CS 378 (Spring 2025)
Introduction to Cryptology

Course Information

Instructor: Yang Xiao (contact: xiaoy[AT]uky.edu)
Meeting Times: Tue/Thu 12:30 PM – 1:45 PM Eastern Time
Office Hour: Hardymon Rm 233, Wed 2:00-4:00 PM (updated from Thu 2:30–4:00 PM)
TA: Yue Li (contact: yue.li[AT]uky.edu), Office Hour: Hardymon Rm 203, Fri 2:00-5:00 PM

Course Description

The study of secrecy in digital systems. Methods of keeping information secure from classical systems dating from ancient times to modern systems based on modern mathematics. Basic methods of encryption using public key systems, block ciphers, and stream ciphers. The mathematical tools for the design and analysis of such systems. Topics will include classical cryptography, modern methods of public and private key encryption, authentication and digital signatures, hashing, and passwords. Number theory, abstract algebra, combinatorics, and complexity theory necessary for the design and analysis of cryptographic systems.

Textbooks and Materials

Textbook (recommended): W. Trappe, L. Washington, Introduction to Cryptography with Coding Theory, third edition, Pearson, 2020.

Course Schedule (Tentative)

Week	Agenda ([R]: Required Reading. [S]: Suggested Reading)	Notes
1	Lecture Notes #1 released. 01/14: Overview: secure communication and basic attacks. (([R]: Notes 1.1, 1.2, [S]: textbook 1.0-1.1.1) 01/16: Overview: cryptographic systems and applications. ([R]: Notes 1.3-1.5, [S]: textbook 1.1.2-1.2)
2	Lecture Notes #2 released. 01/21: Number Theory I: prime numbers and division theory. (([R]: Notes 2.1-2.4, [S]: textbook 3.1) 01/23: Number Theory I: EEA and modular arithmetic. (([R]: Notes 2.5-2.6, [S]: textbook 3.2, 3.3)	HW1 out 01/22
3	Lecture Notes #3 released. 01/28: Modular multiplicative inverse; Classic Cryptosystems. (([R]: Notes 3.1-3.2, [S]: textbook 2.1, 2.2) 01/30: Classic Cryptosystems: shift, affine, Vigenere, substitution. (([R]: Notes 3.3-3.7, [S]: textbook 2.3, 2.4, 2.6)	HW1 due 01/30, HW2 out 01/31
4	Lecture Notes #4 released. 02/04: Number Theory II: CRT, modular exponentiation (([R]: Notes 4.1-4.2, [S]: textbook 3.4-3.5) 02/06: Number Theory II: Fermat's Little Thm, Euler's Thm (([R]: Notes 4.3-4.4, [S]: textbook 3.6)	HW2 due 02/08, HW3 out 02/09
5	02/11: (Class canceled due to inclement weather; self-study and virtual office hour) 02/13: Number Theory II: Euler's Thm (cont.), primitive roots (([R]: Notes 4.5, [S]: textbook 3.7)
6	02/18: Stream Ciphers: One Time Pad and LFSR 02/20: Hill Cipher - a simple block cipher	HW3 due 02/17, HW4 out 02/17
7	02/25: Homework problems review, midterm #1 review (Yang is in travel; TA will walk through the problems) 02/27: Midterm Exam #1 in class (Yang is in travel; TA will proctor)	HW4 due 02/25
8	03/04: (Yang is in travel; watch pre-recorded video) 03/06:
9	03/11: 03/13:
10	03/18: No class – Spring Break 03/20: No class – Spring Break
11	03/25: 03/27:
12	04/01: 04/03:
13	04/08: 04/10:
14	04/15: (Yang is in travel; watch pre-recorded video) 04/17:
15	04/22: 04/24: Midterm Exam #2 in class
16	04/29: Final review – Prep Days 05/01: No class – Reading Days
17	05/08 (Thursday): Final exam, 10:30 AM - 12:30 PM, in classroom

Learning/Research Resources

UK Libraries, Free Tutoring and Coaching at UK, Google Scholar, ACM Digital Library, IEEE Xplore, dblp: computer science bibliography