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\iteman{io-port 06033530}
\itemau{Mroczkowski, Piotr; Szmidt, Janusz}
\itemti{The cube attack on stream cipher Trivium and quadraticity tests.}
\itemso{Fundam. Inform. 114, No. 3-4, 309-318 (2012).}
\itemab
Summary: In 2008 I. Dinur and A. Shamir presented a new type of algebraic attack on symmetric ciphers named cube attack. The method has been applied to reduced variants of stream ciphers Trivium and Grain-128, reduced variants of the block ciphers Serpent and CTC and to a reduced version of the keyed hash function MD6. Previously, a very similar attack named AIDA was introduced by M. Vielhaber, in 2007. In this paper we develop quadraticity tests within the cube attack and apply them to a variant of stream cipher Trivium reduced to 709 initialization rounds. Using this method we obtain the full 80-bit secret key. In this way it eliminates the stage of brute force search of some secret key bits which occured in previous cube attacks.
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\itemli{http://iospress.metapress.com/content/w488x8ul32611185/fulltext.html}
\end