International Association
for Cryptologic Research

In this paper, we present the DORCIS tool, which finds depth-optimized quantum circuit implementations for arbitrary 3- and 4-bit S-boxes. It follows up from the previous LIGHTER-R tool (which only works for 4-bit S-boxes) by extending it in multiple ways, on top of modifications that allow for depth optimization instead of gate cost optimization. LIGHTER-R only deals at the top-level (i.e., Toffoli gates), whereas DORCIS takes quantum decomposition (i.e., Clifford + T gates) into account. We match, if not surpass, other optimized quantum circuit implementations put forth in the other papers. Our tool is easy to use, and we also provide a simple interface to IBM's Qiskit.