Introduction:
- I am Dr. Muhammad Sajjad, an Assistant Professor in NUSASH at the National University of Technology (NUTECH) Islamabad, Pakistan. With a distinguished academic career and research contributions spanning Mathematics, Electrical Engineering, and Computer Science, my primary research interests include Vector Algebra, Number Theory, Coding Theory, Cryptography and Advanced Algebraic Structures. I am deeply committed to exploring innovative solutions for designing efficient error-correcting codes, enhancing data security, and leveraging algebraic frameworks to address complex problems in cryptology. My teaching philosophy emphasizes cultivating a balance between theoretical rigor and practical application, empowering students to navigate interdisciplinary challenges in mathematics and technology.
Assistant Professor, NUTECH School of Applied Sciences and Humanities Islamabad, Pakistan (2024–Present)
- Teach undergraduate courses in Artificial Intelligence (AI), Computer Science (CS), Information Technology (IT), and Electrical Engineering (EE).
- Actively participate in international collaborations with universities in South America, Denmark, and Saudi Arabia.
Visiting Faculty, Department of Mathematics and Computer Science, Quaid-i-Azam University Islamabad, Pakistan (2022–2024)
- Teach undergraduate and graduate courses in Department of mathematics, computer science, and statistics.
- Supported undergraduate and graduate students in developing practical applications of algebra, coding theory and cybersecurity concepts.
Visiting Faculty, National University of Modern Languages (NUML) Islamabad, Pakistan (2022–2024)
- Teach undergraduate courses in AI, CS, and engineering departments.
- Supported students in developing practical applications of algebraic concepts.
Visiting Faculty, Bahria University Islamabad Campus, Pakistan (2021–2022)
- Teach undergraduate courses in computer science department.
Mathematics Lecturer, FG Sir Syed College, the Mall Rawalpindi, Pakistan (2020–2021)
Teach undergraduate courses in mathematics department
Qualification:
- Academia:
- Ph.D. in Mathematics, Quaid-i-Azam University Islamabad, Pakistan (2024)
- M.Phil. in Mathematics, Quaid-i-Azam University Islamabad, Pakistan (2020)
- M.Sc. in Mathematics, The Islamia University of Bahawalpur (2018)
- B.Sc. in Mathematics and Physics, The Islamia University of Bahawalpur (2016)
I have published over 11 peer-reviewed papers in prestigious journals, including Computational and Applied Mathematics, Heliyon, AIMS Mathematics, IEEE Access, and CMC. Additionally, I delivered a talk at the UPTC conference in Colombia. My research focuses on coding theory, cryptography, and algebraic structures such as sedenion integers, octonion integers, quaternion integers, Gaussian integers, and Eisenstein fields. These areas are applied in data transmission, cryptographic security, and error-correcting codes. I also serve as a reviewer for several leading academic journals in mathematics, cryptography, and error-correcting codes. Furthermore, I have contributed to the American Mathematical Society (AMS) reviews on topics such as ROLLO's constant-time implementations, the code equivalence problem in the rank metric, and the zero-error capacity of modulo-additive noise channels.
- Certifications:
- Member of American Mathematical Society (AMS) Certificate, Mathematical Review 2024.
- Conference Talk Certificate, the International Conference MATEMATICAS, Universidad Pedagogica y Technologica de Colombia, 2023.
- Certificate Conference Participant, the International Conference MATEMATICAS, UPTC, 2023.
- Certificate Conference Participant, IEEE Advancing Technology for Humanity Conference, 2023.
- Certificate Conference Participant, Mathematical Advances and Applications, Quaid-i-Azam University Islamabad, Pakistan, 2022.
- Certificate Conference Participant, CMTM, Fatima Jinnah Women’s University, Rawalpindi, 2022.
- Certificate Math Rode Olympiad, Quaid-i-Azam University Islamabad, Pakistan, 2019.
- Trainings
- Faculty Development Program on Academic Planning, Academic Execution, Academic Management, University Ethics and Policies (2022), NUML University Islamabad, Pakistan.
- Awards
- International Computer Scientist Award, China, 2024.
- International Research Award on Cybersecurity and Cryptography, Science Father, 2024.
PakCrypto Finalist, National Centre for Cyber Security (NCCS), 2023
Taught Courses
have taught a comprehensive range of undergraduate and graduate-level courses of Mathematics in various department. Below are the courses I have taught, along with their course codes:
An advanced course exploring encryption and decryption techniques, cryptographic protocols, and their applications in data security, including RSA, AES, and elliptic curve cryptography.
A course focused on error-correcting codes and their applications in data transmission, covering Linear, Cyclic, Hamming, BCH, Reed-Solomon, and MDS codes, along with their decoding algorithms.
- Differential Equations and Linear Algebra (MAT302)
An integrated course combining concepts of differential equations and linear algebra with applications in mathematical modeling.
- Rings and Fields (MAT301)
An advanced algebra course exploring the structures of rings and fields, focusing on their applications in number theory, coding theory, and cryptography.
A graduate-level course that explores the rigorous foundations of calculus, including limits, continuity, differentiation, integration, and convergence of sequences and series.
An introductory course (taught online) covering the basics of algebra, including equations, inequalities, polynomial functions, and graphing.
A course on the algebraic structure of groups, subgroups, and homomorphism’s, with applications.
- Discrete Mathematics (MAT202)
An introductory course covering logic, set theory, graph theory, combinatorics, and algorithms with applications in computer science and mathematics.
- Calculus and Analytical Geometry (MAT102)
A course covering differential and integral calculus, along with the study of conic sections and their applications.
- Numerical Analysis (MAT403)
A course focusing on numerical methods for solving mathematical problems, including interpolation, integration, differentiation, and differential equations.
Research
My research primarily lies at the intersection of algebra, coding theory, and cryptography, with a strong focus on leveraging advanced mathematical structures to address challenges in data security, error correction, and image encryption. I have extensively explored the applications of Galois fields, Gaussian, Eisenstein, Quaternion, Octonion and Sedinion integers, and their generalizations in constructing efficient cryptographic and coding systems. My work has also contributed to the development of novel block cipher components and secure image encryption techniques. I am currently leading multiple projects that aim to enhance modern technology by employing advanced algebraic tools and number-theoretic structures. These projects have applications in secure communication, modern data encryption, and efficient decoding techniques.
- Ongoing Research Projects:
- Primitive BCH Codes over Local Eisenstein Rings
- RSA Cryptosystem over the Eisenstein Primes
- Noncyclic BCH and Srivastava Codes over Eisenstein Fields
- SPN based RGB Image Encryption over Quaternion Integer
- Construction and Decoding of BCH Codes over Quasi-Galois Rings
- The Impact of Alternant Codes over Eisenstein Integers on Modern Technology
- The Implementations of BCH Codes over Local Gaussian Rings in Modern Technology
- Pair of S-boxes over the Residue Classes of Eisenstein Integers and its Applications in RGB Image Encryption
- Nonlinear Components of Block Cipher based Eisenstein Rings and Mordell Elliptic Curve with its applications in RGB Images
- Publications:
- Sajjad, M., & Shah, T. (2024). “Decoding of cyclic codes over quaternion integers by modified Berlekamp–Massey algorithm” Computational and Applied Mathematics.
- Sajjad, M., et al. (2024). “SPN based RGB Image Encryption over Gaussian Integers” Heliyon.
- Sajjad, M., et al. (2023). “Eisenstein field BCH codes constructions and decoding,” AIMS Mathematics.
- Sajjad, M., et al. (2023). “Construction and Decoding of BCH-Codes Over the Gaussian Field,” IEEE Access.
- Sajjad, M., et al. (2023). “Designing pair of nonlinear components of a block cipher over quaternion integers,” AIMS Mathematics.
- Sajjad, M., et al. (2023). “Generalization of RSA cryptosystem based on 2n primes,” AIMS Mathematics.
- Sajjad, M., et al. (2023). “A comparative study of nonlinear fractional Schrödinger equation in optics,” Modern Physics Letters B.
- Sajjad, M., et al. (2023). “Designing Pair of Nonlinear Components of a Block Cipher over Gaussian Integers,” Computers, Materials & Continua.
- Sajjad, M., et al. (2023). “Nonlinear Components of a Block Cipher over Eisenstein Integers,” Computers, Materials & Continua.
- Sajjad, M., et al. (2022). “Fundamental results of cyclic codes over Octonion integers and their decoding algorithm,” Computation.
Sajjad, M., et al. (2023). “Quaternion Integers Based Higher Length Cyclic Codes and Their Decoding Algorithm,” Computers, Materials & Continua
projects
- Primitive BCH Codes over Local Eisenstein Rings (2021–Present): Leading the development of novel BCH codes over Local Eisenstein Rings to enhance error correction capabilities in modern communication systems. This project aims to improve the reliability and efficiency of data transmission in noisy environments.
- RSA Cryptosystem over the Eisenstein Primes (2022–Present): Developing an advanced RSA cryptosystem based on Eisenstein primes to strengthen encryption techniques and improve data security in the post-quantum computing era.
- SPN-based RGB Image Encryption over Quaternion Integers (2023–Present): Designing a secure image encryption scheme using SPN (Substitution-Permutation Network) over quaternion integers to protect multi-color images in real-time applications.
Nonlinear Components of Block Cipher Based on Eisenstein Rings and Mordell Elliptic Curve (2023–Present): Working on the development of nonlinear components for block ciphers based on Eisenstein Rings and the Mordell elliptic curve. This project aims to enhance the security of encryption systems for RGB image protection
