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Mathematics Department

Operator Algebras and Dynamics Seminars

Fall 2022

Dates subject to change depending on the colloquia schedule.

  • Nov
    14
  • Some underrated facts about solenoids
    Rodrigo Trevino
    University of Maryland
    Time: 03:45 PM

    View Abstract

    In this talk I will talk about flat solenoids of various flavors. I will discuss some topological, analytical and dynamical properties of these spaces and show how they interact. Time permitting I will discuss some applications.
  • Nov
    07
  • A summary of Aaron's dissertation titled "c-Differentials and Generalized Cryptographic Properties of Vectorial Boolean and p-ary Functions"
    CDR Aaron Geary
    USNA Math
    Location: CH 320
    Time: 03:45 PM

    View Abstract

    Aaron will present the background, motivation, some techniques, and some results of his dissertation research. The full dissertation abstract is below. This dissertation investigates a newly defined cryptographic differential, called a c-differential, and its relevance to the nonlinear substitution boxes of modern symmetric block ciphers. We generalize the notions of perfect nonlinearity, bentness, and avalanche characteristics of vectorial Boolean and p-ary functions using the c-derivative and a new autocorrelation function, while capturing the original definitions as special cases (i.e., when c=1). We investigate the c-differential uniformity property of the inverse function over finite fields under several extended affine transformations. We demonstrate that c-differential properties do not hold in general across equivalence classes typically used in Boolean function analysis, and in some cases change significantly under slight perturbations. Thus, choosing certain affine equivalent functions that are easy to implement in hardware or software without checking their c-differential properties could potentially expose an encryption scheme to risk if a c-differential attack method is ever realized. We also extend the c-derivative and c-differential uniformity into higher order, investigate some of their properties, and analyze the behavior of the inverse function's second order c-differential uniformity. Finally, we analyze the substitution boxes of some recognizable ciphers along with certain extended affine equivalent variations and document their performance under c-differential uniformity.
  • Oct
    03
  • Word complexity cutoffs for mixing properties of subshifts
    Time: 03:45 PM
  • Sep
    19
  • Cartan Envelopes
    David Pitts
    University of Nebraska-Lincoln
    Time: 03:45 PM
  • Sep
    12
  • Cartan Envelopes
    David Pitts
    University of Nebraska-Lincoln
    Time: 03:45 PM
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