Problem is that it's very difficult to find the hashing algorithm that would be really ASIC resistant, not to mention GPU. For instance, Primecoin which included large integer algorithms that should be difficult for GPUs was soon transferred to GPU mining. All scrypt algos are prone to GPU mining. I tried to find some hashing algorithms that would favor RISC processors, since they dominate modern smartphones, but I've failed to find any. If anybody has some info about such algos it would be very nice to share that info here.
I find it hard to believe that any form of PoW mining (regardless of algorithm) on a smartphone would ever be popular given battery life considerations.
Why do you think so? My smartphone is on charger almost every night, regularly, and I would be very happy if it would do something useful instead of waiting for the alarm clock to fire up. It's trivial to set preference in any application to work only when the phone is on charger.
Just read the John Tromp's
paper and I believe he is on the right track with memory-swapping constrained algorithms. Probably there's a need to examine some algorithms that prefer the RISC based instruction pipeline, and try to incorporate them somehow with Cuckoo Cycle hashing. Idea is to further bias the smartphones since they have less memory and slower processors than desktops, and are almost without exception RISC based. Such combination would be a winner.