Course Title:
Advanced Data Structures, RSA and Quantum Algorithms
Course Description:
The RSA cryptosystem relies on number-theoretic concepts, specifically the difficulty of factoring large composite numbers, which forms its security foundation. It uses two large prime numbers to generate public and private keys, ensuring encryption and decryption are computationally hard for attackers without the private key. Quantum computation, based on principles of quantum mechanics, introduces fundamental building blocks like superposition, entanglement, and quantum gates. Quantum algorithms, such as Shor’s algorithm, can efficiently factor large numbers, threatening RSA’s security. Unlike classical algorithms that rely on sequential steps, quantum algorithms exploit quantum parallelism and entanglement to solve certain problems exponentially faster, marking a significant shift in computational power.
Course instructional level:
Advance
Course Duration:
1-4 weeks
Hours: 42 Hrs
Course coordinator:
Dr. P.D. Belsare
Course coordinator's profile(s):
Dr. P. D. Belsare has teaching experience of 20 years. He has been teaching various subjects such as Quantum Computing, Mechanics, Semiconductors, Nanotechnology, Materials Science. He has more than 20 indexed journals in the field of Materials synthesis with good impact factor and 1 patent granted and two patents filed to his credit.
Course Contents:
| Module/Topic name | Sub-topic | Duration |
| 1. RSA Public Key Cryptography and Basics of Quantum Computing | Introduction to Public Key Cryptography | 9 hrs |
| Euclid's Algorithm and GCD | ||
| Extended Euclid Bezout Coefficients | ||
| RSA Cryptography | ||
| Quantum Physics Computing Basics | ||
| 2. Quantum Computing: Qubits, Quantum Gate, Grover Search Algorithm | Qubits and Super Positions | 13 hrs |
| Unitary Operators and Reversible Computation | ||
| Multi Qubit Quantum States | ||
| Multi Qubit Quantum Gates | ||
| Quantum Parallelism | ||
| No Cloning Theorem | ||
| Bells Inequality Power of Entangled States | ||
| Grover Search Algorithm | 12 hrs | |
| 3. Quantum Computing: Phase Estimation and Shor’s Algorithms | Order Finding and Factoring | |
| Order Finding on a Quantum Computer | ||
| FFT Basics of Complex Numbers and Roots of Unity | ||
| Discrete-Time Fourier Transforms | ||
| FFT Divide and Conquer Algorithm | ||
| Quantum Fourier Transform: Part 1 | ||
| Quantum Fourier Transform: Part 2 | ||
| 4. B-Trees and Tries | Introduction to B-Trees | 8 hrs |
| Structure and Properties of B-Trees | ||
| Simple Example | ||
| Searching for a Key in a B-Tree | ||
| B-Tree Key Insertion Algorithm | ||
| B-Tree Key Deletion Algorithm | ||
| Tries: Basics | ||
| Suffix Tries | ||
| Generalized Suffix Tries | ||
| Ukkonen's Algorithm - Part 1 | ||
| Ukkonen's Algorithm - Part 2 | ||
| Concluding Remarks |
Course Outcomes:
After completion of the course, the learner will be able to:
- Explore how basic number-theoretic concepts are used to build the RSA crypto-system.
- Examine the foundations of quantum computation and its basic building blocks.
- Explore how quantum computers can be used to break the RSA cryptosystem.
- Explore the differences between classical and quantum algorithms.