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Many research focuses on finding S-boxes with good cryptographic properties applying a heuristic method and a balanced, objective function. The design of S-boxes with theoretical resistance against Side-Channel Attacks by power consumption is addressed with properties defined under one of these two models: the Hamming Distance leakage model and the Hamming Weight leakage model. As far as we know, a balanced search criterion that considers properties under both, at the same time, remains an open problem. We define two new optimal objective functions that can be used to obtain S-boxes with good cryptographic properties values, keeping high theoretical resistance for the two leakage models; we encourage using at least one of our objective functions. We apply a Hill Climbing heuristic method over the S-box&#x2019;s space to measure which objective function is better and to compare the obtained S-boxes with the S-boxes in the actual literature. We also confirm some key relationships between the properties and which property is more suitable to be used.

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Improved Objective Functions to Search for 8 &#x00D7; 8 Bijective S-Boxes With Theoretical Resistance Against Power Attacks Under Hamming Leakage Models