Cryptography II
VCSG-706
Spring 2013
Instructor
bldg. 70, room 3657,
(585) 475-5193, spr@cs.rit.edu
http://www.cs.rit.edu/~spr
office hours: TR 4-5pm, M 8-9pm (if nobody comes by 8:15pm I may go home), or send email
Lectures
Monday/Wednesday, 6-8pm, room 70-2455
Books and Other Reading
- Douglas R. Stinson,
Cryptography: Theory and Practice, CRC Press,
third edition 2006 (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).
-
Lectures on
Combinatorial Computing and Cryptography
in Gdańsk, November 22-26, 2010.
- 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.
-
William Stallings,
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).
- Paul Garrett,
Making, Breaking Codes. An Introduction to Cryptology,
Prentice Hall 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
4005-705/4003-482 or permission of the instructor.
Evaluation
Contents
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
required.
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 VCSG-705/VCSS-482 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
-
Interactive protocols
- Touch of complexity theory
- Interactive proof systems; 0-knowledge proof systems
- 0-knowledge authentication
- Electronic cash; Chaum and Brands schemes
- Private information retrieval
-
Selected topics
- AES news
- SHA-3 news
- Private/public/group/share key generation and management
- Digital watermarking, digital fingerprinting
- Steganography
-
Selected topics in quantum computing
- Quantum computers
- Shor's algorithm, future demise of RSA
- Quantum cryptography
- Quantum key distribution and reconciliation
Other useful links