TEW - Algebra, Number Theory and Cryptography (2025)
Speakers and Syllabus
| Name of the Speaker with affiliation | No. of Lectures | Detailed Syllabus |
| Dr. Arindam Banerjee Department of Mathematics IIT Kharagpur, India |
8 | Group, Cyclic group, Ring, Polynomial ring, irreducible polynomial, Finite fields. Division algorithm, modular arithmetic, Chinese remainder theorem, Euler’s theorem, Fermat’s little theorem, Extended Euclid algorithm. |
| Prof. Sourav Mukhopadhyay Department of Mathematics IIT Kharagpur, India |
8 | Introduction to classical cryptography, block cipher, stream cipher, DES, and AES. Prime numbers, Primality Testing and factorization algorithms, Pseudo-primes, Fermat's pseudo-primes, Pollard’s rho method for factorization, primitive Roots, Quadratic reciprocity, |
| Dr. Ratna Dutta Department of Mathematics IIT Kharagpur, India |
8 | Public Key cryptography, Diffie-Hellmann key exchange, Discrete logarithm-based crypto-systems, RSA crypto-system, Signature Schemes, Digital signature standard, RSA Signature schemes, Knapsack problem. Introduction to elliptic curves, Group structure, Rational points on elliptic curves, Elliptic Curve Cryptography. |
References:
- Elementary Number Theory - David M. Burton.
- Algebra – Michael Artin.
- Cryptography: Theory and Practice – Douglas Stinson.
Time Table
|
Day |
Date |
Lecture 1 (9.30–10.30) |
Tea (10.35-10.55) |
Lecturer 2 (11.00–12.00) |
Lecture 3 (12.00–1.00) |
Lunch (1.00 – 2.20) |
Lecture 4 (2.30-3.30) |
Tea (3.35 -3.55) |
Discussion (4.00-500) |
Snacks (5.05 – 5.30) |
|
Mon |
17/03/25
|
AB |
TEA |
AB |
SM |
LUNCH |
SM |
TEA |
AB+VBL |
SNACKS |
|
Tue |
18/03/25
|
AB |
AB |
RD |
RD |
AB+RH |
||||
|
Wed |
19/03/25
|
AB |
AB |
SM |
SM |
SM+PJ |
||||
|
Thu |
20/03/25
|
SM |
SM |
RD |
RD |
SM+SS |
||||
|
Fri |
21/03/25
|
AB |
AB |
RD |
RD |
RD+PJ |
||||
|
Sat |
22/03/25
|
RD |
RD |
SM |
SM |
RD+MJ |
Speakers:
-
Dr. Arindam Banerjee, Assistant Professor, IIT Kharagpur. (AB)
-
Prof. Sourav Mukhopadhyay, Professor, IIT Kharagpur. (SM)
-
Dr. Ratna Dutta, Associate Professor, IIT Kharagpur. (RD)
Name of the tutors:
|
S. No. |
Name |
Affiliation |
|
1 |
Vivek Bhabani Lama (VBL) |
Senior Research Fellow, Department of Mathematics, IIT Kharagpur |
|
2 |
Ritam Halder (RH) |
Junior Research Fellow, Department of Mathematics, IIT Kharagpur |
|
3 |
Sudip Singha (SS) |
Junior Research Fellow, Department of Mathematics, IIT Kharagpur |
|
4 |
Manas Jana (MJ) |
Junior Research Fellow, Department of Mathematics, IIT Kharagpur |
|
5 |
Pratima Jana (PJ) |
Senior Research Fellow, Department of Mathematics, IIT Kharagpur |