Paper 2012/510

Enabling 3-share Threshold Implementations for any 4-bit S-box

Sebastian Kutzner, Phuong Ha Nguyen, and Axel Poschmann


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.

Available format(s)
Secret-key cryptography
Publication info
Published elsewhere. Unknown where it was published
secret-key cryptographysecret-key cryptographyimplemetationblockcipherSERPENTThreshold Implementation coutermeasureSide Channel AttackDPA
Contact author(s)
ng0007ha @ e ntu edu sg
skutzner @ ntu edu sg
hxwang @ ntu edu sg
2012-09-03: received
Short URL
Creative Commons Attribution


      author = {Sebastian Kutzner and Phuong Ha Nguyen and Axel Poschmann},
      title = {Enabling 3-share Threshold Implementations for any 4-bit S-box},
      howpublished = {Cryptology ePrint Archive, Paper 2012/510},
      year = {2012},
      note = {\url{}},
      url = {}
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