Foundations of Cryptography
CSCI-662-01, Fall 2022, Semester 2221
building 70, room 3657,
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
Syllabus, outcomes, general course documents, policies, sample 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
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
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.
electronic newsletter by Bruce Schneier.
- Journal articles.
General knowledge of programming.
Background in combinatorics and discrete mathematics.
(CSCI-661 and (CSCI-603 or CSCI-605, with B or better in all courses))
or equivalent or permission of instructor. Students who complete CSCI-462
may not take CSCI-662 for credit.
- 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
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
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.
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.
Finish chapter 3. Breaking 2DES. More on
DES and modes. Slides 1-21 for chapter 5.
9/21. AES, chapter 4 slides.
Zn[x], irreducible polynomials, fields,
GF(256) in AES, fields.
9/28. GF(4), GF(8), small fields.
Closing chapter 5, GCM-AES. GF(9).
MK-3 with large S-boxes
Learn Spanish on
AES animation, and about Galois with
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,
10/26. Hints on midterm. Chapter 7 slides 1-10.
RSA short public key, Chinese remainder theorem in RSA,
Primes, Miller-Rabin probabilistic primality test.
More on Miller-Rabin test. Finish chapter 7.
More on generators, gen2251.pdf.
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).
Finish chapter 11 slides. More hashing,
from MD5 to sha3.pdf.
Signatures, RSA, DSA, chapter 10.
DSA, ECDSA and bitcoin,
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:
MK-3 with large S-boxes (
from MD5 to sha3.pdf (look closely at slides 18-20),
signatures in bitcoin bitsign.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.