Notation with families of hiding functions

Definition 8.31. A collision-intractable family of hiding functions has 

One may think that this generalization is an unnecessary complication, because in all the following examples, 4 is in fact a pair (x, y). However, when group structures on these sets are introduced, the group structure on the Cartesian product in the factoring case is not a direct xxxluct 

They have not been given names, because they will be written gr and g . These components must have the following additional properties  

This is the terminology of Definition 8.25c with the relation = defined on Gg by =  

Similar to bundling homomorphisms, hiding homomorphisms are basically hiding functions that are homomorphisms. 

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Figure 8.8. Notation with families of hiding functions...

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