Novel notation on cube attack

The development of Boolean algebra based algorithms lied the foundation for a wide variety of cryptanalysis techniques based on the reformulation of a cryptosystem as a polynomial function over F2. Widely used approaches to solve multivariate system of equations include Gröbner bases (see [11]) and linearisation techniques like XL [4] and XSL [5]). Performances of these methodologies were however completely unfeasible for real problems’ size, making it impossible to directly find useful relations between cryptographic schemes’ input and output. At Eurocrypt’09 a new methodology settled in this environment, providing a feasible family of attacks able to retrieve useful in- put/output relations within feasible time: Dinur and Shamir Cube Attack [7]. The attack relied on the new concept of tweakable poly- nomials, polynomials in variables the attacker can set at will during the attack through which a black-box representation of the cipher is analysed. The resonance of this approach was unexpected, making it the forefather of many other approaches ranging from generic finite fields [1, 15] and non-linear [14] approaches to Meet-in-the- Middle [2, 13] and side channels [8] attacks. The idea of tweakable polynomials was also exploited to provide property (cube) testers which generated Conditional [12] and Dynamic [9] cube attacks. All of these approaches come with their own nomenclature, often making it unclear about their real contribute to the state of the art. The aim of this work is to introduce a novel notation to provide a global representation of the cube attacks family.