Foundations of Cryptography
CSCI-662-01, Fall 2020

Instructor

Stanisław Radziszowski

building 70, room 3657, (585) 475-5193
spr@cs.rit.edu, https://www.cs.rit.edu/~spr
office hours: TWR 6:30pm-7:30pm via zoom, or email spr@cs.rit.edu anytime

Lectures

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.
• Wade Trappe and Lawrence C. Washington, Introduction to Cryptography with Coding Theory, Prentice Hall 2002, 2006.
• 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, fifth edition 2011 (popular textbook elsewhere.)
• Bruce Schneier, Applied Cryptography, John Wiley & Sons 1994 (popular textbook elsewhere.)
• Paul Garrett, Making, Breaking Codes. An Introduction to Cryptology, Prentice Hall 2001.
• Richard A. Mollin, An Introduction to Cryptography, Chapman & Hall/CRC 2001.
• Simon Singh, The Code Book, the evolution of secrecy from Mary, Queen of Scots, to quantum cryptography, Doubleday 1999.
• Cryptogram, electronic newsletter.
• Journal articles.

Prerequisites

Evaluation

• 05% class participation
• 45% homeworks
• 20% midterm exam, Monday, October 5, online
• 30% final exam, Monday, December 7, online, starts at 7pm

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.

• Done So Far
  8/19. Course logistics, my homepage, this page, homeworks page. Group S2 seats.
  8/24. Finish course logistics. Group S1 seats. Texbook chapter 1, slides 1-10.
  8/26. Finish textbook slides for chapter 1.
  8/31. Cryptography overview from spr's angle, slides 1-14.
  9/02. Slides 14-18 of the above. Textbook slides 1-14 for chapter 2.
  9/07. Finished textbook slides for chapter 2. Little more on PRNGs from Stinson and CRC Handbook.
  9/09. Finished the above. Textbook slides 1-12 for chapter 3.
  9/14. Finished textbook slides for chapter 3.
  9/16. Slide 28 chapter 3. Breaking 2DES. More on DES. Slides 1-8 for chapter 4.
  9/21. Finished textbook slides for chapter 4. Begin fields.
  9/23. GF(4), Z_n[x], fields, GF(8), GF(256) in AES.
  9/28. More on finite fields, all fields. Modes of operation slides 1-20.
  9/30. Finished chapter 5. MK-3 with large S-boxes (pdf | slides.pdf).
  10/5. Midterm exam.
  10/7. Learn Spanish on AES animation, and about Galois with AES cartoons.
  10/12. Hints on midterm. Chapter 6 slides 1-18.
  10/14. Hints on midterm. Chapter 6 slides 18-24.
  10/19. Euclid algorithm (EA), EEA, Euler function. Finish chapter 6.
  10/21. Euler, Fermat and Lagrange theorems, order of elements, examples.
  10/26. More on generators. Square/multiply, recursive gcd, some RSA slides. Chapter 7 slides 1-15.
  10/28. CRT. Almost finish chapter 7.
  11/2. OAEP, attacks, primes. Finish chapter 7.
  11/4. Primes, Miller-Rabin probabilistic primality test, AKS.
  11/9. DL-based protocols, DH, DHKE, chapter 8.
  11/11. DSA, EC, ECDSA and bitcoin, bitsign.pdf slides 1-16. Textbook chapters 9 and 10.
  11/16. Remaining bitcoin signature slides 17-36.
  11/18. Hashing, chapter 11.
  11/23. More hashing, from MD5 to sha3.pdf (look closely at slides 18-20), SHA-3 finalists.

• To Do. Some of the following slides, beyond the textbook, will be used in the course. It will be pointed in this place which were used and when 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
• RSA Laboratories
• The SHA-3 Zoo
• Combinatorial Computing and Cryptography in Gdańsk, November 22-26, 2010
• Links at Cryptography Research, Inc.
• TimeAI. Cryptogram 9/2019: Their claims are nonsensical. Run away. Run, far, far, away.