Construction of Rotation Symmetric S-Boxes with High Nonlinearity and Improved DPA Resistivity

Abstract

In this paper, we provide an n×n bijective rotation symmetric S-box (RSSB) construction with improved resistance to differential power analysis (DPA) using rotation-symmetric Boolean functions (RSBFs). The RSSB class is generated from an instance of a proposed RSSB construction and then iteratively applying a simulated annealing algorithm in the respective neighborhood of the RSSB followed by a hill climbing algorithm to obtain a good tradeoff of cryptographic properties. The constructed 8×8 RSSBs have a nonlinearity of 102 and transparency order value 7.709 whereas the Rijndael S-box has a higher transparency order of 7.86 . The evaluation of security metric called guessing entropy on the constructed RSSBs shows that a side-channel adversary requires more effort to exploit information leakage from the simulated power traces. In comparison to Rijndael S-box, the correlation based DPA on RSSBs which when incorporated in AES-128, shows requirement of significantly more power traces when implemented on Xilinx Virtex-5 FPGA device on SASEBO-GII development board. While the distributed memory and block memory implementations of the Rijndael S-box required 500 and 2,000 power traces to extract the last round key, our proposed RSSBs required 2,000 and 12,000 power traces respectively.