Foundations of Cryptography
CSCI-662-01, Fall 2023, Semester 2231

Instructor

Stanisław Radziszowski

building 70, room 3657, (585) 475-5193
spr@cs.rit.edu, https://www.cs.rit.edu/~spr
office hours: in person MoWe 6:30pm-8pm 70-3657, on zoom (must prearrange time), or by email spr@cs.rit.edu

Lectures, Monday/Wednesday, 5:00pm-6:15pm, room 70-2455

General Course Documents

Books and Other Reading

• Christof Paar and Jan Pelzl, Understanding Cryptography, SpringerLink, 2010 (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

Evaluation

• 05% class participation
• 45% homeworks
• 20% midterm exam, Wednesday, October 18, 70-2455, in class time
• 30% final exam, Monday, December 18, 70-2455, 7pm-9:30pm

Contents

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, or even better (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.

Schedule

• Done in Fall 2023
  8/28. Course logistics, this page. Start texbook slides chapter 1.
  8/30. Finish textbook slides for chapter 1.
  9/06. Cryptography overview from spr's angle.
  9/11. Overview finished. Start textbook chapter 2.
  9/13. Finish textbook slides for chapter 2.
  9/18. More on LFSRs. Modular arithmetic examples.
  9/20. Little more on PRNGs from Stinson and CRC Handbook. Start chapter 3.
  9/25. Chapter 3, DES.
  9/27. Breaking 2DES. More on DES and modes. Slides 1-13 for chapter 5.
  10/02. Slides 13-21 for chapter 5. AES, chapter 4 slides.
  10/04. Finish chapter 4 slides. Z_n[x], irreducible polynomials, fields.
  10/11. GF(256) in AES, fields, GF(4), GF(8), small fields.
  10/16. All fields. Closing chapter 5, GCM-AES. GF(9).
  10/18. Midterm exam.
  10/23. MK-3 with large S-boxes (pdf | slides.pdf). Learn Spanish on AES animation, and about Galois with AES cartoons.
  10/25. Chapter 6 slides.
  10/30. Euclid Algorithm (EA), Extended Euclid Algorithm EEA, Euler function.
  11/01. Euler and Fermat theorems. Chapter 7 slides 1-11.
  11/06. Square/multiply, RSA short public key, Chinese remainder theorem in RSA, CRT.
  11/08. Primes, Miller-Rabin probabilistic primality test.
  11/13. More on Miller-Rabin test. Finish chapter 7.
  11/15. More on Miller-Rabin test. Primality big picture, AKS, factoring. OAEP.
  11/20. DL-based protocols, DH, DHKE, chapter 8. Generators (primitive elements), gen2251.pdf,
  11/27. Signatures, RSA, DSA, chapter 10.
  11/29. Finish chapter 10. Hashing, chapter 11.

• To do. Done in Fall 2022
  11/16. Hashing, chapter 11 slides 1-13. Birthday paradox, from MD5 to sha3.pdf (slides 18-20).
  11/21. Finish chapter 11 slides. More hashing, from MD5 to sha3.pdf.
  11/28. SHA-3 finalists. Signatures, RSA, DSA.
  11/30. DSA, ECDSA and bitcoin, bitcoin signature. Overview of textbook chapters 9 and 10.
  12/05. Last class. MACs, chapter 12.

• Some of the following slides, beyond the textbook, are used in the course. They will be 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.
• The SHA-3 Zoo.
• Combinatorial Computing and Cryptography in Gdańsk, November 22-26, 2010.
• TimeAI. Cryptogram 9/2019: Their claims are nonsensical. Run away. Run, far, far, away.