In the previous cryptocurrency video I mentioned this situation twice In order to break a security system You have to guess a 256 bit string The first time it was mentioned in the electronic signature section The second time was mentioned in the section on password hash functions For example, if you want to find a message Let its SHA256 hash value equal to a certain 256-bit string Then there is no other good way, you can only guess randomly and check the result On average, this requires 2^256 attempts This number is much larger than what we usually encounter So it’s hard to appreciate its scale But we might as well try 2^256 is 2^32 multiplied by itself 8 times The advantage of thinking this way is that 2^32 is about 4 billion We can at least imagine this number Is the number that appears in the news headline So what we have to do Is to experience the concept of multiplying 4 billion 8 times in a row Most people know The GPU in the computer can quickly perform a large number of parallel calculations So if you specifically let the GPU calculate the password hash function repeatedly A GPU with good performance may be able to calculate close to 1 billion hashes per second If you take a bunch of such GPUs All into the computer Let your computer calculate 4 billion hashes per second So the initial 4 billion represents The number of hash values calculated by each computer per second Imagine 4 billion computers full of GPUs like this For comparison, although Google has not announced the number of their servers But some estimates say there are several million In reality, the computing power of most of their servers Not as good as our computers full of GPUs But let’s assume that Google replaces millions of servers with such computers Then 4 billion computers are about 1,000 such a bloody Google Let’s call this computing power "Thousand Googles" The world’s population is approximately 7.3 billion Next we assume that more than half of people have their own thousand Google Then imagine 4 billion such planets For comparison, the Milky Way has about 100 to 400 billion stars Although we are not sure, the estimate is roughly in this range So this is equivalent to 1% of the stars in the Milky Way will have an Earth And half of the population on this planet has its own thousand Google Then imagine 4 billion such galaxies We call it "Billions of Galaxy Supercomputers" Can guess 2^160 times per second 4 billion seconds is about 126.8 years 4 billion times it is 507 billion years Almost 37 times the age of the universe So even if you have Full of GPUs, thousands of Googles, planets, billions of galaxy computers Keep guessing the time of 37 times the age of the universe There is only one in 4 billion probability to get the correct guess By the way, the current hash power of Bitcoin Add up all the miners Can guess and check 50 billion hashes per second This is equivalent to one-third of the thousand Googles I mentioned earlier This is not because there are really billions of computers with full GPUs But because the miners use machines that are about 1,000 times better than GPUs Called "Application Specific Integrated Circuit" (ASIC) These hardware are tailor-made for Bitcoin mining Otherwise, it will calculate the SHA256 hash value I wanted to greatly increase efficiency We can give up general computing needs And to design integrated circuits for a single task There is another topic that I find a bit difficult to turn around: when it comes to the power of two The number of subscriptions to this Youtube channel recently exceeded 2^18 In order to better interact with some of these 2^18 people I will start a question and answer event I will post the Reddit link to the video introduction You can ask questions or put on the top of the question you want to know the answer Maybe in the next video or Twitter or something I will announce the form of answering questions see you then!