j"1LAnZuoQdcKCkpDBKQMCgziGMoPC4VQUckM÷<div class="post"><div class="quoteheader"><a href="https://bitcointalk.org/index.php?topic=360.msg3174#msg3174">Quote from: mcdett on July 15, 2010, 03:56:42 PM</a></div><div class="quote">What is being hashed in this function? <-- let's call this item x<br/><br/>If the total number of possible x is smaller than 256bit space that sha256 provides than an attack would come in the form of a table of all sha256(x) values.<br/><br/>If all of the possible combination's of x is greater than the 256bit space, then here is some math for you (the attack would be at the hash value itself rather than a table on known sha256(x)):<br/><br/>What follows is from <a href="http://www.atmel.com/dyn/resources/prod_documents/doc8668.pdf">www.atmel.com/dyn/resources/prod_documents/doc8668.pdf</a><br/><br/>If there are 256 bits in the key, then after 2^255 attempts the attacker has a 50% chance of finding the right key and after 2^256 attempts he has tried all possible keys and is guaranteed to have found the key.<br/><br/>Here are some estimates of big numbers:<br/><br/>2^66 Number of grains of sand on the earth<br/>2^76 Number of stars in the universe<br/>2^79 Avogadro's number. The number of carbon atoms in 12 grams of coal.<br/>2^96 Number of atoms in a cubic meter of water<br/>2^190 Number of atoms in the sun<br/>2^255 Number of attempts to find the key value from above<br/><br/>But what about very well funded entities such as the US National Security Agency (NSA)? Could they build a machine to crack a 256 bit key? Assume they could build a theoretical nanocomputer that executes 10^13 instructions per second (approximate rate of atomic vibrations) in a space of a cube with a side that is 5.43nm across (This is the approximate size of a silicon lattice10 atoms wide, or a crystal containing 1000 silicon atoms). Assume that it could calculate an attempt in 10 cycles. Such a computer the size of the earth would take more than 10^13 years (roughly 58 times the estimated age of the earth) to attack a 256 bit algorithm via brute force.<br/></div><br/>Quantum computing and encryption: <a href="http://stackoverflow.com/questions/2768807/quantum-computing-and-encryption-breaking">http://stackoverflow.com/questions/2768807/quantum-computing-and-encryption-breaking</a></div> text/html
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