The HFEv- signature scheme is one of the most studied multivariate schemes and one of the major candidates for the upcoming standardization of post-quantum digital signature schemes. In this paper, we propose three new attack strategies against HFEv-, each of them using the idea of projection. Especially our third attack is very effective and is, for some parameter sets, the most efficient known attack against HFEv-. Furthermore, our attack requires much less memory than direct and rank attacks. By our work, we therefore give new insights in the security of the HFEv- signature scheme and restrictions for the parameter choice of a possible future standardized HFEv- instance.

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We consider resonant vortices around nodal points of the wave function describing electron transport through a mesoscopic device. With a suitable choice of the device geometry, the dominating role is played by single vortices with a preferred orientation. To characterize the strength of the resulting magnetic moment, we have introduced a magnetance, the quantity defined in analogy with the device conductance. Its basic properties and possible experimental detection are discussed.

We consider Schrdinger operators in L2(R3) with a singular interaction supported by a finite curve . We present a proper definition of the operators and study their properties, in particular, we show that the discrete spectrum can be empty if is short enough. If it is not the case, we investigate properties of the eigenvalues in the situation when the curve has a hiatus of length 2. We derive an asymptotic expansion with the leading term which a multiple of ln.