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

1. Mar 20, 2013

### behzad_b

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 dont know how to do the proof

2. Mar 20, 2013

### Fredrik

Staff Emeritus
What is the definition of {0,1}n?

3. Mar 20, 2013

### micromass

Staff Emeritus
Do you mean $\{0,1\}^n$?

What is a "one way" permutation?

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