Yes, I understood your idea. But there is 1 fact. When adding a point with even private keys and then adding them, the Y coordinate can be either even or odd. If you filter in getGPUStartingKeys(), I think that after 1 addition the result can be anything. Yes. Just check the rand key generator, how many even and odd values it generates Try it. I used only 1 nbThread to check the GPU code; you can even print points from the GPU using the printf() function, preloading fixed repeating even or odd ones.