Cuckoo Cycle doesn't rely on cryptographic security of its underlying hash function,
and Dan Bernstein himself attested to its use in Cuckoo Cycle being perfectly sound.
Please provide me a copy of that discussion, because I believe I have already shown it is potentially unsound in some logic I have written down and not yet revealed.
I spoke to him in person at BITCOIN'15 where I presented Cuckoo Cycle.
Did he consider (especially parallelized) multi-collision attacks and their impact on the potential to find an algorithm that can find cycles faster? Can you paraphrase what he said or the gist of his reasoning?
Attacks on hash functions are mostly about doing tons of computation (but less than try all inputs)
to try invert its outputs. Siphash may not stand up to that. But to think that a weakness in inversion
resistance can make finding cycles of length 42 in a graph defined by millions or billions of siphash
outputs easier is just... utterly inconceivable. That's the gist of it.
That's the basic algorithm, not the reference miner, which is in
https://github.com/tromp/cuckoo/blob/master/src/cuckoo_miner.hfor CPUs and
https://github.com/tromp/cuckoo/blob/master/src/cuda_miner.cufor GPUs.
These spend most time doing edge trimming,
so that's what this discussion should focus on.