bldg. 70, room 3657,
(585) 475-5193, firstname.lastname@example.org
Tuesday/Thursday 10am-11am, 6:20pm-8:00pm,
or send email
Tuesday/Thursday, 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 and schedule.
Books and Other Reading
- Douglas R. Stinson,
Cryptography: Theory and Practice, CRC Press,
fourth edition 2019 (required textbook).
Known errors for second edition are posted.
- Alfred J. Menezes, Paul C. van Oorschot and Scott A. Vanstone,
CRC Handbook of Applied Cryptography, CRC Press 1996 (great addition
to your bookshelf).
- Lawrence C. Washington,
Elliptic Curves. Number Theory and Cryptography,
Chapman and Hall, CRC Press 2003.
Henri Cohen and Gerhard Frey,
Handbook of Elliptic and Hyperelliptic Curve Cryptography,
Chapman and Hall, CRC Press 2006.
Cryptography and Network Security. Principles and Practice,
Prentice Hall, fifth edition 2011.
- Bruce Schneier,
Applied Cryptography, John Wiley and Sons 1994
(popular textbook at other universities).
Combinatorial Computing and Cryptography
in Gdańsk, November 22-26, 2010.
- Simon Singh, The Code Book, the evolution of secrecy from Mary,
Queen of Scots, to quantum cryptography, Doubleday 1999.
- Journal articles.
CSCI-462 or CSCI-662, or permission of the instructor.
- 25% homeworks
- 15% take-home midterm exam
research paper and presentation, information and dates
- 25% take home final exam, pdf to be emailed 4/30, due 5/2 AoE
This course investigates advanced topics in cryptography. It begins
with an overview of necessary background in algebra and number theory,
private- and public-key cryptosystems, and basic signature schemes.
The course will cover number theory and basic theory of Galois fields
used in cryptography; history of primality algorithms and the
polynomial-time test of primality; discrete logarithm based
cryptosystems including those based on elliptic curves;
interactive protocols including the role of zero-knowledge proofs in
authentication; construction of untraceable electronic cash on the
net; and quantum cryptography. Other topics may include digital
watermarking, fingerprinting, and steganography. Programming will be
Students will write a term paper, either theoretical based on
literature or reporting student's own implementation or experiments
with a chosen cryptographic scheme. Depending on the size of the group,
some or all students will give a presentation to the class.
The specific topics will include
Review of the prerequisite course CSCI-462/662 Cryptography
- Private-key cryptosystems; Advanced Encryption Standard (AES)
- Overview of modular arithmetic, discrete logarithms, and primality/factoring
- Public-key cryptosystems; ElGamal cryptosystem
- Basic signature schemes
Algebra and number theory
- Rings of polynomials
- Existence and finding primitive roots, Blum integers
- Galois fields GF(p^k)
- Primes; Agrawal, Kayal, Saxena P-time algorithm for recognizing primes
- Elliptic curves
Discrete logarithm based cryptosystems and signatures
- Elliptic Curve Cryptosystem (ECC)
- Digital Signature Standard (DSS)
- Selection of other signature schemes
- Overview of discrete logarithm algorithms
- Ethical aspects of public-key cryptosystems and signatures
Hashing, emerging SHA-3 standard
- Touch of complexity theory
- Interactive proof systems; 0-knowledge proof systems
- 0-knowledge authentication
- Electronic cash; Chaum and Brands schemes
- Private information retrieval
- AES news
- SHA-3 news
- Private/public/group/share key generation and management
- Digital watermarking, digital fingerprinting
Selected topics in quantum computing
- Quantum computers
- Shor's algorithm, future demise of RSA
- Quantum cryptography
- Quantum key distribution and reconciliation
Slides used in class so far
Cryptography - A Crash Overview
ElGamal and Shanks
RSA, Pollard p-1
Euler criterion, CDH and DDH
Pohlig-Hellman and index calculus
Galois field GF(27)
elliptic curves basics
elliptic curves in crypto
Switch to the remote mode from March 24
remote mode information,
join class on zoom,
meeting ID 637 783 735
ECDSA in Bitcoin
EC in signal
X3DH, see also
pages 478-484 of edition 4 of the textbook
NIST update on EC and PQC
SIKE (5 intro slides):
supersingular isogeny key encapsulation PQC competitor
Two more presentations on SIKE:
Full SIKE document (101 pages).
Montgomery and Edwards curves by Tanay Dusane.
Slides to be used in class
full domain hash signatures security
knapsack cryptosystem, broken but still nice