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Let's assume I've encrypted some text with some 24-byte key using 3DES in ECB mode. Is it possible to regain the key if I have both encrypted and decrypted text? (Excluding bruteforce.)

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That would amount to divination. – fgrieu Jan 22 '14 at 9:17
up vote 2 down vote accepted

It is not practically possible. There are several attacks that are slightly faster than bruteforcing $2^{112}$ key candidates, but this is only a small factor. In some sense, they are bruteforce-like, since they require $2^{113}$ smaller steps.

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There are $2^{168}$ possible keys for 24 byte 3DES. It is possible to attack such key with around $2^{112}$ steps, which saves time compares to brute forcing all the possible keys. (But it is still unpractical.) – user4982 May 9 '14 at 16:05

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