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In cryptography, the boomerang attack is a method for the cryptanalysis of block ciphers based on differential cryptanalysis. The attack was published in 1999 by David Wagner, who used it to break the COCONUT98 cipher.

The boomerang attack has allowed new avenues of attack for many ciphers previously deemed safe from differential cryptanalysis.

Refinements on the boomerang attack have been published: the amplified boomerang attack, then the rectangle attack.

The attack

The boomerang attack is based on differential cryptanalysis. In differential cryptanalysis, an attacker exploits how differences in the input to a cipher (the plaintext) can affect the resultant difference at the output (the ciphertext). A high-probability "differential" (that is, an input difference that will produce a likely output difference) is needed that covers all, or nearly all, of the cipher. The boomerang attack allows differentials to be used which cover only part of the cipher.

The attack attempts to generate a so-called "quartet" structure at a point halfway through the cipher. For this purpose, say that the encryption action, E, of the cipher can be split into two consecutive stages, E₀ and E₁, so that E(M) = E₁(E₀(M)), where M is some plaintext message. Suppose we have two differentials for the two stages; say,

\Delta \to \Delta ^{*}

for E₀, and

\nabla \to \nabla ^{*}

for E₁^-1 (the decryption action of E₁).

The basic attack proceeds as follows:

Choose a random plaintext $P$ and calculate $P'=P\oplus \Delta$ .
Request the encryptions of $P$ and $P'$ to obtain $C=E(P)$ and $C'=E(P')$
Calculate $D=C\oplus \nabla$ and $D'=C'\oplus \nabla$
Request the decryptions of $D$ and $D'$ to obtain $Q=E^{-1}(D)$ and $Q'=E^{-1}(D')$
Compare $Q$ and $Q'$ ; when the differentials hold, $Q\oplus Q'=\Delta$ .

Application to specific ciphers

One attack on KASUMI, a block cipher used in 3GPP, is a related-key rectangle attack which breaks the full eight rounds of the cipher faster than exhaustive search (Biham et al., 2005). The attack requires 2^54.6 chosen plaintexts, each of which has been encrypted under one of four related keys, and has a time complexity equivalent to 2^76.1 KASUMI encryptions.

References

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External links

Boomerang attack — explained by John Savard
Nathan Keller's homepage

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+{{no footnotes|date= March 2009}}
+[[Image:Attaque boomerang.png|thumbnail|right|320px|Boomerang attack]]
+In [[cryptography]], the '''boomerang attack''' is a method for the [[cryptanalysis]] of [[block cipher]]s based on [[differential cryptanalysis]]. The attack was published in 1999 by [[David A. Wagner|David Wagner]], who used it to break the [[COCONUT98]] cipher.
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+The boomerang attack has allowed new avenues of attack for many ciphers previously deemed safe from differential cryptanalysis.
+Refinements on the boomerang attack have been published: the '''amplified boomerang attack''', then the '''rectangle attack'''.
+==The attack==
+The boomerang attack is based on [[differential cryptanalysis]]. In differential cryptanalysis, an attacker exploits how differences in the input to a cipher (the plaintext) can affect the resultant difference at the output (the ciphertext). A high-probability "differential" (that is, an input difference that will produce a likely output difference) is needed that covers all, or nearly all, of the cipher. The boomerang attack allows differentials to be used which cover only part of the cipher.
+The attack attempts to generate a so-called "quartet" structure at a point halfway through the cipher. For this purpose, say that the encryption action, ''E'', of the cipher can be split into two consecutive stages, ''E''<sub>0</sub> and ''E''<sub>1</sub>, so that ''E(M)'' = ''E''<sub>1</sub>(''E''<sub>0</sub>(M)), where ''M'' is some plaintext message. Suppose we have two differentials for the two stages; say,
+:<math>\Delta\to\Delta^*</math>
+for ''E''<sub>0</sub>, and
+:<math>\nabla\to\nabla^*</math> for ''E''<sub>1</sub><sup>-1</sup> (the decryption action of ''E''<sub>1</sub>).
+The basic attack proceeds as follows:
+* Choose a random plaintext <math>P</math> and calculate <math>P' = P \oplus \Delta</math>.
+* Request the encryptions of <math>P</math> and <math>P'</math> to obtain <math>C = E(P)</math> and <math>C' = E(P')</math>
+* Calculate <math>D = C \oplus \nabla</math> and <math>D' = C' \oplus \nabla</math>
+* Request the decryptions of <math>D</math> and <math>D'</math> to obtain <math>Q = E^{-1}(D)</math> and <math>Q' = E^{-1}(D')</math>
+* Compare <math>Q</math> and <math>Q'</math>; when the differentials hold, <math>Q \oplus Q' = \Delta</math>.
+==Application to specific ciphers==
+One attack on [[KASUMI (block cipher)|KASUMI]], a block cipher used in [[3GPP]], is a related-key rectangle attack which breaks the full eight rounds of the cipher faster than exhaustive search (Biham et al., 2005). The attack requires 2<sup>54.6</sup> chosen plaintexts, each of which has been encrypted under one of four related keys, and has a time complexity equivalent to 2<sup>76.1</sup> KASUMI encryptions.
+==References==
+* {{cite conference
+    | author = [[David A. Wagner|David Wagner]]
+    | title = The Boomerang Attack
+    | booktitle = 6th International Workshop on [[Fast Software Encryption]] (FSE '99)
+    | pages = 156&ndash;170
+    | publisher = [[Springer-Verlag]]
+    | date = March 1999
+    | location = [[Rome]]
+    | url = http://www.cs.berkeley.edu/~daw/papers/boomerang-fse99.ps
+    | format = [[PDF]]/[[PostScript]]
+    | accessdate = 2007-02-05 }} [http://www.cs.berkeley.edu/~daw/papers/boomerang-fse99-slides.ps (Slides in PostScript)]
+* {{cite conference
+    | author = [[John Kelsey (cryptanalyst)|John Kelsey]], Tadayoshi Kohno, and [[Bruce Schneier]]
+    | title = Amplified Boomerang Attacks Against Reduced-Round MARS and Serpent
+    | booktitle = FSE 2000
+    | pages = 75&ndash;93
+    | publisher = Springer-Verlag
+    | date = April 2000
+    | location = [[New York City]]
+    | url = http://www.schneier.com/paper-boomerang.html
+    | format = PDF/PostScript
+    | accessdate = 2007-02-06 }}
+* {{cite conference
+    | author = [[Eli Biham]], [[Orr Dunkelman]], and Nathan Keller
+    | title = The Rectangle Attack &ndash; Rectangling the Serpent
+    | booktitle = Advances in Cryptology, Proceedings of [[EUROCRYPT]] 2001
+    | pages = 340&ndash;357
+    | publisher = Springer-Verlag
+    | date = May 2001
+    | location = [[Innsbruck]]
+    | url = http://citeseer.ist.psu.edu/biham01rectangle.html
+    | format = PDF/PostScript
+    | accessdate = 2007-07-06 }}
+* {{cite conference
+    | author = Biham, Dunkelman, Keller
+    | title = New Results on Boomerang and Rectangle Attacks
+    | booktitle = FSE '02
+    | pages = 1&ndash;16
+    | publisher = Springer-Verlag
+    | date = February 2002
+    | location = [[Leuven]]
+    | url = http://citeseer.ist.psu.edu/504429.html
+    | format = PDF/PostScript
+    | accessdate = 2007-07-06 }}
+* {{cite conference
+    | author = Jongsung Kim, Dukjae Moon, Wonil Lee, Seokhie Hong, Sangjin Lee, Seokwon Jung
+    | title = Amplified Boomerang Attack against Reduced-Round SHACAL
+    | booktitle = [[ASIACRYPT]] 2002
+    | pages = 243&ndash;253
+    | publisher = Springer-Verlag
+    | date = December 2002
+    | location = [[Queenstown, New Zealand]] }}
+* {{cite conference
+    | author = Biham, Dunkelman, Keller
+    | title =  Rectangle Attacks on 49-Round SHACAL-1
+    | booktitle = FSE '03
+    | pages = 22&ndash;35
+    | publisher = [[Springer-Verlag]]
+    | date = February 2003
+    | location = [[Lund]]
+    | url = http://vipe.technion.ac.il/~orrd/crypt/shacal.pdf
+    | format = PDF
+    | accessdate = 2007-07-02 }}
+* {{cite conference
+    | author = [[Alex Biryukov]]
+    | title = The Boomerang Attack on 5 and 6-Round Reduced AES
+    | booktitle = [[Advanced Encryption Standard]] &mdash; AES, 4th International Conference, AES 2004
+    | pages = 11&ndash;15
+    | publisher = Springer-Verlag
+    | date = May 2004
+    | location = [[Bonn]]
+    | url = http://www.cosic.esat.kuleuven.be/publications/article-206.pdf
+    | format = PDF
+    | accessdate = 2007-07-06 }}
+* {{cite conference
+    | author = Jongsung Kim, Guil Kim, Seokhie Hong, Sangjin Lee, Dowon Hong
+    | title = The Related-Key Rectangle Attack &mdash; Application to SHACAL-1
+    | booktitle = 9th Australasian Conference on Information Security and Privacy (ACISP 2004)
+    | pages= 123&ndash;136
+    | publisher = Springer-Verlag
+    | date = July 2004
+    | location = [[Sydney]] }}
+* {{cite conference
+    | author = Seokhie Hong, Jongsung Kim, Sangjin Lee and [[Bart Preneel]]
+    | title = Related-Key Rectangle Attacks on Reduced Versions of SHACAL-1 and AES-192
+    | booktitle = FSE '05
+    | pages = 368&ndash;383
+    | publisher = Springer-Verlag
+    | date = February 2005
+    | location =[[Paris]] }}
+* {{cite conference
+    | author = Biham, Dunkelman, Keller
+    | title = Related-Key Boomerang and Rectangle Attacks
+    | booktitle = EUROCRYPT 2005
+    | pages = 507&ndash;525
+    | publisher = Springer-Verlag
+    | date = May 2005
+    | location = [[Aarhus]]
+    | url = http://vipe.technion.ac.il/~orrd/crypt/relatedkey-rectangle.ps
+    | format = PostScript
+    | accessdate = 2007-02-16 }}
+* {{cite conference
+    | author = Biham, Dunkelman, Keller
+    | title = A Related-Key Rectangle Attack on the Full KASUMI
+    | booktitle = ASIACRYPT 2005
+    | pages = 443&ndash;461
+    | publisher = Springer-Verlag
+    | date = December 2005
+    | location = [[Chennai]]
+    | url = http://www.cs.technion.ac.il/users/wwwb/cgi-bin/tr-info.cgi/2005/CS/CS-2005-14
+    | format = PDF/PostScript
+    | accessdate = 2007-07-06 }}
+==External links==
+* [http://www.quadibloc.com/crypto/co4512.htm Boomerang attack] &mdash; explained by John Savard
+* [http://www.ma.huji.ac.il/~nkeller Nathan Keller's homepage]
+{{Cryptography navbox | block}}
+[[Category:Cryptographic attacks]]