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

Xiao D.

I’m a PhD computer scientist and published researcher working at the frontier of cryptography. My approach bridges abstract mathematics with real code — turning groups, fields, and theorems into tangible “aha-moment” insights through visualization and implementation. I’ve guided high school students from foundational cryptography to independent research projects published in venues such as the STEM Fellowship Journal and the International Journal of High School Research.
—— Core 10 Lessons (≈1.5 hrs each) ——
A hands-on journey through the mathematical foundations of modern cryptography — number theory and group theory — designed to connect abstract ideas with executable code (e.g., how a cyclic subgraph inherits subgroup properties).
Students explore public-key and symmetric-key cryptography and basic cryptanalysis. For abstract topics like multiplicative-group primitives or elliptic curves, I use visualizations rarely seen even in college courses to spark intuition.
They implement real-world systems — RSA, Diffie–Hellman, digital signatures, elliptic curves, AES, and hash functions — to uncover how browsers, SSH, and digital signatures actually work. Perfect for ambitious learners who want to reach a research-ready level far beyond standard classrooms.
—— High School Research Option (≈12 sessions) ——
For highly motivated students, I mentor independent research blending CS, Cryptography, and AI. Projects emphasize curiosity, originality, and scientific thinking — often leading to publishable work that strengthens college and scholarship applications.
—— Optional 8-Lesson Extension (Advanced Topics) ——
Homomorphic Encryption — from partial (ElGamal, Paillier) to leveled (BFV, BGV, CKKS)
Zero-Knowledge Proofs — proving knowledge without revealing secrets
Privacy-Preserving ML — encrypted inference and AI on ciphertext
Outcome: Students gain mathematical rigor, coding fluency, and the mindset to think like cryptographers, reason like scientists, and communicate like researchers.