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| It seems reasonable then that DES using key K1 has a range of X and using key K2 has a range of Y where X and Y are different and the symmetric difference is non-empty ([[latex2($\left( X \bigtriangleup Y \neq \emptyset \right)$)]]. This is actually true so that [[latex2($E_{K1}(E_{K2}(P) \neq E_{K3}(P)$)]] | It seems reasonable then that DES using key K1 has a range of X and using key K2 has a range of Y where X and Y are different and the symmetric difference is non-empty [[latex2($\left( X \bigtriangleup Y \neq \emptyset \right)$)]]. This is actually true so that [[latex2($E_{K1}(E_{K2}(P) \neq E_{K3}(P)$)]] Using two keys doesn't do much good either though because we can use a meet in the middle attack. While DES requires effort on the order of 2^54 Double DES requires only effort on the order of 2^56. This type of attack works on any block cipher. So we go to 3DES. Cost of attack on 3DES which uses two keys [[latex2($E_{K1}(D_{K2}(E_{K1})))$)]] is [[latex($2^112$)]]. |
Symmetric Block Ciphers
Triple DES
First some stats to think about:
Single DES uses a 56 bit key. So the number of keys is 2^56.
The number of bits in a block is 64 so any block can be mapped to one of 2^64 different blocks.
It seems reasonable then that DES using key K1 has a range of X and using key K2 has a range of Y where X and Y are different and the symmetric difference is non-empty latex2($\left( X \bigtriangleup Y \neq \emptyset \right)$). This is actually true so that latex2($E_{K1}(E_{K2}(P) \neq E_{K3}(P)$)
Using two keys doesn't do much good either though because we can use a meet in the middle attack. While DES requires effort on the order of 254 Double DES requires only effort on the order of 256. This type of attack works on any block cipher. So we go to 3DES.
Cost of attack on 3DES which uses two keys latex2($E_{K1}(D_{K2}(E_{K1})))$) is latex($2^112$).
Blowfish
RC5
Characteristics of Advanced Symmetric Block Ciphers
RC4 Stream Cipher
Review Questions