Eliminating Variables in Boolean Equation Systems

Systems of Boolean equations of low degree arise in a natural way when analyzing block ciphers. The cipher's round functions relate the secret key to auxiliary variables that are introduced by each successive round. In algebraic cryptanalysis, the attacker attempts to solve the resulting equation system in order to extract the secret key. In this paper we study algorithms for eliminating the auxiliary variables from these systems of Boolean equations. It is known that elimination of variables in general increases the degree of the equations involved. In order to contain computational complexity and storage complexity, we present two new algorithms for performing elimination while bounding the degree at $3$, which is the lowest possible for elimination. Further we show that the new algorithms are related to the well known \emph{XL} algorithm. We apply the algorithms to a downscaled version of the LowMC cipher and to a toy cipher based on the Prince cipher, and report on experimental results pertaining to these examples.Comment: 21 pages, 3 figures, Journal pape

Fast resolution change in neutral helium atom microscopy

In neutral helium atom microscopy, a beam of atoms is scanned across a surface. Though still in its infancy, neutral helium microscopy has seen a rapid development over the last few years. The inertness and low energy of the helium atoms (less than 0.1 eV) combined with a very large depth of field and the fact that the helium atoms do not penetrate any solid material at low energies open the possibility for a non-destructive instrument that can measure topology on the nanoscale even on fragile and insulating surfaces. The resolution is determined by the beam spot size on the sample. Fast resolution change is an attractive property of a microscope because it allows different aspects of a sample to be investigated and makes it easier to identify specific features. However up till now it has not been possible to change the resolution of a helium microscope without breaking the vacuum and changing parts of the atom source. Here we present a modified source design, which allows fast, step wise resolution change. The basic design idea is to insert a moveable holder with a series of collimating apertures in front of the source, thus changing the effective source size of the beam and thereby the spot size on the surface and thus the microscope resolution. We demonstrate a design with 3 resolution steps. The number of resolution steps can easily be extended.publishedVersio

Fast resolution change in neutral helium atom microscopy

In neutral helium atom microscopy, a beam of atoms is scanned across a surface. Though still in its infancy, neutral helium microscopy has seen a rapid development over the last few years. The inertness and low energy of the helium atoms (less than 0.1 eV) combined with a very large depth of field and the fact that the helium atoms do not penetrate any solid material at low energies open the possibility for a non-destructive instrument that can measure topology on the nanoscale even on fragile and insulating surfaces. The resolution is determined by the beam spot size on the sample. Fast resolution change is an attractive property of a microscope because it allows different aspects of a sample to be investigated and makes it easier to identify specific features. However up till now it has not been possible to change the resolution of a helium microscope without breaking the vacuum and changing parts of the atom source. Here we present a modified source design, which allows fast, step wise resolution change. The basic design idea is to insert a moveable holder with a series of collimating apertures in front of the source, thus changing the effective source size of the beam and thereby the spot size on the surface and thus the microscope resolution. We demonstrate a design with 3 resolution steps. The number of resolution steps can easily be extended