Algebraic attacks over GF(q)

Recent algebraic attacks on LFSR-based stream ciphers and S-boxes have generated much interest as they appear to be extremely powerful. Theoretical work has been developed focusing around the Boo- lean function case. In this paper, we generalize this theory to arbitrary finite fields and extend the theory of annihilators and ideals introduced at Eurocrypt 2004 by Meier, Pasalic and Carlet. In particular, we prove that for any function f in the multivariate polynomial ring over GF(q), f has a low degree multiple precisely when two low degree functions appear in the same coset of the annihilator of f ^{q – 1} – 1. In this case, many such low degree multiples exist.

TOF-SIMS analysis using C60. Effect of impact energy on yield and damage

C₆₀ has been shown to give increased sputter yields and, hence, secondary ions when used as a primary particle in SIMS analysis. In addition, for many samples, there is also a reduction in damage accumulation following continued bombardment with the ion beam. In this paper, we report a study of the impact energy (up to 120 keV) of C₆₀ on the secondary ion yield from a number of samples with consideration of any variation in yield response over mass ranges up to m/z 2000. Although increased impact energy is expected to produce a corresponding increase in sputter yield/rate, it is important to investigate any increase in sample damage with increasing energy and, hence, efficiency of the ion beams. On our test samples including a metal, along with organic samples, there is a general increase in secondary ion yield of high-mass species with increasing impact energy. A corresponding reduction in the formation of low-mass fragments is also observed. Depth profiling of organic samples demonstrates that when using C₆₀, there does not appear to be any increase in damage evident in the mass spectra as the impact energy is increased.