Absolute structure determination using CRYSTALS

A study of post‐refinement absolute structure determination using previously published data was carried out using the CRYSTALS software package. We show that absolute structure determination may be carried out optimally using the analyses available in CRYSTALS, and that it is not necessary to have the separate procedures absolute structure determination and no interest in absolute structure as proposed by Flack [Chimia (2014), 68 , 26–30].     

On optimal neural network learning

We introduce optimal learning with a neural network, which we define as building a network with a minimal expectation generalisation error. This procedure may be analysed exactly in idealized problems by exploiting the relationship between sampling a space of hypotheses and the replica method of statistical physics. We find that the optimally trained spherical perceptron may learn a linearly separable rule as well as any possible computer, and present simulation results supporting our conclusions. Optimal learning of a well-known unlearnable problem, the “mismatched weight” problem, gives better asymptotic learning than conventional techniques, and may be simulated more easily. Unlike many other perceptron learning schemes, optimal learning extends to more general networks learning more complex rules.     

Vectorial Approach to Fast Correlation Attacks

A new, vectorial approach to fast correlation attacks on binary memoryless combiners is proposed. Instead of individual input sequences or their linear combinations, the new attack is targeting subsets of input sequences as a whole thus exploiting the full correlation between the chosen subset and the output sequence. In particular, the set of all the input sequences can be chosen as the target. The attack is based on a novel iterative probabilistic algorithm which is also applicable to general memoryless combiners over finite fields or finite rings. To illustrate the effectiveness of the introduced approach, experimental results obtained for random balanced combining functions are presentedMost of this work was done while he was with Rome CryptoDesign Center, Gemplus, Italy