Cube Attacks on Tweakable Black Box Polynomials

By Itai Dinur, Adi Shamir. IACR Cryptology ePrint Archive, 2009

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KATAN and KTANTAN - A Family of Small and Efficient Hardware-Oriented Block Ciphers (2009, background): “Given the low algebraic degree of the combining function, it may look as if KATAN and KTANTAN are susceptible to algebraic attacks or cube attack [7].”
KLEIN: A New Family of Lightweight Block Ciphers (2010, background): “The algebraic attack as well as the Cube Attack [17], requires the algebraic form describing the output bits has a relatively small degree in terms of the input bits being processed.”
Quark: A Lightweight Hash (2010, background): “The recently proposed “cube attacks” [24] and “cube testers” [25] are higher-order differential cryptanalysis techniques that exploit weaknesses in the algebraic structure of a cryptographic algorithm.”