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1

DES is a Feistel cipher that doesn't require the $F$ function to be reversible, where the S-Boxes are used. DES has a non-reversible $F$ function in which the 8 S-boxes $S:\{0,1\}^6\to \{0,1\}^4$ is used. AES is based on Susbstition Permutation Network (SPN) where everything must be reversible. AES is using S-boxes $S:\{0,1\}^8\to \{0,1\}^8$. Therefore it is ...

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To throw something, here are simple proofs for 2-4 rounds, applicable to almost any Feistel Network. Some notation: $F_i$ denotes $i$-th Feistel round without swaps, $f_i$ denotes the Feistel function at $i$-th round, $S$ denotes the swap. Since the initial permutation IP and the final permutation FP are inverses of each other, we can strip them away: for ...

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3DES What is described here is not 3DES (Triple DES or TDES and officially the Triple Data Encryption Algorithm (TDEA or Triple DEA)). Let us call the $E$ as DES encryption and $D$ as DES decryption. Then we can write 3DES encryption as $$E(k_3,D(k_2,E(k_1,message)))$$ with independent keys $k_1,k_2,k_3$. The provided security by 3DES with 3 key is not 192-...

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For each key a block cipher selects a permutation from all possible permutations from $\{0,1\}^\ell \to \{0,1\}^\ell$ where $\ell$ is the block cipher. For DES, $\ell = 64$. The number of permutations is $2^{64}!$ and the number of possible effective keys of DES is $2^{56}$. by Stirling's approximation  2^{64}! \approx \sqrt{2\pi 2^{64}} \bigl(2^{64}/e\...

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Can we get the same result as if we would encrypt the plain text using single DES but with different key, say K2. It has not been formally proven, but it is extremely plausible to assume that there isn't an equivalent 'double key', that is, for a K1, there isn't a K2 where DES(K1, DES(K1, M)) = DES(K2, M) for all values M (or even a number of values of M. ...

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