Fastest device to perform single-threaded SHA256 hashing I am in the process of designing a cryptographic Proof of Storage (PoS) that relies on single threaded computation of SHA256 hashes. In practice, my algorithm is equivalent to computing for some string S the value SHA256^N(S) = SHA256(SHA256(SHA256(...(SHA256(S)))).

This forces anything computing that function to use only one thread, as each SHA256 step needs the output of the previous as input.

Now, I know that ASIC miners exist that can compute SHA256 hashes at an enormous rate. This, however, is due to their parallelism: completing Proofs of Work (i.e., finding zeros of hash functions) is an embarassingly parallel problem and can be computed very fast on massively parallel devices. This is not what I am looking for.

What I am looking for is the fastest device that would be able to compute my function, i.e., single-threaded computation of a SHA256, then the SHA256 of its output, the SHA256 of the result and so on.

I thought that maybe in this case the best hardware would be the fastest CPU in terms of single threaded performance: I found here that Intel Core i7-7700K could be a good place to start looking for.

Is there any other known specialized hardware device that could carry out the task faster?
Well, existing Bitcoin mining hardware would indeed not be any good for iterated hashing, as it's not designed to do that. However, SHA-256 is not a hardware resistant hash function. The most complex operation in the hash function is addition modulo 2³², which is quite easy to implement in hardware.

An attacker could implement a fast SHA core on a chip, which would consist of calculating a single round as fast as possible. This is the opposite optimization as a Bitcoin miner: miners prefer very many parallel cores that run at slower clock speeds to save energy per hash. Such a hypothetical chip would definitely be much faster than a CPU at calculating iterated hashes.

What you want is a memory-hard hash function such as Argon2. Its execution requires fast cache, which is plentiful on commodity CPUs but costly to build into other hardware. It has a parallelism parameter where you can allow up to, say, 4 cores. Iteration of the function will not be any faster past that number of cores, and custom hardware will not increase the attacker's speed.