Foundations of Cryptography
CSCI-662-01, Fall 2020
building 70, room 3657,
zoom, or email firstname.lastname@example.org anytime
Monday/Wednesday, 5:00pm-6:15pm, room 70-2590,
AB-S delivery mode, zoom
S1 group has in-person classes on Mondays, and participates in class remotely on Wednesdays.
S2 group has in-person classes on Wednesdays, and participates in class remotely on Mondays.
General Course Documents
Syllabus, outcomes, general course documents, policies, sample schedule:
special COVID-19 addendum.
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.
- 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
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.
- 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, Monday, October 5, mode TBA
- 30% final exam, December TBA
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
textbook website, or
Many video lectures by the textbook's authors.
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.
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), Zn[x],
fields, GF(8), GF(256) in AES.
9/28. More on finite fields,
Modes of operation slides 1-20.
9/30. Finished chapter 5.
MK-3 with large S-boxes
10/5. Midterm exam.
10/7. Learn Spanish on
AES animation, and about Galois with
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,
More on generators.
Square/multiply, recursive gcd, some RSA
slides. Chapter 7 slides 1-15.
10/28. CRT, start primes. Almost finish chapter 7.
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:
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,
progress report NISTIR 8309 , July 2020.
Common encryption types explained on CompariTech
- The SHA-3 Zoo
Combinatorial Computing and Cryptography
in Gdańsk, November 22-26, 2010
- Links at
Cryptography Research, Inc.
Their claims are nonsensical. Run away. Run, far, far, away.