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Invariant Hopping Attacks on Block Ciphers

Block ciphers are in widespread use since the 1970s. Their iterated structure is prone to numerous round invariant attacks for example in Linear Cryptanalysis (LC). The next step is to look at non-linear polynomial invariants cf. Eurocrypt'95. Until recently, researchers have found extremely few such attacks, with some impossibility results. Eventually recent papers show how to construct polynomial invariant attacks for block ciphers, however many such results were of degree 2. In this paper we propose a new incremental methodology for constructing high degree polynomial invariant attacks on block ciphers. A trivial attack on one cipher setup will be transposed to show the existence of a more advanced attack on a stronger cipher in several steps. The key tool is the manipulation of the roots of the so called Fundamental Equation. Examples are constructed with an old historical block cipher T-310.