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In this paper we present an extension of the generalized linear equivalence relation, proposed in [7]. This mathematical tool can be helpful for the classification of non-linear functions f : Fpm→ Fpn based on their cryptographic properties. It thus can have relevance in the design criteria for substitution boxes (S-boxes), the latter being commonly used to achieve non-linearity in most symmetric key algorithms. First, we introduce a simple but effective representation of the cryptographic properties of S-box functions when the characteristic of the underlying finite field is odd; following this line, we adapt the linear cryptanalysis technique, providing a generalization of Matsui's lemma. This is done in order to complete the proof of Theorem 2 in [7], also by considering the broader class of generalized affine transformations. We believe that the present work can be a step towards the extension of known cryptanalytic techniques and concepts to finite fields with odd characteristic. Keywords: Boolean functions, generalized linear equivalence, linear cryptanalysis, S-boxes. [ABSTRACT FROM AUTHOR]

The important alterations in the respiratory function of morbidly obese patients in the perioperative period may play a significant part in determining pulmonary complications in the intra- and postoperative periods. In morbidly obese patients, adequate ventilatory settings in the intraoperative period and ICU admission in the postoperative period may help to reduce the incidence of pulmonary complications. [ABSTRACT FROM AUTHOR]