Research

Research Overview

My research journey has been centered around exploring the deep connections between Algebraic Geometry and modern cryptographic systems. This interdisciplinary approach has allowed me to apply geometric principles to enhance security protocols and develop new perspectives on cryptographic challenges.

During my undergraduate studies, I undertook an independent study of Algebraic Geometry under the guidance of Dr. Sohail Iqbal. This exploration revealed the profound connections between geometric structures and algebraic equations, providing me with powerful tools to analyze and improve cryptographic systems.

My Final Year Project, "Elliptic Curve Cryptography," represents a practical application of these mathematical concepts, where I investigated the security advantages and computational efficiency of elliptic curves in cryptographic protocols.

Currently, I continue to deepen my understanding of Algebraic Geometry, focusing on its theoretical foundations while maintaining connections to applicable domains where geometric insights can solve complex computational problems in cryptography and beyond.

Research Highlights

Study of Algebraic Geometry under faculty guidance
Application of geometric principles to cryptographic systems
FYP on Elliptic Curve Cryptography implementation and analysis
Exploration of computational aspects of algebraic varieties
Integration of theoretical mathematics with practical applications

Final Year Project

Elliptic Curve Cryptography

Final Year Project - Bachelors in Mathematics

This project explores the mathematical foundations and practical implementations of Elliptic Curve Cryptography (ECC), a public-key cryptography approach that offers stronger security per bit compared to traditional cryptographic systems.

The research investigates the algebraic structure of elliptic curves over finite fields and their application in creating efficient cryptographic protocols. Key areas of focus include:

Mathematical properties of elliptic curves and their group structure
Elliptic Curve Discrete Logarithm Problem (ECDLP) and its security implications
Implementation of ECC for key exchange and digital signatures
Comparative analysis with DLP and other cryptographic systems
Computational efficiency and security advantages of ECC

This work demonstrates how abstract mathematical concepts from algebraic geometry and number theory can be applied to create practical, secure communication systems.

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Research Supervisor

Dr. Sohail Iqbal

FYP Supervisor & Course Instructor

Dr. Sohail Iqbal has been instrumental in guiding my research journey, particularly in my independent study of Algebraic Geometry and its applications to cryptography. His expertise in mathematical structures and computational methods has provided invaluable insights throughout my undergraduate research.

Under his mentorship, I developed a comprehensive understanding of advanced mathematical concepts and learned to apply theoretical knowledge to practical problems in cryptography and security systems.

sohail.iqbal@comsats.edu.pk

Department of Mathematics, COMSATS University Islamabad

Research Interests

Algebraic Geometry

Study of geometric structures defined by polynomial equations and their algebraic properties, with applications to cryptographic systems.

Cryptography

Mathematical foundations of secure communication, focusing on elliptic curve cryptography and other advanced cryptographic protocols.

Computational Mathematics

Algorithmic approaches to solving mathematical problems, particularly in algebra and number theory with cryptographic applications.