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We discuss properties of the two-dimensional Landau Hamiltonian perturbed by a family of identical <i></i> potentials arranged equidistantly along a closed loop. It is demonstrated that for the loop size exceeding the effective size of the point obstacles and the cyclotronic radius such a system exhibits persistent currents at the bottom of the spectrum. We also show that the effect is sensitive to a small disorder.

Recently, the Little Dragon Two and Poly-Dragon multivariate based public-key cryptosystems were proposed as efficient and secure schemes. In particular, the inventors of the two schemes claim that Little Dragon Two and Poly-Dragon resist algebraic cryptanalysis. In this paper, we show that MXL2, an algebraic attack method based on the XL algorithm and Ding’s concept of Mutants, is able to break Little Dragon Two with keys of length up to 229 bits and Poly-Dragon with keys of length up to 299. This contradicts the security claim for the proposed schemes and demonstrates the strength of MXL2 and the Mutant concept. This strength is further supported by experiments that show that in attacks on both schemes the MXL2 algorithm outperforms the Magma’s implementation of F4.

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