International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Low-Latency Boolean Functions and Bijective S-boxes

Shahram Rasoolzadeh , Radboud University, Nijmegen, The Netherlands
DOI: 10.46586/tosc.v2022.i3.403-447
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Abstract: In this paper, we study the gate depth complexity of (vectorial) Boolean functions in the basis of {NAND, NOR, INV} as a new metric, called latency complexity, to mathematically measure the latency of Boolean functions. We present efficient algorithms to find all Boolean functions with low-latency complexity, or to determine the latency complexity of the (vectorial) Boolean functions, and to find all the circuits with the minimum latency complexity for a given Boolean function. Then, we present another algorithm to build bijective S-boxes with low-latency complexity which with respect to the computation cost, this algorithm overcomes the previous methods of building S-boxes.As a result, for latency complexity 3, we present n-bit S-boxes of 3 ≤ n ≤ 8 with linearity 2n−1 and uniformity 2n−2 (except for 5-bit S-boxes for whose the minimum achievable uniformity is 6). Besides, for latency complexity 4, we present several n-bit S-boxes of 5 ≤ n < 8 with linearity 2n−2 and uniformity 2n−4.
  title={Low-Latency Boolean Functions and Bijective S-boxes},
  journal={IACR Transactions on Symmetric Cryptology},
  publisher={Ruhr-Universität Bochum},
  volume={2022, Issue 3},
  author={Shahram Rasoolzadeh},