Sartaj Ul Hasan - Research

Research Interests

Finite Fields
Cryptography
Coding Theory

I'm interested in all aspects of finite fields and their applications in cryptography, coding theory, combinatorics, number theory, and discrete mathematics.

Publication

(with Kirpa Garg, Chunlei Li, Hridesh Kumar, Mohit Pal) Permutation polynomials with a few terms over finite fields, Advances in Mathematics of Communications, to appear.
(with Kirpa Garg and Pantelimon Stanica) The differential properties of certain permutation polynomials over finite fields, International Journal of Foundations of Computer Science, to appear.
(with Kirpa Garg, Constanza Riera and Pantelimon Stanica) The second-order zero differential spectra of some APN and other maps over finite fields, Journal of Algebra and Its Applications, to appear.
(with Hridesh Kumar) Local permutation polynomials and their companions, Finite Fields and Their Applications, Vol. 109, Article No. 102717, 2026.
(with Ramandeep Kaur) Some new classes of permutation polynomials and their compositional inverses, Finite Fields and Their Applications, Vol. 108, Article No. 102685, 2025.
(with Kirpa Garg, Constanza Riera and Pantelimon Stanica) The second-order zero differential spectra of some functions over finite fields, Cryptography and Communication, Vol. 17, pp. 665 - 694, 2025 Volume
(with Kirpa Garg, Constanza Riera and Pantelimon Stanica) The revised boomerang connectivity tables and their connection to the difference distribution table, Designs, Codes and Cryptography, Vol 93, pp. 1951 - 1984, 2025.,s 1–1984, (2025)
(with Kirpa Garg and Pantelimon Stanica) Differential properties of some classes of permutation polynomials, Journal of Computational Algebra, Volumes 13-14, Article No. 100035, 2025.
(with Mohit Pal) Dembowski-Ostrom polynomials and Dickson polynomials, Advances in Mathematics of Communications, Vol. 18, pp. 1084 - 1099, 2024.
(with Kirpa Garg and Pantelimon Stanica) Boomerang uniformity of some classes of functions over finite fields, Discrete Applied Mathematics, Vol. 343, pp. 166 - 179, 2024.
(with Mohit Pal and Pantelimon Stanica) The binary Gold function and its c-boomerang connectivity table, Cryptography and Communication, Vol. 14, pp. 1257 - 1280, 2022.
(with Mohit Pal and Pantelimon Stanica) The c-differential uniformity and boomerang uniformity of two classes of permutation polynomials, IEEE Transactions on Information Theory, Vol. 68, No. 1, pp. 679 - 691, 2022.
(with Mohit Pal and Pantelimon Stanica) Boomerang uniformity of a class of power maps, Designs, Codes and Cryptography, Vol. 89, pp. 2627- 2636, 2021.
(with Neranga Fernando and Mohit Pal) Dembowski-Ostrom polynomials and reversed Dickson polynomials, Discrete Applied Mathematics, Vol. 298, pp. 66-79, 2021.
(with Mohit Pal, Constanza Riera and Pantelimon Stanica) On the c-differential uniformity of certain maps over finite fields, Designs, Codes and Cryptography, Vol. 89, pp. 221-239, 2021.
(with Daniel Panario and Qiang Wang) Nonlinear vectorial primitive recursive sequences, Cryptography and Communication, Volume 10, Issue 6, pp. 1075-1090, 2018.
(with Susil Kumar Bishoi and Himanshu Kumar Haran) A note on the multiple-recursive matrix method for generating pseudorandom vectors, Discrete Applied Mathematics, 222, pp. 67-75, 2017.
(with Stephen D. Cohen, Daniel Panario and Qiang Wang) An asymptotic formula for the number of irreducible transformation shift registers, Linear Algebra and its Applications, 484, pp. 46-62, 2015.
(with Peter Beelen and Sudhir R. Ghorpade) Linear codes associated to determinantal varieties, Discrete Mathematics, 338, pp. 1493-1500, 2015.
(with Daniel Panario and Qiang Wang) Word-oriented transformation shift registers and their linear complexity, in Proceedings of SEquences and Their Applications - SETA 2012, T. Helleseth and J. Jedwab Eds., Lecture Notes in Computer Science, Springer, Berlin, Vol. 7280, pp. 190-202, 2012.
(with Sudhir R. Ghorpade and Meena Kumari) Primitive polynomials, Singer cycles, and word-oriented linear feedback shift registers, Designs, Codes and Cryptography, Vol. 58, No. 2, pp. 123-134, 2011.

Research Grants

Start-up Research Grant - SRG (SRG/2019/000295) by Science and Engineering Research Board, Govt. of India, Dec 2019- March 2022.
Mathematical Research Impact Centric Support - MATRICS (MTR/2019/000744) by Science and Engineering Research Board, Govt. of India, Feb 2020 - Feb 2023.
Core Research Grant - CRG (CRG/2022/005418) by Science and Engineering Research Board, Govt. of India, Jan 2023 - Jan 2026.
CARS Project - CARS (SAG/4600/TCID/CARS/C-63) by Defence Research and Development Organisation, Govt. of India, March 2023 - March 2025

Doctoral Students

Mohit Pal

Mohit successfully defended his doctoral thesis titled "Some classes of polynomials over finite fields" on October 12, 2021. He is currently a postdoctoral fellow at the University of Bergen in Norway.

Academic Visits

The Selmer Center in Secure Communication, University of Bergen, Bergen, Norway, July 15 - September 16, 2022. (Host: Chunlei Li)
The Selmer Center in Secure Communication, University of Bergen, Bergen, Norway, June 01 - 29, 2024. (Host: Chunlei Li)

Reviewer for Journals

Advances in Mathematics of Communications.
Cryptography and Communications.
Designs, Codes and Cryptography.
Discrete Applied Mathematics.
European Journal of Combinatorics.
Finite Fields and Their Applications.
IEEE Transactions on Information Theory.
Journal of Computer Science and Technology.
Theoretical Computer Science.

Reviewer for Conferences

Boolean Functions and their Applications–BFA.
IEEE International Symposium on Information Theory–ISIT.
SEquences and Their Applications–SETA.

Member of Professional Bodies

Life member of Ramanujan Mathematical Society (RMS).
Life member of Cryptology Research Society of India (CRSI).
Life member of Indian Mathematical Society (IMS).
Associate member of The Mathematics Consortium (TMC).

Awards/Honours

DRDO Young Scientist of the Year Award, Defence Research and Development Organisation, 2014.
Laboratory Scientist of the Year Award, Scientific Analysis Group, Defence Research and Development Organisation, 2009.
Senior Research Fellowship [From Ministry of Human Resources Development (MHRD), Govt. of India], for the Graduate Study at Indian Institute of Technology Bombay, August 2004-February 2007.
Junior Research Fellowship [From Ministry of Human Resources Development (MHRD), Govt. of India], for the Graduate Study at Indian Institute of Technology Bombay, July 2002-July 2004.
Qualified in the Graduate Aptitude Test in Engineering (GATE), an All-India Examination conducted by the Indian Institutes of Technology and the Indian Institute of Science, Bangalore, on behalf of the National Coordinating Board - GATE, Department of Education, Ministry of Human Resources Development (MHRD), Government of India, February 2002.
Qualified in the National Eligibility Test for Lectureship (NET), an All-India Examination jointly conducted by Council of Scientific & Industrial Research and University Grant Commission, India, June 2002.
University Medal for the best performance in the faculty of science and life science, Master of Science, Aligarh Muslim University, Aligarh, India, 2001.
Sir Ziauddin Medal for the best performance in Mathematics, Master of Science, Aligarh Muslim University, Aligarh, India, 2001.
M.Sc. Scholarship from National Board of Higher Mathematics (NBHM), Department of Atomic Energy, Govt. of India, 1999-2001.
Ranked first in G.F. College which is affiliated to M.J.P. Rohilkhand University, Bareilly, India, Bachelor of Science, 1999.

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