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This expression appears on my cryptography homework:

$$G'(k) = G(k \oplus 1^s)$$

It is a description of a Pseudorandom Number Generator where $G:\{0,1\}^s \to \{0,1\}^n$

I just cant see what the "prime" adds, to me it would read the same as:

$$G(k) = k \oplus 1^s$$

Am I missing something?

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up vote 1 down vote accepted

Given one generator $G \colon \{0,1\}^s \to \{0,1\}^n$ we define another generator as follows: Given $k$, first swap all bits, that is xor with $1^s$, then apply $G$, as a formula: We define $G'\colon \{0,1\}^s \to \{0,1\}^n$ by $G'(k) = G(k \oplus 1^s)$.

For example: $G'(100) = G(001)$, $G'(111) = G(000)$ and so on.

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Ahh so G prime means something like "a specific instance of G" – jsj Nov 8 '12 at 15:10

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