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Name a well-known and standardized function $F : \{0,1\}^{256} × \{0,1\}^{128} → \{0,1\}^{128}$ that is believed to be a pseudorandom permutation.

I was thinking SHA256, but I am not sure. Can someone clarify this please?

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    $\begingroup$ Welcome to crypto.stackexchange - Here's a hint: $F$ takes 2 arguments, one of which is 256 bits in size, and the other is 128 bits in size. What common type of algorithm uses two inputs of those size and is invertible? $\endgroup$ – Ella Rose May 2 at 16:28
  • $\begingroup$ @EllaRose, is it a hash function? sorry i don't know $\endgroup$ – user0x777fffffff May 2 at 16:44
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    $\begingroup$ Hint: hash functions typically are not modeled as pseudorandom permutations... $\endgroup$ – poncho May 2 at 18:32
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    $\begingroup$ Counting the number of input arguments to the sha256 function is not hard. This homework question is answerable by looking at function signatures in a cryptography API without knowing anything about cryptography. Crypto stack exchange expects you to show some effort. Call it "proof of work". You're trying to get answers without opening the book. $\endgroup$ – Z.T. May 2 at 19:17
  • $\begingroup$ Hint: it is also defined for 128, 192 and 256 bit keys. $\endgroup$ – Frank Denis May 3 at 8:26
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An $n$-bit hash function is typically defined as $F:\{0,1\}^\ast\rightarrow\{0,1\}^n$. Furthermore, hashes are not classified as pseudorandom permutations. What you are likely looking for is a block cipher. A block cipher with block size $n$ and key size $k$ would be $F:\{0,1\}^n\times\{0,1\}^k\rightarrow\{0,1\}^n$. Can you think of a popular cipher which has a 128-bit block size and takes a 256-bit key? Hint:

It's a NIST standard.

You may want to read about the differences between a PRP and a PRF.

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