DES
The Feistel scheme and the DES cipher: blocks, key and rounds, the round function and S-boxes, decryption with the subkeys in reverse order, the weakness of the key, triple DES and the meet-in-the-middle attack.
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DES: what is it?
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A symmetric block cipher standardised in the United States in 1977, built on a Feistel network, and since replaced by AES.
64-bit blocks, a 56-bit key, 16 rounds. Its key is no longer enough: an exhaustive search of the 2^56 keys is within reach of specialised hardware.
A toy Feistel round: L = 1011, R = 0110, subkey 1100 and F(R, K) = R ⊕ K. Which block (L' R') comes out of the round?
0110 00010001 01100110 10100110 1101
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0110 0001L' = R = 0110. F(R, K) = 0110 ⊕ 1100 = 1010, then R' = L ⊕ F = 1011 ⊕ 1010 = 0001.
0001 0110forgets to cross the halves,0110 1010forgets the exclusive or with L.DES encrypts blocks of … bits with a key of … bits, in … rounds.
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DES encrypts blocks of 64 bits with a key of 56 bits, in 16 rounds.
The key takes 64 bits on paper, but 8 of them are parity bits: 56 useful bits remain.
Feistel network: what is it?
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A construction that splits the block into two halves (L, R) and, at each round, replaces them with (R, L ⊕ F(R, subkey)).
F does not need to be invertible: the exclusive or is enough to recover the original half, so the same circuit encrypts and decrypts.