A block cipher is an encryption algorithm which encrypts fixed-size blocks of plaintext to same-sized blocks of ciphertext. For good ciphers every bit of the ciphertext block depends on every bit of the plaintext block and every bit of the key.

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implementing a cryptographic hash with a block cipher [duplicate]

How can a cryptographic hash function be implemented/created using the block cipher? I was wondering if we can use AES in cipher block chaining mode to implement it.
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XOR with constant key in CBC mode

I have a hypothetical encryption scheme where somebody uses the one-time pad in CBC mode. That is, the block cipher is $E(k, m) :=k⊕m$, and that block cipher is used in CBC mode. Now, I am assuming ...
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Can a commutative block cipher be indistinguishable from a random one, assuming a random permutation of keyspace?

Define a commutative block cipher with keyspace the finite set $K$, and message space the finite set $S$, to be an application $$\begin{align} E:K\times S&\mapsto S\\ (k,x)&\mapsto ...
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Can a commutative block cipher be indistinguishable from a random permutation, for fixed key?

Define a commutative block cipher with keyspace the finite set $K$, and data space the finite set $S$, to be an application $$\begin{align} E:K\times S&\mapsto S\\ (k,x)&\mapsto E(k,x)\text{ ...