The length-based approach is a heuristic for solving randomly generated equations in groups that possess a reasonably behaved length function. We describe several improvements of the previously suggested length-based algorithms, which make them applicable to Thompson's group with significant success rates. In particular, this shows that the Shpilrain-Ushakov public key cryp- tosystem based on Thompson's group is insecure, and suggests that no practical public key cryp- tosystem based on the difficulty of solving an equation in this group can be secure.
The present invention relates to a method for the determination of the electron density in a part volume in a patient by means of an X-ray tube, said tube comprising an anode symmetrical with respect to rotation as an electron beam rotates relative to the axis of rotation. As a result an X-ray emission from several points is obtained. By means of the scattered X-rays the electron densities can be measured.