Searching for Balanced S-Boxes with High Nonlinearity, Low Differential Uniformity, and Improved DPA-Resistance

摘要

Substitution boxes (S-boxes) are one of the most crucial primitives in the field of block ciphers. Recently, differential power analysis (DPA), a very powerful technique which targets implementations of block ciphers, causes the modern block ciphers to be much more vulnerable than ever before. Up to now, the revised transparency order is one of the best metrics to assess the resistance of S-boxes against DPA attacks. In this paper, we present an efficient algorithm to search for cryptographically significant S-boxes with improved DPA-Resistance. Applying our developed algorithm, we generate an 8 x 8 balanced S-box with algebraic degree 7, nonlinearity 112, differential uniformity 4, absolute indicator 32, revised transparency order 6.8820 (whereas the Rijn-dael S-box has revised transparency order 6.9161) and thereby improved resistance towards DPA attacks. Moreover, many other balanced S-boxes with a much better trade-off of cryptographic characteristics than previous works (e.g. S-boxes given by B. Mazumdar and D. Mukhopadhyay in IEEE Trans. Computers 2017) are also captured. The comparison between ours and previous results manifests that our S-boxes are more secure and robust.