Advanced Cryptography
CSCI762
Spring 2020
Instructor
bldg. 70, room 3657,
(585) 4755193, spr@cs.rit.edu
http://www.cs.rit.edu/~spr
Office hours:
Tuesday/Thursday 10am11am, 6:20pm8:00pm,
or send email
Lectures
Tuesday/Thursday, 5:00pm  6:15pm, room 701455
General Course Documents
Syllabus, outcomes, general course documents, policies, sample schedule:
college syllabus,
general 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.

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).

Lectures on
Combinatorial Computing and Cryptography
in Gdańsk, November 2226, 2010.
 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
CSCI462 or CSCI662, or permission of the instructor.
Evaluation
 25% homeworks
 15% takehome midterm exam
 25%
research paper and presentation, information and dates
 10%
class participation
 25% final exam, Thursday, April 30, 7pm9:30pm room 701455
Contents
This course investigates advanced topics in cryptography. It begins
with an overview of necessary background in algebra and number theory,
private and publickey 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
polynomialtime test of primality; discrete logarithm based
cryptosystems including those based on elliptic curves;
interactive protocols including the role of zeroknowledge 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 CSCI462/662 Cryptography
 Privatekey cryptosystems; Advanced Encryption Standard (AES)
 Overview of modular arithmetic, discrete logarithms, and primality/factoring
 Publickey 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 Ptime 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 publickey cryptosystems and signatures

Hashing, emerging SHA3 standard

Interactive protocols
 Touch of complexity theory
 Interactive proof systems; 0knowledge proof systems
 0knowledge authentication
 Electronic cash; Chaum and Brands schemes
 Private information retrieval

Selected topics
 AES news
 SHA3 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
Slides used in class so far
Cryptography  A Crash Overview
ElGamal and Shanks
RSA, Pollard p1
Pollardrho
Euler criterion, CDH and DDH
PohligHellman and index calculus
Galois field GF(27)
Slides to be used in class
elliptic curves basics
elliptic curves in crypto
ECDSA in Bitcoin
more signatures
knapsack cryptosystem, broken but still nice
Other useful links