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gwern, if you're reading, this section is misleading if not wrong ...:

"But that doesn’t seem very true any more. Devices can differ dramatically now even in the same computers; to take the example of Bitcoin mining, my laptop’s CPU can search for hashes at 4k/sec, or its GPU can search at 54m/second."

This is an example of parallelism and parallelism only.

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Are you implying that GPUs execute each hash as slowly as a CPU and are better at hashing simply because they have more processing elements? I knew GPUs had a lot of small cores, but I was unaware that mine had 54000000 / 4000 = 13500 cores.

I think you were using a bad algorithm on your CPU. Assuming any half-recent x86 processor you should be looking at a number like 4 Mhash/second, not 4K.

More or less, yes, that is my implication. Luckily, my sibling comment provides some extra information.

For the example of SHA-1 computation, you mention using FPGAs that finish in 400 clock cycles, which is at most an order of magnitude away from a naive CPU implementation of around 4000 clock cycles. I'm not as familiar with SHA-256.

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