Analyzing the Impact of Quantum Computing on Classical Cryptographic Algorithms Security

1. Introduction 1.1 Background of Quantum Computing 1.2 Motivation for Study 1.3 Research Objectives 1.4 Structure of the Paper 2. Classical Cryptographic Algorithms 2.1 Symmetric Cryptography 2.2 Asymmetric Cryptography 2.3 Hash Functions 2.4 Key Sizes and Security Levels 3. Quantum Computing Fundamentals 3.1 Quantum Bits and Superposition 3.2 Quantum Gates and Circuits 3.3 Quantum Algorithms Overview 3.4 Limitations and Challenges 4. Impact of Shor’s Algorithm 4.1 Factorization and RSA Cryptography 4.2 Discrete Logarithm Problem 4.3 Potential Security Compromises 5. Impact of Grover’s Algorithm 5.1 Searching Unstructured Databases 5.2 Symmetric Key Implications 5.3 Advances in Quantum Search 6. Security Implications for Hash Functions 6.1 Quantum Attack Vectors 6.2 Resistance of Current Hashes 6.3 Future-Proofing Strategies 7. Post-Quantum Cryptography Solutions 7.1 Lattice-Based Cryptography 7.2 Multivariate Polynomial Solutions 7.3 Hash-Based Cryptosystems 7.4 Code-Based Cryptography 8. Future Research Directions 8.1 Quantum Cryptographic Protocols 8.2 Scalability of Quantum Systems 8.3 Collaboration Between Disciplines 8.4 Ethical and Societal Implications