What properties should an ideal straight P-Box exhibit?
Straight P-Boxes should have only 1 input for each output and the same number of inputs as outputs.
Straight P-Boxes will also be invert-able.
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This is not an answerable question. The requirements for a P-box (whatever that is) depend upon the cipher it is embedded in; that cipher imposes some requirements on the P-box. Therefore, you cannot do P-box design in the abstract, without knowing what the requirements are. There is no one, single answer that is valid for all ciphers.
P.S. Where did you hear the term "P-box"? As far as I know, this is not an accepted or widely used term, let alone "straight P-box".