In cryptography, **impossible differential cryptanalysis** is a form of differential cryptanalysis for block ciphers. While ordinary differential cryptanalysis tracks differences that propagate through the cipher with greater than expected probability, impossible differential cryptanalysis exploits differences that are impossible (having probability 0) at some intermediate state of the cipher algorithm.

Lars Knudsen appears to be the first to use a form of this attack, in the 1998 paper where he introduced his AES candidate, DEAL. The first presentation to attract the attention of the cryptographic community was later the same year at the rump session of CRYPTO '98, in which Eli Biham, Alex Biryukov, and Adi Shamir introduced the name "impossible differential" and used the technique to break 4.5 out of 8.5 rounds of IDEA and 31 out of 32 rounds of the NSA-designed cipher Skipjack. This development led cryptographer Bruce Schneier to speculate that the NSA had no previous knowledge of impossible differential cryptanalysis. The technique has since been applied to many other ciphers besides IDEA and Skipjack: Khufu and Khafre, E2, variants of Serpent, MARS, Twofish, Rijndael, CRYPTON, Zodiac, Hierocrypt-3, TEA, XTEA, Mini-AES, ARIA, Camellia, and SHACAL-2.

Biham, Biryukov and Shamir also presented a relatively efficient specialized method for finding impossible differentials that they called a *miss-in-the-middle* attack. This consists of finding "two events with probability one, whose conditions cannot be met together."

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### Famous quotes containing the words impossible and/or differential:

“It is *impossible* for me to envisage a picture as being other than a window, and ... my first concern is then to know what it looks out on.”

—André Breton (1896–1966)

“But how is one to make a scientist understand that there is something unalterably deranged about *differential* calculus, quantum theory, or the obscene and so inanely liturgical ordeals of the precession of the equinoxes.”

—Antonin Artaud (1896–1948)