In　this　paper,　we　investigate　an　intelligent　reflecting　surface　(IRS)　aided　secure　dual-functional　radar　and　communication　system　where　a　dual-functional　base　station　(BS)　desires　to　securely　deliver　messages　to　an　intended　receiver　and　detect　a　malicious　radar　target　simultaneously　with　the　aid　of　an　IRS.　We　generate　two　separate　beams　towards　the　receiver　and　target,　respectively,　while　using　an　integrated　waveform.　We　aim　to　maximize　the　secrecy　rate　while　satisfying　the　radar　detection　constraint　by　jointly　designing　the　power　allocation　factor　between　the　two　beams,　the　beamforming　vector　w　at　the　BS　and　the　phase　shift　matrix　Q　at　the　IRS.　We　propose　the　Riemannian　conjugate　gradient　(RCG)　algorithm　based　alternating　optimization　(AO)　scheme　to　solve　the　formulated　non-convex　problem　for　any　given　.　To　be　specific,　we　first　use　the　penalty　function　method　to　reformulate　the　original　problem　and　then　iteratively　design　w　and　Q　leveraging　the　RCG　algorithm.　We　finally　search　the　optimal　numerically.　Simulation　results　demonstrate　the　significance　of　IRS　in　achieving　a　secure　DFRC　system　and　uncover　the　tradeoff　between　the　performance　of　secure　transmission　and　radar　detection.　©　2022　IEEE.