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.
While we were finalizing our paper for publication, a very elegant specialized attack on the same cryptosystem was announced by Matucci @cite_15 . The main contribution of the present paper is thus the generalization of the length-based algorithms to make them applicable to a wider class of groups. Moreover, while our general attack can be easily adapted to other possible cryptosystems based on Thompson's group, this may not be the case for Matucci's specialized methods.
@cite_15
1530291176
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.