CS 378 (Spring 2026)
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
TA: TBD, Office Hour: TBD

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	Date	Agenda (Weekly lecture notes uploaded to Canvas pre-class)	Reading ([L] LecNotes, [T] Textbook)	Assignment (H: Homework, P: Project)
1	01/13 T 01/15 R	(Lecture Notes #1 released on Sunday) Overview: secure communication and basic attacks. Overview: cryptographic systems and applications. Starting Number Theory I: divisibility and prime numbers.	[L] 1.1-1.2, [T] 1-1.1.1 [L] 1.3-1.5, 2-2.2, [T] 1.1-1.2, 3.1
2	01/20 T 01/22 R	(Lecture Notes #2 released on Sunday) Number Theory I: Division Theorem, gcd(), EA, EEA. Number Theory I: EEA recap + Modular Arithmetic.	[L] 2.3-2.6, [T] 3.1.3-3.2 [L] 2.7, [T] 3.2-3.3	H1 out (Wed)
3	01/27 T 01/29 R	(Lecture Notes #3 released on Sunday) Classic ciphers: shift, affine, Vigenere. Frequency analysis; Playfair cipher, substitution cipher.	[L] 3.1-3.3, [T] 2.1-2.3.1 [L] 3.4-3.7, [T] 2.3.2-2.4, 2.6-2.7	H1 due; H2 and P1 out (Fri)
4	02/03 T 02/05 R	(Lecture Notes #4 released on Sunday) Number Theory II: CRT, modular exponentiation Number Theory II: Fermat's Little Thm (FLT), Euler's Thm (ET)	[L] 4.1-4.2, [T] 3.4-3.5 [L] 4.3-4.4.2, [T] 3.6
5	02/10 T 02/12 R	(Lecture Notes #5 released on Sunday) Number Theory II: ET cont., primitive roots Stream ciphers: One Time Pad (OTP) and Pseudo-random Bits	[L] 4.4.3-4.5, [T] 3.7 [L] 5.1-5.3, [T] 4.1-4.2, 5.1	H2 due (Mon) H3 out
6	02/17 T 02/19 R	(Lecture Notes #6 released on Sunday) Stream ciphers: LFSR and more; starting block cipher Block ciphers: Hill Cipher	[L] 5.4, [T] 5.2-5.3 [L] 6, [T] 6.1-6.2	H3 due; P1 due (Fri); H4 out
7	02/24 T 02/26 R	(Lecture Notes #7 released last week) Block ciphers: DES, Feistel network DES cont.; block cipher modes of operation	[L] 7.1-7.3, [T] 7.1-7.4 [L] 7.4-7.5, 8, [T] 7.6, 6.3
8	03/03 T 03/05 R	Midterm review; homework recap; practice problems Midterm exam, in class		H4 due (Mon)
9	03/10 T 03/12 R	Block ciphers: AES basics; finite fields AES algorithms; a simple demo
10	03/17 T 03/19 R	No class – Spring Break No class – Spring Break
11	03/24 T 03/26 R
12	03/31 T 04/02 R
13	04/07 T 04/09 R
14	04/14 T 04/16 R
15	04/21 T 04/23 R
16	04/28 T 04/30 R	(Prep Days) (Reading Days) No Class
17	05/05 T 05/07 R	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.