Probabilistic Evaluation of the Exploration–Exploitation Balance during the Search, Using the Swap Operator, for Nonlinear Bijective S-Boxes, Resistant to Power Attacks

During the search for S-boxes resistant to Power Attacks, the S-box space has recently been divided into Hamming Weight classes, according to its theoretical resistance to these attacks using the metric variance of the confusion coefficient. This partition allows for reducing the size of the search space. The swap operator is frequently used when searching with a random selection of items to be exchanged. In this work, the theoretical probability of changing Hamming Weight class of the S-box is calculated when the swap operator is applied randomly in a permutation. The precision of these probabilities is confirmed experimentally. Its limit and a recursive formula are theoretically proved. It is shown that this operator changes classes with high probability, which favors the exploration of the Hamming Weight class of S-boxes space but dramatically reduces the exploitation within classes. These results are generalized, showing that the probability of moving within the same class is substantially reduced by applying two swaps. Based on these results, it is proposed to modify/improve the use of the swap operator, replacing its random application with the appropriate selection of the elements to be exchanged, which allows taking control of the balance between exploration and exploitation. The calculated probabilities show that the random application of the swap operator is inappropriate during the search for nonlinear S-boxes resistant to Power Attacks since the exploration may be inappropriate when the class is resistant to Differential Power Attack. It would be more convenient to search for nonlinear S-boxes within the class. This result provides new knowledge about the influence of this operator in the balance exploration–exploitation. It constitutes a valuable tool to improve the design of future algorithms for searching S-boxes with good cryptography properties. In a probabilistic way, our main theoretical result characterizes the influence of the swap operator in the exploration–exploitation balance during the search for S-boxes resistant to Power Attacks in the Hamming Weight class space. The main practical contribution consists of proposing modifications to the swap operator to control this balance better.

Updatable Probabilistic Evaluation of Failure Rates of Mechanical Components in Power Take-Off Systems of Tidal Stream Turbines

This paper presents a method for the probabilistic evaluation of the failure rates of mechanical components in a typical power take-off (PTO) system of a horizontal-axis tidal stream turbine (HATT). The method is based on a modification of the method of the influence factors, when base failure rates, relevant influence factors and, subsequently, resulting failure rates are treated as random variables. The prior (i.e., initial) probabilistic distribution of the failure rates of a HATT component is generated using data for similar components from other industries, while taking into account actual characteristics of the component and site-specific operating and environmental conditions of the HATT. A posterior distribution of the failure rate is estimated numerically based on a Bayesian approach as new information about the component performance in an operating HATT becomes available. The posterior distribution is then employed to obtain the updated mean and lower and upper confidence limits of the failure rate. The proposed method is illustrated by applying it to the evaluation of the failure rates of two key components of the PTO system of a typical HATT—main seal and main bearing. In particular, it is shown that uncertainty associated with the method itself has a major influence on the failure rate evaluation. The proposed method is useful for the reliability assessment of both PTO designs of new HATTs and PTO systems of operating HATTs.

Probabilistic Assessment of Sandwiched Concrete Slabs in Deflection

This study presents a probabilistic evaluation of concrete sand-witched hollow core slabs in accordance with the design requirements of BS8110 (1985; 1997) and Eurocode 2 (2008). The First Order Reliability Method (FORM) was used in computing the probability of failure. For the deflection failure, the effect of varying the load ratio and the breadth of slab on the reliability analysis were carried out at the following values of concrete strengths ݂ܿu: 25N/mm2 , 30 N/mm2 , 40 N/mm2 , 50 N/mm2 . The results indicate that deflection characteristics of the slab are directly affected by the concrete strength, loadings, breadth of slab selected. Thus, the deflection of the slab increases with increases in loading, hollow core, breadth of slab and decrease in concrete strength. This shows that the safety index of reinforced sandwiched concrete slab in deflection generally decreases as the load ratio and breadth of slab increase for each combination of concrete strength. Keywords: Probabilistic Analysis, Sandwiched Concrete, Reliability Analysis, Stochastic Model, FORM

Collapse Probability of Immediate and Special Moment Frames in Tehran under MCE

Residential buildings in most cities, which make up the most significant percentage of buildings, generally contain the most financial and human losses in the face of strong earthquakes. The purpose of this study is to investigate the possibility of the collapse of intermediate and unique steel moment frames against maximum ground excitations. In this study, through the first two steps of PEER methodology, using four steel structural frames with intermediate and unique moment frames, after designing according to the codes of national building regulations of Iran and standard 2800, this probabilistic evaluation was used to ensure their safety against collapse. In the next step, to deepen the results, 7 other sites from Tehran were selected. Their hazard spectrum was used to calculate the probability of collapse. In the end, it was observed that, with the reduction of the number of structural floors, the IDA curves at the lower IM level become horizontal in this project. The results showed that some of the 5-story steel structures under study in some parts of Tehran have a higher probability of collapse than acceptable.