Magnum Opus Research Project - Academic Year 2024-2025
This comprehensive research project explores the fundamental impact of quantum computing on modern cryptographic systems. The study investigates how quantum algorithms, particularly Shor's algorithm, pose a significant threat to widely-used encryption methods like RSA and ECC.
The project includes both theoretical research and practical implementation, featuring a hands-on experiment where Shor's algorithm is simulated using IBM's Qiskit framework to demonstrate the potential of quantum computing in breaking classical encryption.
Exploration of qubits, superposition, and entanglement - the building blocks of quantum computing.
Analysis of RSA and ECC encryption methods and their mathematical foundations.
Detailed study of the quantum algorithm that can efficiently factor large numbers.
Investigation of quantum-resistant encryption algorithms being developed by NIST.
The project includes a practical demonstration of Shor's algorithm using IBM's Qiskit quantum computing framework. The implementation factors the number 15 into its prime components (3 and 5), demonstrating the quantum approach to integer factorization.
# Shor's Algorithm Implementation
from qiskit import QuantumCircuit
from qiskit_aer import Aer
def shors_algorithm(N):
# Quantum period finding
qc = QuantumCircuit(4, 4)
# Apply Hadamard gates
for i in range(2):
qc.h(i)
# Quantum Fourier Transform
qc.h(0)
qc.cp(-np.pi/2, 0, 1)
return factorsQuantum computers with sufficient qubits (estimated 4,000-8,000 logical qubits) could break RSA-2048 encryption within hours or days, compared to millions of years for classical computers.
Experts predict cryptographically relevant quantum computers will be available between 2030 and 2040, meaning organizations must start transitioning to post-quantum cryptography now.
Adversaries are already storing encrypted data with the intention of decrypting it once quantum computers become available, making the threat immediate for long-term sensitive data.
NIST has already selected post-quantum cryptographic algorithms (CRYSTALS-Kyber, CRYSTALS-Dilithium, FALCON, SPHINCS+) that are resistant to quantum attacks and can run on classical computers.