I want to prove if the composite are equal to each other

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In summary, the conversation discusses the definition of f′(x∘r) and how to prove that it is a one way permutation if f(⋅) is a one way permutation. The speaker mentions using a composition of two bijection functions in the proof but is stuck and asks for clarification on the definition of {0,1}n and a "one way" permutation.
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behzad_b
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Given f:{0,1}n→{0,1}n, define f′:{0,1}2n→{0,1}2n as follows: for x,r∈{0,1}n define f′(x∘r):=f(x)∘r (where ∘ denotes concatenation). Prove that if f(⋅) is one way permutation then so is f′(⋅).

i don't understand f′(x∘r):=f(x)∘r how to decompose it in order to prove it

I tried proving it by using a composition of tow bijection, as a permutation is a sect of bijection function.

I am stuck on the proof, I don't know how to do the proof
 
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  • #2
What is the definition of {0,1}n?
 
  • #3
Do you mean ##\{0,1\}^n##?

What is a "one way" permutation?
 

FAQ: I want to prove if the composite are equal to each other

How can I prove if two composites are equal to each other?

To prove if two composites are equal to each other, you can use a variety of methods such as mathematical equations, logical reasoning, or empirical evidence. It is important to carefully define what it means for two composites to be equal before starting your proof.

What are some common properties of equal composites?

Some common properties of equal composites include having the same number of elements, being composed of the same materials, and having the same overall structure or arrangement. These properties are often used as a starting point for proving equality between composites.

Can two composites be equal even if they look different?

Yes, two composites can be equal even if they have different physical appearances. For example, two composites could have the same number of elements and be composed of the same materials, but have different shapes or textures. This is why it is important to consider different properties when proving equality between composites.

What is the significance of proving equality between composites?

Proving equality between composites can have important implications in various fields such as mathematics, science, and engineering. It can help verify the accuracy of mathematical models, determine the effectiveness of different materials, and improve our understanding of natural phenomena.

Are there any limitations to proving equality between composites?

Yes, there can be limitations to proving equality between composites. These limitations can arise from factors such as measurement error, variability in materials, or incomplete knowledge about the properties of the composites. It is important to carefully consider these limitations when conducting a proof of equality between composites.

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