The Principles of Modern Cryptography
Course website for The Principles of Modern Cryptography
These documents are not to be sold, published, or distributed without the author’s consent.
Instructor: Dr. Ming Ming Tan
Email: mtan@augusta.edu
Course Description:
- Learn the fundamental concepts of number theory and abstract algebra needed for modern number-theoretic encryption schemes.
- Learn to derive properties/theorems needed for modern number-theoretic encryption schemes.
- Gain exposure to the modern number-theoretic encryption schemes and their underlying assumptions.
- Learn to formulate and understand the security properties given by the encryption schemes.
Suggested Textbook and Reference Books:
- Textbook Introduction to Modern Cryptography by Jonathan Katz and Yehuda Lindell
Syllabus: Spring2025
course website: https://mmtan.github.io/cryptography/
Schedule and references
Thursday (01/09/25) and Tuesday (01/14/25)
- References: Textbook Section 1.1-1.3
- Notes: Notes1
- Problem sets: Homework1
- Content: Historical ciphers, perfectly secure, perfectly indistinguishable
Thursday (01/16/25) and Tuesday (01/21/25)
- References: Textbook Section KL 1.4 and 2.1, KL 2.2-2.3, 3.1, and 3.2.1
- Notes: Notes2
- Problem sets: Homework2
- Discussion: Homework2 discussion
- Content: One-time pad, adversarial indistinguishability, limitations of perfect secrecy, Shannon’s Theorem, computational security
Thursday (01/23/25) and Tuesday (01/27/25)
- References: Textbook Section KL 3.3
- Notes: Notes3
- Problem sets: Homework3
- Discussion: Homework3 discussion
- Content: Pseudorandomness. The pseudo-OTP. Proofs by reduction.
Thursday (01/30/25) and Tuesday (02/04/25)
- References: Textbook Section KL 3.4 and 3.5
- Notes: Notes4
- Problem sets: Homework4
- Discussion: Homework4 discussion
- Self-study Assignment (due 18 Feb 2025): Assignment1
- Content: Single vs Multi Messages security. Evedropper security vs CPA security. Pseudorandom functions vs random functions.
Thursday (02/06/25) and Tuesday (02/08/25)
- References: Textbook Section KL 3.6 and KL 3.7, KL 4.1, 4.2, 4.3 and 4.4.1
- Notes: Notes5
- Recordings: Lecture
- Content: Hybrid argument. Encryption from stream ciphers and block ciphers.
Thursday (02/13/25) and Tuesday (02/20/25)
- References: KL 5.1.1, 5.2, 5.3.1, 5.4.1, and 5.6.1-5.6.3
- Notes: Notes6
- Problem sets: Homework5
- Discussion: Homework5_discussion
- Content: Hash functions and collision resistance. Birthday attacks on hash functions. Additional applications of hash functions.
Thursday (02/20/25) and Tuesday (02/27/25)
- References: KL 8.1.1-8.1.2, 8.1.3, 8.3.1-8.3.3, 8.4.2, and 10
- Notes: Notes7
- Problem sets: Homework6
- Discussion: Homework6_discussion
- Content: Groups. Hardness assumptions in cyclic groups: the discrete-logarithm assumption and Diffie-Hellman problems. Hash Functions Construction. The Diffie-Hellman key-exchange protocol.
Thursday (02/27/25) and Tuesday (03/04/25) and Tuesday (03/11/25)
- References: KL 11.1 11.2, 11.4.1, and 11.4.4
- Notes: Notes8
- Problem sets: Homework7
- Discussion: Homework7_discussion
- Content: Pohlig-Hellman algorithm. Primality Testing.
Thursday (03/13/25) and Tuesday (03/18/25)
- References: KL 11.1 11.2, 11.4.1, and 11.4.4
- Notes: Notes9
- Problem sets: Homework8
- Discussion: Homework8_discussion
- Content: RSA
Thursday (03/20/25) and Tuesday (03/25/25)
- References: KL 11.1 11.2, 11.4.1, and 11.4.4
- Notes: Notes10
- Problem sets: Homework9
- Discussion: Homework9_discussion
- Content: Rabin
Thursday (03/27/25) and Tuesday (04/03/25)
- Proposal and presentation
- Proposal Submission: April 3, 2025
- Proposal Approval: April 4, 2025
- Homework Approval: April 14, 2025
- Presentations Scheduled: 15 (Hugo), 22(Justin), 29 April, 2025 (Alex), in-class.