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2 results

  • 10 - Functions on Abelian groups

  • Tim Beyne, Katholieke Universiteit Leuven, Belgium, Vincent Rijmen, Katholieke Universiteit Leuven, Belgium
  • Book:
    Linear Cryptanalysis
    Published online:
    17 December 2025
    Print publication:
    20 November 2025, pp 133-149

  • Summary

    Chapter 11 reconstructs the theory of linear cryptanalysis from a more general point of view. To do this, we need to cover some mathematical ground. We first discuss linear algebra over the field of complex numbers, and then turn to the Fourier analysis of functions on a finite Abelian group. Both of these topics play a central role in Chapter 11.

  • 1 - Vector Spaces

  • Yisong Yang, New York University
  • Book:
    Advanced Linear Algebra
    Published online:
    27 May 2025
    Print publication:
    12 June 2025, pp 1-37

  • Summary

    In this chapter, we study vector spaces and their basic properties and structures. We start by stating the definition and discussing examples of vector spaces. Next we introduce the notions of subspaces, linear dependence, bases, coordinates, and dimensionality. And then we consider dual spaces, direct sums, and quotient spaces. Finally, we cover normed vector spaces.