Electron lenses are extremely poor: if glass lenses were as bad, we should see as well with the naked eye as with a microscope! The demonstration by Otto Scherzer in 1936 that skilful lens design could never eliminate the spherical and chromatic aberrations of rotationally symmetric electron lenses was therefore most unwelcome and the other great electron optician of those years, Walter Glaser, never ceased striving to find a loophole in Scherzer's proof. In the wartime and early post-war years, the first proposals for correcting C s were made and in 1947, in a second milestone paper, Scherzer listed these and other ways of correcting lenses; soon after, Dennis Gabor invented holography for the same purpose. These approaches will be briefly summarized and the work that led to the successful implementation of quadupole-octopole and sextupole correctors in the 1990s will be analysed. In conclusion, the elegant role of image algebra in describing image formation and processing and, above all, in developing new methods will be mentioned.

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Abstract.Recently proposed algebraic attacks [2,6] and fast algebraic attacks [1,5] have provided the best analyses against some deployed LFSR-based ciphers. The process complexity is exponential in the degree of the equations. Fast algebraic attacks were introduced [5] as a way of reducing run-time complexity by reducing the degree of the system of equations. Previous reports on fast algebraic attacks [1,5] have underestimated the complexity of substituting the keystream into the system of equations, which in some cases dominates the attack. We also show how the Fast Fourier Transform (FFT) [4] can be applied to decrease the complexity of the substitution step. Finally, it is shown that all functions of degree d satisfy a common, function-independent linear combination that may be used in the pre-computation step of the fast algebraic attack. An explicit factorization of the corresponding characteristic polynomial yields the fastest known method for performing the pre-computation step.

It is not easy to understand how the electron microscopes and electron microscope techniques that we know today developed from the primitive ideas of the first microscopists of the 1930s. Newcomers to the subject in particular, their time almost fully occupied with grasping practical methods and modern computing techniques, can rarely devote much attention to the history of their subject. For some, however, this is a source of frustration: If a guide to the principal stages in the development of the subject and to the main actors and their publications were available, they would find the time to study it.