  Frontiers of Information Technology & Electronic Engineering, (China), 2019 20(10):1378-1389Impact Factor: 1.033


14.  Umar Hayat, Naveed Ahmad Azam, A novel image encryption scheme based on an elliptic curve, Signal Processing, (Netherlands),  Volume 55(2019)  Pages 391-402. Impact factor: 3.470


13. Naveed Ahmad Azam, Umar Hayat, Ikram Ullah  An lnjective s-box design scheme over an ordered isomorphic elliptic curve and its characterization, Security and Communication Networks, (United Kingdom),  Volume 2018, Article ID 3421725, 9 pages. Impact factor: 0.904



12 .    Umar Hayat, Naveed Ahmed Azam, Muhammad Asif, A method of generating 8 × 8       substitution boxes based on elliptic curves, Wireless Personal Communications, (Netherlands),  Volume 101(2018), Issue 1, pp 439–451. Impact Factor: 1.20


11. Umar Hayat, Daniel López-Aguayo, Akhtar AbbasFixed points of automorphisms of certain non-cyclic p-groups and the dihedral group, Symmetry, (Switzerland),  10(7) 2018, 238. Impact factor: 2.143

10. Adnan Barkat, Aamir Ali, Umar Hayat, Quentin G Crowley, Khaista Rehman, Naila Siddique, Takreem Haidar, Talat IqbalTime series analysis of soil radon in Northern Pakistan: Implications for earthquake forecasting, Applied Geochemistry, (United Kingdom),  Volume 97 (2018),Pages 197-208. Impact factor: 3.0884.

9. U. Hayat, A Note on the canonical divisor of the quasi-homogeneous  affine algebraic varieties, Communications in Algebra, (United States of America), Volume 44 issue 3, 1275-1279, 2016.. Impact Factor: 0.481 

8. U. Hayat , The Cramer varieties Cr(r,r+s,s),  Journal of Geometry and     Physics, (Netherlands),  79 (2014), 53-58. Impact Factor: 0.712

7.  M. Bustamante and U. Hayat, Complete classification of discrete resonant        Rossby/Drift wave triads on periodic domains,   Communications in Nonlinear Science and    Numerical  Simulation, (Netherlands), 18(2013), 2402-2419. Impact Factor: 3.181

6. Q. Mushtaq and U. Hayat, Horadam generalized Fibonacci numbers and the modular group, Indian Journal of Pure and Applied   Mathematics, (India),  38(5): 345-352, October 2007. Impact Factor: 0.252

5. Q. Mushtaq and U. Hayat, Pell Pell-Lucas numbers and the modular  group, Algebra Colloquium, (China), Volume 14  issue:  1(2007)  pp. 97- 102. Impact Factor: 0.394


4. U. HayatA note on the canonical divisor of the generalised affine Stiefel algebraic varieties. International Journal of Algebra, (Bulgaria), Vol. 13, 2019, no. 8, 485-492

3. Fawad Ali, Umar Hayat, Youngjin LiFixed points of automorphisms of

certain finite groups, International Journal of Algebra, (Bulgaria), Vol. 13, 2019, no. 4, 167 – 183

2. U. Hayat, F.  Ali, Fixed points of  automorphisms of  , Journal of Mathematical Analysis, (Kosovo),  Volume 7 Issue  6(2016), Pages 91-101.

1. Umar Hayat, Ghulam Farid, Erdal Karapinar,  Relationships between tropical eigenvectors and tropical fixed points of the group GL(2, R). Italian Journal of Pure and Applied Mathematics, (Italy), Accepted for volume 44.


Recent Conferences/Seminar Participation

Conference Title




Sponsoring Agency

Symposium on Earthquake Studies

National Centre for Physics, Islamabad, Pakistan

National Centre for Physics, Islamabad, Pakistan

4th Dec.-5th Dec. 2019

National Centre for Physics, Islamabad, Pakistan

Seminar on Informatics Asia

Prof. Hiroshi Nagamochi

Kyoto University, Japan

19th Feb.- 21th  Feb, 2019

Kyoto University

3rd International conference on Mathematical Sciences

International Islamic University, Islamabad

Quaid-e-Azam Auditorium, Old Campus, Faisal mosque, Islamabad.

27th April to 28th April, 2017

International Islamic University, Islamabad

Project Title

Principal / Co-Principal Investigator


Sponsoring Agency


Generalised Stiefel manifolds and their applications

Principal Investigator

 172000 PKR

Quaid-i-Azam University, Islamabad

One year


Classification of Rossby and Rossby-Haurwitz wave triads and their applications"




Principal Investigator



1,665,683 PKR






Two years

Quaid-i-Azam University Islamabad, 45320, Pakistan.
Tel: +92-51 9064 0000,