Construção de S-Boxes com Valores Ótimos de Não Linearidade Baseada em uma Relação entre o Multigrafo de Ramanujan e a Matriz da Transformação Afim

  • Marcio Belleza LNCC
  • Fábio Borges LNCC

Resumo


Uma S-Box (caixa de substituição) deve ter pelo menos valores ótimos para não linearidade (N L), uniformidade diferencial e grau algébrico. Segundo a literatura, uma S-Box criptograficamente forte deve ter N L > 100. O AES (Advanced Encryption Standard) usa uma matriz binária não singular S para construir sua S-Box. Muitos trabalhos escolhem S em aproximadamente 262 matrizes não singulares ou constroem S-Box aleatoriamente, sem garantir N L > 100. Neste trabalho, identificamos que S pode ser estudada como uma matriz de adjacência (A(G)) de um multigrafo de Ramanujan e verificamos esta relação com outras A(G) do tipo rotacionais. Dessa forma, reduzimos a busca por S para a ordem de 1011 e construímos S-Boxes com N L > 100.

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Publicado
02/09/2019
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BELLEZA, Marcio; BORGES, Fábio. Construção de S-Boxes com Valores Ótimos de Não Linearidade Baseada em uma Relação entre o Multigrafo de Ramanujan e a Matriz da Transformação Afim. In: SIMPÓSIO BRASILEIRO DE SEGURANÇA DA INFORMAÇÃO E DE SISTEMAS COMPUTACIONAIS (SBSEG), 19. , 2019, São Paulo. Anais [...]. Porto Alegre: Sociedade Brasileira de Computação, 2019 . p. 225-238. DOI: https://doi.org/10.5753/sbseg.2019.13974.