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	Lecture Notes #5 released. 02/18: Hill Cipher - a simple block cipher (([R]: Notes 5, [S]: textbook 6.1-6.2) Lecture Notes #6 released. 02/20: One Time Pad and LFSR; midterm #1 topics review (([R]: Notes 6, [S]: textbook 4.1-4.2, 5.1-5.2)	HW3 due 02/17, HW4 out 02/18
7	02/25: Homework & midterm #1 practice problems (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 02/24
8	Lecture Notes #7 released. 03/04: Block Cipher: DES (Yang is in travel; watch pre-recorded video) (([R]: Notes 7, [S]: textbook 7.1-7.4) Lecture Notes #7 updated and #8 released. 03/06: Block Cipher: DES cont., block cipher modes (([R]: cs572lec09 ref., Notes 8, [S]: textbook 7.6, 6.3)
9	Lecture Notes #9 released. 03/11: Block Cipher: AES overview, finite fields (([R]: Notes 9.1-9.3, [S]: textbook 8.1, 3.11) 03/13: Block Cipher: AES algorithm (([R]: Notes 9.4-9.6, [S]: textbook 8.2-8.4)	HW5 out 03/10, HW6 (project) out 03/15
10	03/18: No class – Spring Break 03/20: No class – Spring Break
11	03/25: Public Key Cryptosystem; intro to RSA 03/27: RSA algorithm	HW5 due 03/24, HW7 out 03/25
12	04/01: Discrete logarithm I 04/03: Discrete logarithm II (Diffie-Hellman)	HW7 due 04/03, HW8 out 04/04
13	04/08: Hash functions 04/10: Digital signature	HW8 due 04/11
14	04/15: Secret sharing (Yang and TA in travel; Yang's PhD student Ifteher subtitutes) 04/17: Elliptic curve	HW6 due 04/14, HW9 out 04/14
15	04/22: Elliptic curve, cont.; Midterm Exam #2 topics review 04/24: Midterm Exam #2 in class	HW9 due 04/22
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