Foundations of Cryptography
CSCI-662-01, Fall 2022, Semester 2221

Instructor

Stanisław Radziszowski

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

Lectures, Monday/Wednesday, 5:00pm-6:15pm, room 70-1455

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 12, 70-1455, in class time
• 30% final exam, Monday, December 12, 70-1455, 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 Online Resources

• Your textbook website, or even better.
• Many video lectures by the textbook's authors.
• Some video lectures by Professor Monika Polak.

Schedule

• Done so Far in Fall 2022
  8/22. Course logistics, this page. Texbook chapter 1, slides 1-14.
  8/24. Finish textbook slides for chapter 1. Cryptography overview from spr's angle, slides 1-4.
  8/29. Overview continued.
  8/31. Overview finished. Start textbook chapter 2.
  9/07. Almost finished textbook slides for chapter 2. Modular arithmetic examples.
  9/12. Little more on PRNGs from Stinson and CRC Handbook. Start chapter 3.
  9/14. Chapter 3, DES.
  9/19. Finish chapter 3. Breaking 2DES. More on DES and modes. Slides 1-21 for chapter 5.
  9/21. AES, chapter 4 slides.
  9/26. Z_n[x], irreducible polynomials, fields, GF(256) in AES, fields.
  9/28. GF(4), GF(8), small fields.
  10/03. All fields. Closing chapter 5, GCM-AES. GF(9).
  10/05. MK-3 with large S-boxes (pdf | slides.pdf). Learn Spanish on AES animation, and about Galois with AES cartoons.
  10/12. Midterm exam.
  10/17. Chapter 6 slides.
  10/19. Euclid algorithm (EA), EEA, Euler function.
  10/24. Euler, Fermat and Lagrange theorems, order of elements, examples.
  10/26. Hints on midterm. Chapter 7 slides 1-10.
  10/31. Square/multiply, RSA short public key, Chinese remainder theorem in RSA, CRT.
  11/02. Primes, Miller-Rabin probabilistic primality test.
  11/07. More on Miller-Rabin test. Finish chapter 7. OAEP.
  11/09. More on generators, gen2251.pdf. AKS, factoring, Pollard RHO.
  11/14. DL-based protocols, DH, DHKE, chapter 8.
  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, chapter 10.

• To do
  12/*. DSA, ECDSA and bitcoin, bitcoin signature. Textbook chapters 9 and 10.
  12/*. 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.