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Well, the standard answer is to preserve compatibility with DES; a hardware circuit that implemented 3DES (with EDE) could also be used to do DES as well (by, say, making all three subkeys the same). Now, there is one slight problem with this straightforward argument; 3DES (EEE, that is, with three encrypt operations) would have this property as well; if we ...

The main difference is that with two 56 bit keys the maximal security level is 112 bit, and thus an attack that has a cost of $2^{112}$ operations is no attack, whereas for three 56 bit keys the maximal security level is 168 bits, and an attack that has a cost of $2^{112}$ operations counts as an attack. This means that two-key 3DES is still a bit weaker ...

<------------- key -------------> <-- plaintext -> <- ciphertext -> E62CABB93D1F3BDC 524FDF91A279C297 DD16B3D004069AB3 8ADDBD2290E565CE B619F870574A9E80 DAE6AB34C22CD626 058B92A4B28FB4EB A53DDC6B3098008F 6132C42C3E5E94EF 7A5152BF19AB739D 91993307EFBFB13C D13105386083E517 0245EAFE62DF92BF E319C29E9E2C3EA1 58BAA732CF5DBD77 EF37441D1FE7B73A ...

If you're asking why the X9.31 rng was designed the way it was, rather than some other way, I'm not certain if anyone other than the original authors could say. The core design dates back to at least 1985 (it was included in X9.17), and it originally used DES (and was later upgraded to use 3DES). I suspect that the original authors would not have been ...

I do not understand how can we decrypt a cypher which was encrypted with $K_1$, with $K_2$. Triple DES essentially involves three encryptions on the plain text. First is using $K_1$, second using $K_2$, and third using $K_3$. Now one may argue that $K_2$ is not being used for encryption but decryption. Well, technically speaking, encryption and ...

3DES is a block cipher which processes "blocks" of 64 bits. A block cipher is not sufficient to encrypt a message, defined as a sequence of potentially many bytes. Hence the use of a mode of operation which organizes things; this may imply some padding, and an Initialization Vector. TripleDESCryptoServiceProvider can do all that: you specify the key, the ...

I think another reason for using the complicated construction which replaces $V$ after each production of a new $R$ is a (maybe implicit) requirement that the state of the PRNG should not allow recovering previous outputs. For a block cipher in CTR mode, recovering previous outputs is easy, as you still have all the input available, or easily ...