In this thesis we study a class of authentication codes with secrecy. We obtain the maximum success probability of the impersonation attack and the maximum success probability of the substitution attack on these authentication codes with secrecy. Moreover we determine the level of secrecy provided by these authentication codes. Our methods are based on the theory of algebraic function fields over finite fields. We study a certain class of algebraic function fields over finite fields related to this class of authentication codes. We also determine the number of rational places of this class of algebraic function fields.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-01-13T13:41:39Z No. of bitstreams: 1 marianadealmeidanerycoutinho.pdf: 1084614 bytes, checksum: dded13e49c590fa1685ce4a2b9e5cf3c (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-01-25T17:33:13Z (GMT) No. of bitstreams: 1 marianadealmeidanerycoutinho.pdf: 1084614 bytes, checksum: dded13e49c590fa1685ce4a2b9e5cf3c (MD5) / Made available in DSpace on 2016-01-25T17:33:13Z (GMT). No. of bitstreams: 1 marianadealmeidanerycoutinho.pdf: 1084614 bytes, checksum: dded13e49c590fa1685ce4a2b9e5cf3c (MD5) Previous issue date: 2015-03-10 / FAPEMIG - Fundação de Amparo à Pesquisa do Estado de Minas Gerais / O estudo das curvas algébricas sobre corpos finitos, o qual está intrinsecamente relacionado à teoria dos corpos de funções sobre corpos finitos, é de grande interesse na álgebra abstrata, com destaque para aplicações na teoria dos números e na teoria dos códigos. Com essa motivação, estamos aqui interessados em estudar a existência de corpos de funções F/Fq com um número prescrito de lugares de determinados graus, estando baseados em algumas seções do artigo de ANBAR e STICHTENOTH (2013). Para isso, faremos também uma abordagem acerca da teoria geral dos corpos de funções, apresentando os principais elementos que nos auxiliarão na compreensão dos resultados anteriormente mencionados. / The study of algebraic curves over finite fields, which is intrinsically related to the theory of function fields over finite fields, is of great interest in abstract algebra, especially for applications in number theory and coding theory. With this motivation, we are here interested in studying the existence of function fields with a prescribed number of places of certain degrees, based on some sections of the paper of ANBAR and STICHTENOTH (2013). For this, we will also make a study of the general theory of function fields, showing the main elements that will assist us in understanding the results mentioned above.