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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 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($2^112$).
Blowfish
RC5
Characteristics of Advanced Symmetric Block Ciphers
RC4 Stream Cipher
Review Questions