Introduction to Cryptography
CSCI-462-03, Spring 2025, Term 2245

Instructor

Stanisław Radziszowski

building 70, room 3657, (585) 475-5193
spr@cs.rit.edu, https://www.cs.rit.edu/~spr

Office hours: in person TuWe 6:30pm-8pm, @70-3657,
on zoom (must prearrange time), or by email spr@cs.rit.edu

Lectures, Tuesday/Thursday, 5:00pm-6:15pm, room 70-2590

General Course Documents

Syllabus, outcomes, general course documents, policies, sample schedule: college syllabus, general schedule.
This page gives the current offering's contents, further links and schedule.

Books and Other Reading

Christof Paar and Jan Pelzl, Understanding Cryptography, SpringerLink 2010, first edition. Christof Paar, Jan Pelzl and Tim Güneysu, Understanding Cryptography, from Established Symmetric and Asymmetric Ciphers to Post-Quantum Algorithms, Springer 2024, second edition (required textbook). Your textbook website includes the textbook, textbook-associated slides and videos of lectures. For additional slides used in this course see links below in Online Resources.
Douglas R. Stinson and Maura B. Paterson, Cryptography: Theory and Practice, CRC Press, fourth edition 2019.
A. J. Menezes, P. C. van Oorschot and S. A. Vanstone, CRC Handbook of Applied Cryptography, CRC Press 1996/2001 (great addition to your bookshelf.)
Niels Ferguson, Bruce Schneier and Tadayoshi Kohno, Cryptography Engineering, John Wiley & Sons 2010 (complementary reading.)
William Stallings, Cryptography and Network Security. Principles and Practice, Prentice Hall, seventh edition 2018 (popular textbook elsewhere.)
Simon Singh, The Code Book, the evolution of secrecy from Mary, Queen of Scots, to quantum cryptography, Doubleday 1999.
Crypto-Gram, electronic newsletter by Bruce Schneier.
Journal articles.

Prerequisites

General knowledge of programming. Background in combinatorics and discrete mathematics. (CSCI-243 and MATH-190, with B or better in both courses) or permission of instructor. Students who complete CSCI-462 may not take CSCI-662 for credit.

Evaluation

08% class participation
42% homeworks
20% midterm exam, Tuesday, March 4, 70-2590, 5pm-6:15pm
30% final exam, Thursday, May 1, 70-2590, 4:15pm-6:45pm

The course is devoted to the review of basic cryptographic algorithms, their implementations and usage. Classical encryption techniques and those of Diffie-Hellman and Rivest-Shamir-Adleman will be seen in depth, and an overview of several others will be presented, especially those denominated as public-key cryptosystems. The symmetric systems DES and AES, and others, will be studied. The course also presents digital signatures, hash functions, authentication schemes and some interactive proof protocols.

The specific topics will include:

Introduction, need of security. History.
Substitution and monoalphabetic ciphers.
Vigenere cipher, coincidence index.
A touch of number theoretical algorithms.
Private key cryptography.
Data Encryption Standard - DES.
Rijndael, Advanced Encryption Standard - AES.
Secure hashing algorithms - SHA-family, NIST competition.
Public key cryptography. One-way functions.
Rivest-Shamir-Adleman cryptosystem - RSA. RSA-xxx challenge.
Overview of ElGamal cryptosystem, discrete logarithms, digital signatures.

Main Resources

Your textbook website (includes the main slides shown in class).
Many video lectures by the textbook's authors.
Some tutoring is available.
Some video lectures by Professor Monika Polak at RIT.

Schedule

Done so far
1/14. Course logistics, this page. Start texbook Chapter 1.
1/16. Chapter 1. KMGTPE... kilo,mega,giga
1/21. Finish Chapter 1 slides. Started cryptography overview from spr's angle.
1/23. Finished the above. Textbook slides 1-7 for Chapter 2.
1/28. Textbook slides 7-21 for Chapter 2.
1/30. Finish textbook slides for Chapter 2. Modular arithmetic examples.
2/04. Chapter 3 slides 1-19, DES.
2/06. Finish Chapter 3. Breaking 2DES.
2/11. More on DES and modes. Slides 1-22 for Chapter 5.
2/13. AES, Chapter 4 slides.
2/18. Finish Chapter 4 slides. Z_n[x], irreducible polynomials, fields.
2/20. GF(256) in AES, fields, GF(8), GF(9), small fields.
2/25. GF(4). All fields. Closing Chapter 5, GCM-AES.
2/27. MK-3 with large S-boxes (pdf | slides.pdf). Start Chapter 6.
3/04. Midterm exam.
3/06. Class met on zoom. More Chapter 6. Watch an AES animation, and learn about Galois with AES cartoons.
3/18. Chapter 6: Euclid Algorithm (EA), Extended Euclid Algorithm EEA, Euler function.
3/20. Euler and Fermat theorems. Square/multiply.
3/25. Chapter 7, up to RSA short public key.
3/27. Chinese remainder theorem in RSA, CRT.
4/01. Primes, Fermat primality test. Miller-Rabin probabilistic primality test.
4/03. Finish Chapter 7. Primality big picture, AKS.
4/08. DL-based protocols, DH, DHKE, ElGamal, Chapter 8.
4/10. Elliptic curves, Chapter 9.
4/15. OAEP, gen2251.pdf, other RSA recommendations. Signatures, RSA, Chapter 10.
4/17. DSA, finishing Chapter 10. Start hashing, Chapter 11.
4/22. Hashing, Chapter 11.
4/24. Birthday paradox, Chapter 11, from MD5 to sha3.pdf (in particular slides 18-20).
Done in Fall 2024
other links
Some of the following slides, beyond the textbook, are used in the course, pointed to as we go: overview, modtabs.txt, expgcd.pdf, prng.pdf, desplus.pdf, gf.pdf, MK-3 with large S-boxes ( pdf | slides.pdf), gen2251.pdf, crt.pdf, primes.pdf, AKS.pdf, oaep.pdf, cts.jpg, rho.pdf, from MD5 to sha3.pdf (look closely at slides 18-20), SHA-3 finalists, signatures in bitcoin bitsign.pdf, knap.pdf.

Other Online Resources

Some lectures by Scott Aaronson on Quantum Computing Since Democritus, in particular Lecture 8: Crypto.
Post-Quantum Cryptography Program, NIST report 8309, July, CCC white paper, November 2020.
Common encryption types explained on CompariTech.
Combinatorial Computing and Cryptography in Gdańsk, November 22-26, 2010.
CSCI-764 course on Quantum-Resistant Cryptography.
TimeAI. Cryptogram 9/2019: Their claims are nonsensical. Run away. Run, far far away.

Introduction to Cryptography CSCI-462-03, Spring 2025, Term 2245