Abstract

The abstract briefly summarizes the key points of the paper, including the threat quantum computing poses to traditional cryptography, the role of algorithms like Shor's and Grover's in this paradigm shift, and the exploration of emerging quantum-resistant cryptographic solutions.

1. Introduction

• Overview of quantum computing's evolution and its fundamental principles.
• Brief description of traditional cryptography, focusing on the security it provides to digital communications and data.
• Introduction to the problem: how quantum computing challenges the foundations of current cryptographic methods.

2. Fundamentals of Quantum Computing

• Explanation of qubits, superposition, and entanglement, contrasting with classical bits.
• Overview of quantum supremacy and its significance.
• Key quantum algorithms:
  • Shor's Algorithm: Explanation of its ability to factor large integers efficiently, threatening RSA encryption.
  • Grover's Algorithm: Description of its potential to speed up searches, impacting symmetric key cryptography.

3. Current State of Quantum Computing

• Latest developments in quantum processors and qubit coherence times.
• Milestones achieved by leading research institutions and companies in quantum computing.
• Discussion on the timeline and challenges towards a fully functional quantum computer capable of breaking current cryptographic systems.

4. Implications for Cryptography

• Detailed analysis of vulnerabilities in RSA and ECC due to Shor's algorithm.
• Examination of the reduced but existing threat to symmetric encryption from Grover's algorithm.
• Discussion on the practical implications for data security, including historical data currently encrypted but potentially at