Enabling 3-share threshold implementations for all 4-bit S-boxes

• Main Authors: Kutzner, Sebastian, Nguyen, Phuong Ha, Poschmann, Axel
• Other Authors: School of Physical and Mathematical Sciences
• Format: Conference or Workshop Item
• Language: English
• Published: 2014
• Subjects: DRNTU::Science::Mathematics
• Online Access: https://hdl.handle.net/10356/102051; http://hdl.handle.net/10220/18869; http://eprint.iacr.org/2012/510
• Institution: Nanyang Technological University

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, we study the limitations of decomposition and introduce factorization to enable the 3-share TI for any optimal 4-bit S-box. We propose an algorithm which can decompose any optimal 4-bit S-box to quadratic vectorial boolean functions with a time complexity of $2^{19}$. Furthermore, we use our new methodology in combination with decomposition to optimize ciphers utilizing many different S-boxes, and, to highlight the strength of our new methodology, we construct a 3-share Threshold Implementation of SERPENT which was believed to be not possible until now. Last, we show how to implemented all SERPENT S-boxes with only one mutual core.