Weekly Syllabus, Math 302 Advanced Cryptography, Spring 2025
Be sure to check back, because this will be updated during the semester.
- All section numbers refer to An Introduction to Mathematical Cryptography, 2nd Edition by Hoffstein, Pipher, and Silverman, available through Wheaton's library as an ebook.
- PCA due refers to Pre-Class Assignments submitted through Canvas
- PS due refers to Problem Sets uploaded to Canvas
| Week | Major Topics | References | Notes / Due this week | |
|---|---|---|---|---|
| 1 | Jan 22 - Jan 24 |
Welcome to Advanced Cryptography! Semester overview |
Sections 1.1, 1.2, & 1.3 | |
| 2 | Jan 27 - Jan 31 |
Fermat's Little Theorem Primitive roots |
Sections 1.4, 1.5 |
PCA due Mon 1/27 @ 9:00 am PS #1 due Fri 1/31 @ 2:00 pm |
| 3 | Feb 3 - Feb 7 | Pollard's \( \rho \) for the DLP | Section 5.5 |
PCA due Mon 2/3 @ 9:00 am PS #2 due Fri 2/7 @ 2:00 pm |
| 4 | Feb 10 - Feb 14 |
The Chinese Remainder Theorem The Pohlig-Hellman Algorithm |
Sections 2.8, 2.9 |
PCA due Mon 2/10 @ 9:00 am PS #3 due Fri 2/14 @ 2:00 pm |
| 5 | Feb 17 - Feb 21 | More with Pohlig-Hellman | Section 2.9 |
PCA due Mon 2/24 @ 9:00 am Cheat Sheet due Mon 2/17 @ 9:00 am Exam 1 due Fri 2/21 @ 5:00 pm |
| 6 | Feb 24 - Feb 28 | Miller-Rabin witnesses for primality testing | Section 3.4 |
PCA due Mon 2/24 @ 9:00 am |
| 7 | Mar 3 - Mar 7 |
Introduction to elliptic curves Elliptic curves over \( \mathbb{F}_p \) |
Sections 6.1, 6.2 |
PCA due Mon 3/3 @ 9:00 am PS #4 due Fri 3/7 @ 2:00 pm |
| Mar 13 - Mar 17 | Spring Break | |||
| 8 | Mar 17 - Mar 21 |
The elliptic curve DLP Elliptic Curve Diffie-Hellman |
Sections 6.3, 6.4 |
No class Wed 3/19, MAP Day Groups for Kryptos & Presentations due Fri 3/21 via email |
| 9 | Mar 24 - Mar 28 |
Refresher on Shor's Algorithm Introduction to lattices |
Sections 7.3, 7.4, 7.5 |
PCA due Mon 3/24 @ 9:00 am PS #5 due Fri 3/28 @ 2:00 pm Register for Kryptos by Fri 3/28 |
| 10 | Mar 31 - Apr 4 |
Babai's Algorithm LLL Lattice Reduction Algorithm |
Sections 7.6, 7.13 |
PCA due Mon 3/31 @ 9:00 am Cheat Sheet due Mon 3/31 @ 9:00 am Exam 2 due Fri 4/4 @ 5:00 pm |
| 11 | Apr 7 - Apr 11 |
Learning with errors Module LWE problem |
See Pre-Class Assignments page |
PCA due Mon 4/7 @ 9:00 am Topic for Presentation due Fri 4/11 Krytpos 2025 competition, 4/10 - 4/14 |
| 12 | Apr 14 - Apr 18 |
Post-quantum KEM CRYSTALS Kyber |
See Pre-Class Assignments page |
PCA due Mon 4/14 @ 9:00 am Abstract for Presentation due Fri 4/18 |
| 13 | Apr 21 - Apr 25 |
Flex week Topics determined during semester |
See Pre-Class Assignments page |
PCA due Mon 4/21 @ 9:00 am Slides for Presentation (draft) due Wed 4/23 |
| 14 | Apr 28 - May 2 | Semester wrap-up | You'll decide! | Group Presentations! Slides for Presentation (final) due Thu 5/1 |
| May 5 - May 9 | Finals Week | Final Assignment due Tue 5/6 @ 11:59 pm |