We show that Multivariate Public Key Cryptosystems (MPKCs) over fields of small odd prime characteristic, say 31, can be highly efficient. Indeed, at the same design security of 2^{80} under the best known attacks, odd-char MPKC is generally faster than prior MPKCs over \GF{2^k}, which are in turn faster than "traditional'' alternatives. This seemingly counter-intuitive feat is accomplished by exploiting the comparative over-abundance of small integer arithmetic resources in commodity hardware, here embodied by SSE2 or more advanced special multimedia instructions on modern x86-compatible CPUs. We explain our implementation techniques and design choices in implementing our chosen MPKC instances modulo small a odd prime. The same techniques are also applicable in modern FPGAs which often contains a large number of multipliers.

We report on transport properties of the super-honeycomb lattice, the band structure of which possesses a flat band and Dirac cones, according to the tight-binding approximation. This super-honeycomb model combines the honeycomb lattice and the Lieb lattice and displays the properties of both. The super-honeycomb lattice also represents a hybrid fermionic and bosonic system, which is rarely seen in nature. By choosing the phases of input beams properly, the flat-band mode of the super-honeycomb will be excited and the input beams will exhibit strong localization during propagation. On the other hand, if the modes of Dirac cones of the super-honeycomb lattice are excited, one will observe conical diffraction. Furthermore, if the input beam is properly chosen to excite a sublattice of the super-honeycomb lattice and the modes of Dirac cones with different pseudospins, e.g., the three-beam interference pattern, the pseudospin-mediated vortices will be observed.

In this paper we show how to totally break the fully homomorphic encryption scheme of eprint 2017/458.

We combine the method of searching for an invariant subspace of the unbalanced Oil and Vinegar signature scheme and the Minrank method to defeat the new TTS signature scheme, which was suggested for low-cost smart card applications at CHES 2004. We show that the attack complexity is less than 2^{50}.

A product formula is proved which involves the unitary group generated by a semibounded self-adjoint operator and an orthogonal projection P. It gives a partial answer to the question about existence of the limit which describes quantum Zeno dynamics in the subspace Ran P.