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:  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."
Lars Knudsen (February 21, 1998). "DEAL - A 128-bit Block Cipher". Technical report no. 151. Department of Informatics, University of Bergen, Norway . Retrieved . 2015-05-28
^ Shamir, A. (August 25, 1998)
Impossible differential attacks. CRYPTO '98 rump session (video at Google Video—uses Flash)
^ Biryukov, A. (August 25, 1998)
Miss-in-the-middle attacks on IDEA. CRYPTO '98 rump session (video at Google Video—uses Flash)
^ Biham, E. (August 25, 1998)
Impossible cryptanalysis of Skipjack. CRYPTO '98 rump session (video at Google Video—uses Flash)
Bruce Schneier (September 15, 1998). "Impossible Cryptanalysis and Skipjack". Crypto-Gram Newsletter.
E. Biham; A. Biryukov; A. Shamir (March 1999). . 6th International Workshop on Miss in the Middle Attacks on IDEA, Khufu and Khafre Fast Software Encryption (FSE 1999). Rome: Springer-Verlag. pp. 124&ndash, 138. Archived from the original ( on 2011-05-15 gzipped PostScript) . Retrieved . 2007-02-14
Orr Dunkelman (March 1999). An Analysis of Serpent-p and Serpent-p-ns (PDF/PostScript). Rump session, 2nd AES Candidate Conference. Rome: NIST . Retrieved . 2007-02-27
E. Biham; A. Biryukov; A. Shamir (May 1999). Cryptanalysis of Skipjack Reduced to 31 Rounds using Impossible Differentials (PDF/PostScript). Advances in Cryptology - EUROCRYPT '99. Prague: Springer-Verlag. pp. 12&ndash, 23 . Retrieved . 2007-02-13
Kazumaro Aoki; Masayuki Kanda (1999). "Search for Impossible Differential of E2" (PDF/PostScript) . Retrieved . 2007-02-27
Eli Biham, Vladimir Furman (April 2000). Impossible Differential on 8-Round MARS' Core (PDF/PostScript). 3rd AES Candidate Conference. pp. 186&ndash, 194 . Retrieved . 2007-02-27
Eli Biham; Vladimir Furman (December 2000). Improved Impossible Differentials on Twofish (PDF/PostScript). INDOCRYPT 2000. Calcutta: Springer-Verlag. pp. 80&ndash, 92 . Retrieved . 2007-02-27
Deukjo Hong; Jaechul Sung; Shiho Moriai; Sangjin Lee; Jongin Lim (April 2001). Impossible Differential Cryptanalysis of Zodiac (PDF). 8th International Workshop on Fast Software Encryption (FSE 2001). Yokohama: Springer-Verlag. pp. 300&ndash, 311 . Retrieved . 2006-12-30
Raphael C.-W. Phan; Mohammad Umar Siddiqi (July 2001). "Generalised Impossible Differentials of Advanced Encryption Standard" (PDF). . Electronics Letters 37 (14): pp. , 896&ndash, 898. doi: 10.1049/el:20010619 . Retrieved . 2007-07-17
Jung Hee Cheon, MunJu Kim, and Kwangjo Kim (September 2001). Impossible Differential Cryptanalysis of Hierocrypt-3 Reduced to 3 Rounds (PDF). Proceedings of 2nd NESSIE Workshop . Retrieved . 2007-02-27
Jung Hee Cheon; MunJu Kim; Kwangjo Kim; Jung-Yeun Lee; SungWoo Kang (December 26, 2001). Improved Impossible Differential Cryptanalysis of Rijndael and Crypton. 4th International Conference on Information Security and Cryptology (ICISC 2001). Seoul: Springer-Verlag. pp. 39&ndash, 49. CiteSeerX . 10.1.1.15.9966
Dukjae Moon; Kyungdeok Hwang; Wonil Lee; Sangjin Lee; AND Jongin Lim (February 2002). Impossible Differential Cryptanalysis of Reduced Round XTEA and TEA (PDF). 9th International Workshop on Fast Software Encryption (FSE 2002). Leuven: Springer-Verlag. pp. 49&ndash, 60 . Retrieved . 2007-02-27
Raphael C.-W. Phan (May 2002). "Classes of Impossible Differentials of Advanced Encryption Standard" (PDF). . Electronics Letters 38 (11): pp. , 508&ndash, 510. doi: 10.1049/el:20020347 . Retrieved . 2007-07-17
Raphael C.-W. Phan (October 2003). "Impossible Differential Cryptanalysis of Mini-AES" (PDF). . XXVII (4): pp. , 283&ndash, 292. Cryptologia doi: 10.1080/0161-110391891964. ISSN 0161-1194. Archived from the original (PDF) on 2007-09-26 . Retrieved . 2007-02-27
Raphael C.-W. Phan (July 2004). "Impossible Differential Cryptanalysis of 7-round AES". Information Processing Letters. 91 (1): pp. , 29&ndash, 32. doi: 10.1016/j.ipl.2004.03.006 . Retrieved . 2007-07-19 Wenling Wu; Wentao Zhang; Dengguo Feng (2006). "Impossible Differential Cryptanalysis of ARIA and Camellia" (PDF) . Retrieved . 2007-02-27