From Math to Code: Learn Cryptography & Algorithms with a PhD Mentor

Xiao D.

I’m a PhD computer scientist who uses Python coding to demystify cryptography and algorithms. My approach bridges abstract math with hands-on coding, so groups, fields, and theorems become concrete through programs students write and run. I have taught college students and provided private lessons to high schoolers and professional developers worldwide, helping each group master cryptography at the right depth. The result is both programming fluency and deeper understanding of modern cryptography.

Core 12 Lessons (≈1.5 hours each)
Covers the mathematical foundations of cryptography—group theory, cyclic groups, finite fields, Fermat’s little theorem, Euler’s theorem—and their applications. Students then implement real-world cryptosystems such as RSA, Diffie–Hellman, AES, hash functions, digital signatures, and elliptic curves.

Optional 8-Lesson Extension (Advanced Topics)
For motivated learners, an additional track explores:
Homomorphic Encryption – partial (RSA, Paillier) to leveled (BGV, BFV, CKKS) to fully homomorphic schemes
Zero-Knowledge Proofs – proving knowledge without revealing the secret
Privacy-Preserving Machine Learning – encrypted inference and AI on ciphertext

High School Research Option (≈15 one-hour sessions)
For ambitious students, I also guide independent research projects combining CS, cryptography, and AI. Sample directions include:
Privacy-preserving educational tools using encryption + ML
AI to detect harmful language while protecting confidentiality
Linking art and literature through multimodal AI
Exploring how AI interprets scientific diagrams and explanations

Outcome: Students learn to think programmatically about mathematics, implement cryptosystems in Python, and strengthen their mathematical maturity and intuition. Ambitious students who pursue the research option develop critical thinking, scientific intuition, and curiosity, with strong potential to produce a research paper or publication that enhances college applications.