Fast Calculation of Cube and Inverse Cube Roots Using a Magic Constant and Its Implementation on Microcontrollers

Cube-magic labelings of grids

The graphs considered in this paper are finite, undirected and simple. For a graph G, we denote its vertex set by V (G) and its edge set by E(G). A graph labeling, as introduced in [8], is an assignment of integers to the vertices or edges, or both, subject to certain conditions. Over the years, a large variety of different types of graph labelings have been studied, see [2] for an extensive su...

Extension of Cube Attack with Probabilistic Equations and its Application on Cryptanalysis of KATAN Cipher

Cube Attack is a successful case of Algebraic Attack. Cube Attack consists of two phases, linear equation extraction and solving the extracted equation system. Due to the high complexity of equation extraction phase in finding linear equations, we can extract nonlinear ones that could be approximated to linear equations with high probability. The probabilistic equations could be considered as l...

Fast calculation of inverse square root with the use of magic constant - analytical approach

We present a mathematical analysis of transformations used in fast calculation of inverse square root for single-precision floating-point numbers. Optimal values of the so called magic constants are derived in a systematic way, minimizing either absolute or relative errors at subsequent stages of the discussed algorithm.

O'Beirne's Cube and Its Origins

Roots of cube polynomials of median graphs