Cryptology RIT, Fall 2006

Research Focus:

This is a seminar that will cover some recent papers in mathematical cryptography. The plan is to have a student lecture each week on a recent paper in cryptology with mathematical emphasis.

Prerequisites:

Basic knowledge of groups and finite fields. Some knowledge of cryptology.

Meeting Times:

Wednesdays 10-10:50 (Note change in time)

Room:

Math 1311

Contact:

Larry Washington (lcw at math)

Registering:

To register, sign up for Section 5501 for 1 credit. If you are an undergrad, the course number is 498. If you are a grad student, it's 698. If you need to get permission, send an email to Larry Washington.

Talks in Spring 2007:

  • February 21, 10am (note time): Juliana Belding: Elliptic curves over the dual numbers
  • February 28, 10am: Nicholas Sze: Finding square roots mod p
  • March 7, 10am: Greg Bard: Algebraic cryptanalysis of Keeloq

    Talks in Fall 2006:

  • September 6: organizational meeting
  • September 13, 20: No meeting
  • September 27: Greg Bard: SAT solvers
  • October 4: Enver Ozdemir: AGM for elliptic curves
  • October 11: Nicholas Sze: Primality testing with Gaussian periods
  • October 18: No meeting
  • October 25: Susan Schmoyer: "New explicit conditions of elliptic curve traces for FR-reduction," by Miyaji, Nakabayashi, and Takano
  • November 1: Juliana Belding: Torus-based cryptography

  • November 8: No meeintg
  • November 15: Walter Ray-Dulany: Codes from curves
  • No more talks in Fall 2006

    Talks in Spring 2006:

  • January 30: Short organizational meeting
  • February 6: Kate Truman: Zero knowledge and RSA
  • February 13: Juliana Belding: Elliptic curve Paillier schemes
  • February 20: No talk
  • February 27: Susan Schmoyer: Cubic fields and cryptography
  • March 6: Emma Riggs: A public key encryption scheme based on the polynomial reconstruction problem.
  • March 27: Walter Ray-Dulany: Traffic analysis
  • April 10: Walter Ray-Dulany: Traffic analysis (continued)

    Talks in Fall 2005:

  • September 14: Organizational meeting
  • September 21: Larry Washington: Breaking RSA might sometimes be easier than factoring; based on a paper by Boneh and Venkatesan (but their Lemma 3.2 is usually false).
  • Monday, September 26, 3pm, Room 1308: Greg Bard: Matrices over GF(2) and Stream Cipher Cryptanalysis, an Introduction
  • Monday, October 3, 3pm, Room 1308: Juliana Belding: An elliptic curve cryptosystem over the ring F[X]/(X^2)
  • Wednesday, October 12, 2pm (note time and date), Room 1311: Kate Truman: Braid group cryptography
  • Monday, October 17, 3pm, Room TBA: Enver Ozdemir: Chameleon hashes
  • Wednesday, October 26, 2pm: Prathap Sridharan: How to Break MD5 and Other Hash Functions by Wang et al.
  • Wednesday, November 2, 2:15pm: Emma Riggs: "Cracking" a random number generator
  • Monday/Wednesday November 7/9: no talk
  • Wednesday, November 16, 2pm: Susan Schmoyer: Hyperelliptic curve cryptography
  • Monday, November 28, 3pm: Walter Ray-Dulany: Breaking a cryptosystem based on (usual) logarithms

    Talks in Spring 2005:

  • February 9: Juliana Belding: Multicollisons in hash functions
  • February 23: Avi Dalal: Lucas' primality test
  • March 2: Greg Bard: Hash functions
  • March 9: Julie Staub: Cryptographic Details of Chaum's E-Voting Scheme a paper by Chaum and an analysis by Bryans/Ryan
  • March 16: Enver Ozdemir: Applications of Multilinear Forms to Cryptography
  • March 30: No meeting
  • April 6: No meeting
  • April 13: Kate Truman: Non-commutative NTRU
  • April 20: Greg Bard: Pseudorandom Function Domain Extension Using Directed Acyclic Graphs

    Talks in Fall 2004:

  • September 22: Greg Bard: Modes of Encryption Secure Against Chosen Plaintext Blockwise Adaptive Attack
  • September 29: Greg Bard (continued)
  • October 6: Julie Staub: An Introduction to Chaum's Verified-Voting Scheme. A paper by Chaum, A paper by Naor and Shamir on Visual Cryptography
  • October 13: Avi Dalal: Deterministic Polynomial Time Equivalence of Computing the RSA Secret Key and Factoring
  • October 20: No meeting
  • October 29: Eric Errthum
  • November 3: No meeting
  • November 10: No meeting
  • November 17: Enver Ozdemir: Fuzzy identity-based encryption
  • December 1: Juliana Belding:

    Talks from Spring 2004:

  • Feb. 11: Enver Ozdemir: Factoring N=p^r*q for some large r
  • Feb. 18: Kate Truman: NSS and Cryptanalysis of the Revised NTRU Signature Scheme
  • Feb. 25: Julie Staub: Practical threshold RSA signatures without a trusted dealer
  • March 3: Julie Staub: continued
  • March 10: Greg Bard: Solving Systems of Polynomial Equations in GF(2)
  • March 17: Avi Dalal: A Polynomial-Time Algorithm for Primality Testing
  • March 31: Larry Washington: Breaking the basic Merkle-Hellman knapsack scheme
  • April 7: Eric Errthum: An elliptic curve analogue of RSA

    Talks from Fall 2003:

  • Sept. 10: Susan Schmoyer: Key exchange with imaginary quadratic fields
  • Sept. 17: Greg Bard: Cryptanalysis of nonlinear stream ciphers using very large matrices One paper and A second paper
  • Sept. 24: Larry Washington: Lattice reduction and applications
  • Oct. 1: Larry Washington (continued)
  • Oct. 8: Chris Zorn: Cryptanalysis of Unbalanced RSA with Small CRT-Exponent
  • Oct. 15: Eric Errthum: Bilinear Pairings in Cryptography Description: I'll give a quick intro to the different Diffie-Hellman problems and the properties of bilinear pairings. Then I will show some applications of the pairings in public key cryptography via signatures, identity-based encryption, and tripartite key agreement. Finally, I'll make a short comment on the existence of multilinear forms.
  • Oct. 22: Kate Truman: NTRU
  • Oct. 29: Chiu Yuen Koo: Robust sharing of secrets when the dealer is honest or cheating
  • Nov. 5: Aram Khalili: Efficient generation of shared RSA keys and a related paper
  • Nov. 12: Aram Khalili (continued)
  • Nov. 19: Avinash Dalal: A generalized birthday problem
  • Nov. 26: No meeting
  • Dec. 3: Alvaro Cardenas, Survey of quantum cryptography
    References: Peter W. Shor, "Polynomial-Time algorithms for prime factorization and discrete logarithms on a quantum computer," SIAM journal of comput., October 1997
    Bennet, Bessette, Brassard, Salvail and Smolin, "Experimental quantum cryptography" September 1991
    Rieffel and Polak "An introduction to quantum computing for non-physicists"
  • Dec. 10: Prabha Ramachandran, New Lattice based Cryptographic Constructions

    Possible subjects and papers for future talks:

  • Lattice-based cryptosystems
  • Braid groups and attacks on some braid group protocols
  • Multiparty Computation from Threshold Homomorphic Encryption
  • Finding multicollisions (not in hash functions)
  • more possibilities will be listed soon