Advanced Cryptography
CSCI-762
Spring 2020

Instructor

Stanisław Radziszowski

bldg. 70, room 3657,
(585) 475-5193, spr@cs.rit.edu
http://www.cs.rit.edu/~spr
Office hours: Tuesday/Thursday 10am-11am, 6:20pm-8:00pm, or send email

Lectures

Tuesday/Thursday, 5:00pm - 6:15pm, room 70-1455

General Course Documents

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 22-26, 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

Evaluation

• 25% homeworks
• 15% take-home midterm exam
• 25% research paper and presentation, information and dates
• 10% class participation
• 25% take home final exam, pdf to be emailed 4/30, due 5/2 AoE

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 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
• 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

Slides used in class so far

Cryptography - A Crash Overview
ElGamal and Shanks
RSA, Pollard p-1
Pollard-rho
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

ECDSA in Bitcoin
more signatures
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: short and long.
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

Other links

• FIPS 186-5 draft
• SP 800-186 draft
• 250 digit RSA (829 bits) challenge is solved, February 28, 2020
• NSA Suite B Cryptography
• Computer Security Resource Center, official government site at NIST
• Links at Cryptography Research, Inc.