Confidential　computational　geometry　problems　are　one　of　the　more　popular　classes　of　topics　in　secure　multi-party　computation.　In　the　secure　computation　of　geometric　problems,　the　cross　product　can　be　used　to　judge　the　intersection　of　line　segments.　In　this　paper,　we　transform　the　problem　of　judging　line　segment　intersection　into　the　problem　of　computing　cross　product,　propose　a　cross　product　computation　protocol　for　protecting　private　information　under　the　semi-honest　model,　and　analyze　the　security　and　correctness.　And　further,　this　paper　design　a　confidential　protocol　for　computing　cross　product　under　malicious　model　and　then　judge　line　segment　intersection,　which　utilizes　segmentation-selection　method　and　zero-knowledge　proof　to　prevent　or　detect　malicious　behavior,　and　prove　the　security　of　the　protocol　with　ideal-practical　examples.　©　The　Author(s),　under　exclusive　license　to　Springer　Nature　Switzerland　AG　2024.