Banca de DEFESA: RAVI BARRETO DORIA FIGUEIREDO

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
STUDENT : RAVI BARRETO DORIA FIGUEIREDO
DATE: 09/08/2023
TIME: 14:00
LOCAL: Sessão por videoconferência. Link: meet.google.com/tyi-matd-xrs
TITLE:

TANGENT-CHEBYSHEV MAPS OVER FINITE FIELDS: THEORETICAL CONTRIBUTIONS AND APPLICATION SCENARIOS.

KEY WORDS:

Finite fields, maps over finite fields, polynomials over finite fields, Chebyshev polynomials, finite field trigonometry, permutations, involutions, cryptography, error correcting codes.

PAGES: 92
BIG AREA: Engenharias
AREA: Engenharia Elétrica
SUMMARY:

The study of maps defined over finite fields has attracted the attention of researchers interested both in theoretical aspects and in application scenarios. In particular, there are several families of polynomial and rational maps, whose usefulness in cryptography and in error- correcting codes, for example, has been demonstrated. In this context, the present work has as its starting point the recently introduced tangent-Chebyshev rational maps, whose definition, which is similar to that of the well-known Chebyshev polynomials of the first kind, employs finite field trigonometric functions. As original contributions of this thesis, new properties of the referred maps are presented, which include their fixed points, their relationship with other maps and their representation by means of graphs. Furthermore, the definition of a new type of tangent-Chebyshev map is proposed; in a certain sense, it is analogous to the Chebyshev polynomial of the third kind. Properties of such maps are also studied, which includes their computation by means of recurrence equations, their relationship with tangent-Chebyshev maps (of the first kind) and the specification of their zeros and poles. Finally, the applicability of the investigated maps in the construction of interleavers for error correcting codes is preliminarily evaluated and the possibility of their use in public key cryptography schemes is illustrated.

COMMITTEE MEMBERS:
Externo à Instituição - FRANCISCO MADEIRO BERNARDINO JUNIOR - UPE
Interno - 3101263 - JOSE RODRIGUES DE OLIVEIRA NETO
Externo ao Programa - 1168575 - JOSE SAMPAIO DE LEMOS NETO - nullPresidente - 1882484 - JULIANO BANDEIRA LIMA
Interno - 1130403 - RICARDO MENEZES CAMPELLO DE SOUZA