One-day Seminar on “Number Theory and Cryptography”

The one-day seminar on Number Theory and Cryptography was held on 23 August 2024 at Manipur Technical University campus. The event was organized by the Department of Mathematics, Manipur Technical University, Imphal.

Seminar Overview:

Topic: Number Theory and Cryptography
About the Seminar: The seminar is organised by the Department of Mathematics, Manipur Technical University to help students explore the fundamental concepts of number theory and their applications in modern cryptography and engineering. Participants will gain insights into fundamental concepts from number theory. These include divisibility, prime numbers, and modular arithmetic. These mathematical principles underpin many cryptographic algorithms. We’ll also delve into RSA (Rivest–Shamir–Adleman) encryption, a widely used public-key cryptosystem. Understanding its mathematical foundations is essential for secure communication. Participants will also learn about the Diffie-Hellman key exchange, which enables secure key sharing between parties. It relies on number theory principles. Discussing potential attacks on cryptosystems is crucial. We will explore vulnerabilities and countermeasures.
Objective: The primary goal is to introduce participants to cryptosystems and their significance. Cryptosystems are essential for secure communication and data privacy.
Coordinators:
o Thokchom Chhatrajit Singh
o Anand Jyoti Sanasam
o Huidrom Malemnganbi
o P. Ramwungzan
Participants: Researchers, students, and professionals interested in cryptography and mathematical foundations.
Date: 23 August 2024 (Friday)
Venue: Manipur Technical University

Outcome: During the seminar, attendees gained insights into the following key areas:

Introduction to Number Theory
o Basics of prime numbers, divisibility, and modular arithmetic.
o Role of number theory in cryptography.
Cryptography Fundamentals
o Symmetric and asymmetric encryption.
o Public-key cryptography.
o Digital signatures.
Applications of Number Theory in Cryptography
o RSA algorithm: Key generation, encryption, and decryption.
o Diffie-Hellman key exchange.
o Elliptic curve cryptography.
Challenges and Future Directions
o Quantum computing and its impact on cryptography.
o Post-quantum cryptography research.

Key Takeaways:

Understanding the mathematical foundations of secure communication.
Appreciating the elegance of number theory in designing cryptographic algorithms.
Awareness of current trends and challenges in the field.

Acknowledgment: We extend our heartfelt gratitude to the following individuals and organizations for their valuable contributions to the seminar:

Resource Persons
o Prof. Shanta Laishram, Head of the Theoretical Statistics and Mathematics Unit (Stat-Math Unit), Indian Statistical Institute (ISI), Delhi Centre, New Delhi, India.
Participants
o Researchers, students, and professionals who actively engaged in discussions and made the seminar a success.
Host Institution
o We express our gratitude to Manipur Technical University for providing the venue and logistical and financial support.

This seminar served as a platform for intellectual exchange, fostering a deeper understanding of number theory’s role in safeguarding our digital world. We look forward to future collaborations and continued exploration in this exciting field.