I have over 30 GPUs mining various coins, a half dozen Sia coin ASIC miners, another half dozen Dash ASIC's, some BTC ASICs and more than just that. Lets consider ONLY my BTC miners. There are only three ASICs running which together average about 35TH/s. Ignoring all my other equipment, I can't make heads or tails out of my internet usage, which averages about 300GB/month.

Something just doesn't add up.  35 TH/s is 35,000,000,000,000 hashes per second. Multiply that by 3600 seconds in an hour, 24 hours in a day and 30 days in a month, that's 90,720,000,000,000,000,000 hashes per month. Even if each hash only required a single byte to be exchanged in each direction between the miner and the mining pool, this would require 600 million times more internet bandwidth than I am using.

So what exactly is a hash? I thought (apparently naively) that the pool sends you a big 256 bit number and you "hash" it by XORing its bits with a key and with rotated versions of portions of itself, generate a new number and send it back to the pool, and if your miners are generating 35TH/s, then this happens 35 trillion times per second. I guess that's obviously not what's happening.

Just to put my question in context, I'm a computer science professor, but obviously not an expert in this field, however I have had several of my students under my direction implement portions of cryptonightV8 on an FPGA and checked the sub-results against the mining software. I have also developed a complete Keccak implementation on an FPGA for mining Smartcash and I dissected cpuminer to check my hash from my FPGA solution against the hash produced by the software. Right now I'm trying to understand the front-end aspects of mining so I can implement the entire protocol on my FPGA (my FPGA contains a CPU which is C programmable, so I can think more abstractly for some of the front-end tasks, and leave the low-level FPGA stuff for the actual hashing - which is complete). In other words, I think I know what hashing is. However, I can't reconcile the ratings of the miners against the bandwidth of my connection.

So, I need some help understanding what 35 TH/s really means, how it is calculated, and how to relate this to the amount of information exchanged between the miner and the pool. Can anyone help?
-gt-