MAD 6209 Advanced Topics in Cryptology

Course Information

• (Combinatorial) Group Theory and Cryptography
• (Group) Key Establishment
• Multivariate Cryptography
• Quantum Cryptography
• Simulatability-Based Security Modeling

Topics Discussed in Class

• 01/09/06-01/18/06: Security requirements for signature schemes using an example from multivariate cryptography
  Suggested reading for (going beyond) the material covered in class:
  • SFLASHv3, a fast asymmetric signature scheme
  • A short comment on the affine parts of SFLASH^{v3}
  • On Subliminal Channels in Deterministic Signature Schemes
  • Key substitution attacks revisited: Taking into account malicious signers
• 01/20/06-01/27/06: Using braid groups in cryptography
  Suggested reading for (going beyond) the material covered in class:
  • Braid-based cryptography
  • An Algebraic Method for Public-Key Cryptography
  • Cryptography and Braid Groups
  • K. Murasugi, B. Kurpita: A Study of Braids (Mathematics and Its Applications, Kluwer Academic Publishers, ISBN 0-792-35767-1)
• 01/30/06-02/08/06: Introduction to Key Establishment
  The introduction in class was based on Chapter 1 of
  • C. Boyd, A. Mathuria: Protocols for Authentication and Key Establishment (Information Security and Cryptography Texts and Monographs, Springer, ISBN 3-540-43107-1)
• 02/10/06-02/15/06: An example of a formal model for group key establishment
  Suggested reading for (going beyond) the material covered in class:
  • Secure Group Key Establishment Revisited
  • A protocol proposed by J. Katz and M. Yung at CRYPTO 2003
  • Provably-Secure Mutual Authentication and Key Establishment Protocols Lounge
• 02/17/06: An example of an identity-based scheme: Okamoto's identity-based key agreement
  The discussion in class was based on Chapter 5.6 of
  • C. Boyd, A. Mathuria: Protocols for Authentication and Key Establishment (Information Security and Cryptography Texts and Monographs, Springer, ISBN 3-540-43107-1)
• 02/20/06: Secret sharing; CAPTCHAs
  Suggested reading for (going beyond) the material covered in class:
  • How to Share a Secret
  • Telling Humans and Computers Apart (Automatically)
  • Inaccessibility of CAPTCHA
• 02/22/06-02/24/06: The idea of threshold cryptography
  The introduction in class was based on
  • Distributed Cryptography
• 02/27/06-03/01/06: Presentation of Homework Project #1 (a normal form in the braid group)
  Suggested literature:
  • J. C. Cha et al.: An Efficient Implementation of Braid Groups
• 03/03/06: Informal discussion of a more complex protocol task: digital cash
  The discussion in class was based on Chapter 6.4 of
  • B. Schneier: Applied Cryptography (Protocols, Algorithms, and Source Code in C), John Wiley & Sons, ISBN 0-471-12845-7)
• 03/13/06-03/15/06: Presentation of Homework Project #1 (a provably secure group key establishment)
  Suggested literature:
  • E. Bresson and D. Catalano: Constant Round Authenticated Group Key Agreement via Distributed Computation
• 03/17/06-03/20/06: Presentation of Homework Project #1 (JFK)
  Suggested literature:
  • W. Aiello et al.: Just Fast Keying: Key Agreement In A Hostile Internet
• 03/20/06-03/22/06: Presentation of Homework Project #1 (a conceptual key establishement proposal)
  Suggested literature:
  • M. Cherepnev: Schemes of public key distribution of keys based on a non-commutative group
• 03/24/06-04/03/06: The idea of universal composability
  Suggested reading for (going beyond) the material covered in class:
  • R. Canetti: Universally Composable Security: A new Paradigm for Cryptographic Protocols (Extended Abstract)
  • R. Canetti: Universally Composable Security: A New Paradigm for Cryptographic Protocols
  • M. Backes, B. Pfitzmann and R. Waidner: Secure Asynchronous Reactive Systems
• 04/05/06: Constructing meaningful hash collisions for PostScript files
  Suggested literature:
  • M. Gebhardt, G. Illies, W. Schindler: A Note on the Practical Value of Single Hash Collisions for Special File Formats
• 04/07/06: An example for the use of parallel architectures in cryptanalysis: matrix-by-vector multiplication on a mesh architecture
  Suggested literature:
  • A. K. Lenstra et al.: Analysis of Bernstein's factorization circuit (the discussion in class was based on Section 5.4)
  • W. Geiselmann et al.: Improved routing-based linear algebra for the Number Field Sieve
• 04/10/06: A "One hour course on quantum Mechanics" (Dr. J. Sam Faulkner)
  Up to date information on current work in quantum computing and quantum cryptography can be found in the
  • section on quantum physics of arXiv.org
• 04/12/06: Discussion on "how to use a one time pad"
  Several issues addressed in class are discussed in
  • D. Raub et al.: On the Security and Composability of the One Time Pad
• 04/14/06-04/17/06: Introduction to Quantum Key Establishment
  The discussion in class was based on
  • Chapter 6.2 of J. Gruska: Quantum Computing, McGraw-Hill, ISBN 007 709503 0
  • Ch. Bennett et al.: Experimental Quantum Cryptography
• 04/19/06-04/24/06 Message Authentication Codes
  The discussion in class was based on
  • Chapter 4.4 of D. R. Stinson: Cryptography, Theory and Practice, 3rd ed., Chapman & Hall/CRC, ISBN 1-58488-508-4
  • FIPS PUB 180-2: Secure Hash Standard
  • FIPS PUB 198: The Keyed-Hash Message Authentication Code (HMAC)
  For more information on cryptographic hash functions, you may like to take a look at B. Preneel: Analysis and Design of Cryptographic Hash Functions.