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Bent function and Upper Bounds on the Nonlinearity of Vectorial Functions

Kudarzi, Bahareh | 2018

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 51144 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Khazaie, Shahram
  7. Abstract:
  8. the theses is composed of two main parts related to the nonlinearity of vectorial functions. The first part is devoted to maximally nonlinear vectorial function (bent vectorial functions) which contribute to an optimal resistance to both linear and differential attacks on symmetric cryptosystems. They can be used in block ciphers at the cost of additional diffusion-compression-expansion layers, or as building blocks for the construction on substitution boxes (S-boxes) and they are also useful for construction robust codes and algebraic manipulation detection codes. A main issue on bent vectorial bent functions is to characterize bent monomial trace functions leading to a classification of those bent functions. The second part is devoted to nonlinearity of vectorial functions on a vector space of order 2n to a vector space of order 2m. no tight upper bound is known when n 2 < m < n. The only known upper bound in this range is the covering radius bound(the Sidelnikov-Chabaud-Vaudenay bound coincides with it when m = n1 and it has no sense when m < n 1). We discuss about some of such upper bound for functions which are sufficiently unbalanced or which satisfy some conditions. These upper bounds imply some necessary conditions for vectorial functions to have large nonlinearity
  9. Keywords:
  10. Bent Functions ; Nonlinearity ; Boolean Functions

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