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I am solving a four-round Feistel network using pseudo-random round function is a strong pseudo-random function for security against adversaries, but I don't understand that how to solve I know 3 round.

Can you please explain the procedure?

I am assuming ${F : \{0,1\}^λ × \{0,1\}^λ → \{0,1\}^λ }$ be a secure PRF with in = out = λ, and define ${F^∗ : \{0,1\}^{4λ} × \{0,1\}^{2λ} → \{0,1\}^{2λ}}$

Then ${F^∗ }$is a secure strong PRP.

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  • $\begingroup$ How $F^*$ is defined? Why it maps $4\lambda+2\lambda$ bits into $2\lambda$ bits? Feistel network would map $2\lambda$ bits to $2\lambda$ bits. $\endgroup$ – Fractalice Jun 18 at 8:56
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    $\begingroup$ @Fractalice I think $F^*$ is a 4 rounds feistel network with $F$ as the round function, the $2λ$ is the input to the feistel network, and the $4λ$ is for round keys or something $\endgroup$ – Irad Nuriel Jun 23 at 5:39