Equivalence Algorithms: Difference between revisions
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= The hierarchy of equivalences = | = The hierarchy of equivalences = | ||
Given two vectorial boolean functions <math>f,g : F_2^n \rightarrow F_2^n </math> there are various ways to define equivalence between <math> f </math> and <math>g </math> | Given two vectorial boolean functions <math>f,g : F_2^n \rightarrow F_2^n </math> there are various ways to define equivalence between <math> f </math> and <math>g </math>. We will study the algorithms for determining Linear, Affine, Extended Affine and CCZ equivalence between vectorial boolean functions. | ||
= Linear Equivalence = | |||
Given two vectorial boolean functions <math>f </math> and <math> g </math> we want to determine if there exist Linear permutations <math> A_1</math> and <math>A_2 </math> such that <math> f = A_2 \circ g \circ A_1 </math>. | |||
==The to and from algorithm== | |||
This algorithm is from <ref name="back">Biryukov, Alex, et al. "A toolbox for cryptanalysis: Linear and affine equivalence algorithms." Advances in Cryptology—EUROCRYPT 2003: International Conference on the Theory and Applications of Cryptographic Techniques, Warsaw, Poland, May 4–8, 2003 Proceedings 22. Springer Berlin Heidelberg, 2003. </ref> | |||
Revision as of 14:00, 19 November 2024
The hierarchy of equivalences
Given two vectorial boolean functions [math]\displaystyle{ f,g : F_2^n \rightarrow F_2^n }[/math] there are various ways to define equivalence between [math]\displaystyle{ f }[/math] and [math]\displaystyle{ g }[/math]. We will study the algorithms for determining Linear, Affine, Extended Affine and CCZ equivalence between vectorial boolean functions.
Linear Equivalence
Given two vectorial boolean functions [math]\displaystyle{ f }[/math] and [math]\displaystyle{ g }[/math] we want to determine if there exist Linear permutations [math]\displaystyle{ A_1 }[/math] and [math]\displaystyle{ A_2 }[/math] such that [math]\displaystyle{ f = A_2 \circ g \circ A_1 }[/math].
The to and from algorithm
This algorithm is from [1]
- ↑ Biryukov, Alex, et al. "A toolbox for cryptanalysis: Linear and affine equivalence algorithms." Advances in Cryptology—EUROCRYPT 2003: International Conference on the Theory and Applications of Cryptographic Techniques, Warsaw, Poland, May 4–8, 2003 Proceedings 22. Springer Berlin Heidelberg, 2003.