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Side Channel Attacks (SCA) were introduced in 1997 by Kocher et al. and exploit the fact that while a device is processing data, information about this data is leaked through different channels, e.g., power consumption, electromagnetic emanation and so forth. DPA is a more advanced technique using statistical methods to analyze data collected from many measurements. Threshold Implementation (TI) is an elegant and widely accepted countermeasure against 1-st order Differential Power Analysis (DPA) in Side Channel Attacks. The 3-share TI is the most efficient version of TI, but so far, it can only be applied to 50% of all 4-bit S-boxes. In this paper, the authors study the limitations of decomposition and introduce factorization to enable the 3-share TI for any optimal 4-bit S-box.
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