Designing a cryptographic S-Box in Logisim
Since you are asking how to create the S-box of the linked document: This S-box is a lookup table of 4 bits input to 4 bits output.

The P-layer is "just" wiring. I would generate a sub-circuit for this.

Please be aware that Logisim is limited to 32 bits per multibit-wire. You will need multiple wires.



Alternative 1:

Use the ROM component with 4 bits input and 4 bits output for the S-box.



Alternative 2:

You can use the Combinatorial Analysis window to enter the translation table for the S-box. Then let Logisim build the circuit.

Use it as a component for your main circuit.



Note: Admittedly it is simpler to use a high level hardware description language. To look into the bits, it is still a good exercise to do this on lower levels. Some years ago I built a simple 4-bit computer with Logisim.