Choosing a topic for your EPQ can be challenging, but it's great that you have an interest in cryptography. Here are a few specific ideas related to cryptography that you could consider for your EPQ:
Comparative analysis of cryptographic algorithms: Choose a few popular cryptographic algorithms (such as RSA, AES, and Elliptic Curve Cryptography) and compare their strengths, weaknesses, and applications. Discuss their mathematical foundations, computational complexity, and resistance to attacks.
Implementing a cryptographic algorithm in Python: Select a specific cryptographic algorithm and explore its implementation in Python. You can explain the underlying mathematics, step-by-step algorithm implementation, and demonstrate its functionality through code examples. This would involve self-study and learning beyond what you've been taught in school, which aligns with the EPQ's purpose.
Cryptanalysis techniques: Explore different cryptanalysis techniques used to break cryptographic algorithms. Focus on a particular type, such as differential cryptanalysis or linear cryptanalysis, and explain the underlying principles, attacks, and countermeasures. You can discuss real-world examples and their implications for cryptographic security.
The impact of quantum computing on cryptography: Investigate the potential impact of quantum computers on modern cryptographic systems. Explain the basics of quantum computing and how it differs from classical computing. Discuss the vulnerabilities of current cryptographic algorithms to quantum attacks and explore post-quantum cryptography as a potential solution.
Remember that these are just suggestions, and you can modify or combine them to suit your interests and EPQ requirements. It's important to conduct thorough research, gather reliable sources, and consult with your EPQ advisor to ensure your chosen topic is suitable and achievable within the given timeframe.
Additionally, if you're looking for more inspiration or examples of EPQ topics in computer science, you can search online databases or forums dedicated to EPQ projects. These resources often provide a range of topics and project ideas that other students have pursued.
Good luck with your EPQ, and I hope you find a captivating topic in the field of cryptography that allows you to explore and showcase your skills and knowledge!