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

  Darren Creutz

  USNA

  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

  Abstract