Cryptographic attacks are typically constructed by blackbox methods and combinations of simpler properties, for example in [Generalised] Linear Cryptanalysis. In this article we work with a more recent white-box algebraic-constructive methodology. Polynomial invariant attacks on a block cipher are constructed explicitly through the study of the space of Boolean polynomials which does not have a unique factorization and solving the so-called Fundamental Equation (FE). Some recent invariant attacks are quite symmetric and exhibit some sort of clear structure, or work only when the Boolean function is degenerate. As a proof of concept we construct an attack where a highly irregular product of 7 polynomials is an invariant for any number of rounds for T-310 under certain conditions on the long term key and for any key and any IV. A key feature of our attack is that it works for any Boolean function which satisfies a specific annihilation property. We evaluate very precisely the probability that our attack works when the Boolean function is chosen uniformly at random.