For more information about this meeting, contact Robert Vaughan.

Title: | Ambiguity and deficiency of permutations |

Seminar: | Algebra and Number Theory Seminar |

Speaker: | David Thomson, Carleton University, Ottawa and Penn State University |

Abstract: |

The difference map of a function f between finitegroups is given by D_{f,a}(x) = f(x+a) - f(x). For cryptographic purposes, permutation functions whose difference maps are nearly injective are preferred. The ambiguity and deficiency of a function was recently introduced by Panario, et al (2011) to give a fine measure of the injectivity of the difference maps of candidate functions for symmetric key ciphers.
In this talk, we discuss some of the motivations of considering the ambiguity and deficiency, as well as introducing some of their basic properties. We will
focus our attention primarily on permutation functions defined over finite Abelian groups. We give lower-bounds on both measures and show that permutations which achieve optimal ambiguity and deficiency also achieve high
non-linearity. We will also prove some differential properties of a subset of an important class of polynomials, namely the Dembowski-Ostrom polynomials. |

### Room Reservation Information

Room Number: | MB106 |

Date: | 09 / 20 / 2012 |

Time: | 11:15am - 12:05pm |