Overview
Selected for the first edition of the Undergraduate Seminar organized by the Math Society in Spring 2025. I conducted this research over a 3-week intensive period, culminating in a paper and a technical presentation.
This project explores the intersection of quantum mechanics and modern cryptography. Specifically, I analyzed how Shor's Algorithm poses a theoretical threat to RSA encryption by leveraging quantum superposition to find the period of modular functions efficiently.
* The paper is currently being reviewed by Dr. Prof. Mallahi Keivan Karai.
Presentation
Technical Implementation
The project focused on a theoretical derivation of the algorithm's complexity and its circuit implementation requirements using Python and Qiskit for visualization. Key analytical components include:
- Cryptographic Context: Modeled the RSA key generation and the reduction of factorization to order-finding.
- Theoretical Analysis: Analyzed the feasibility of implementing the algorithm on current vs. fault-tolerant hardware.
- Circuit Construction: Constructed the modular exponentiation unitary operators to visualize the gate depth and resource requirements.
Conclusion
The research highlighted the significant resource gap between current NISQ era devices and the requirements for running Shor's algorithm on cryptographically relevant integers. It concluded with a feasibility analysis of when we might expect quantum computers to break standard RSA-2048 encryption.