_ Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top up vote down vote favorite 5 I am doing a presentation on Bitcoins and I was looking for some calculations to make people feel safe about the private key encryption.Please first answer, how long in bytes the private key is, then how many combinations of numbers it will contain, and then what is the fastest computer or network of supercomputers and how long it would take to crack a private key using that computer.I think the result would be very educational based on my own calculations.security encryption up vote down vote "how long in bytes the private key is" 32 bytes, or 256 bits "then how many combinations of numbers it will contain" There are 2^256 different private keys.That's a little larger than a 1 followed by 77 zeroes."what is the fastest computer or network of supercomputers" At its peak around August 2011, the Bitcoin network was checking 15 trillion sha256 hashes per second.

(See http://bitcoin.sipa.be/) "how long it would take to crack a private key using that computer" If we assume it takes the same time to run an ECDSA operation as it takes to check an sha256 hash (it takes much longer), and we use an optimisation that allows us to only need 2^128 ECDSA operations, then the time needed can be calculated: >>> pow(2,128) / (15 * pow(2,40)) / 3600 / 24 / 365.25 / 1e9 / 1e9 0.6537992112229596 It's 0.65 billion billion years.That's an very conservative estimate for the time taken to break one single Bitcoin address.Edit: it was pointed out that computers tend to get exponentially faster over time, according to Moore's Law.Assuming computing speed doubles every year (Moore's law says 2 years, but we'll err on the side of caution), then in 59 years it'll only take 1.13 years.So your coins are safe for the next 60 years without a change to the algorithms used to protect the blockchain.However, I would expect the algorithms to be changed long before it's feasible to break the protection they provide.

up vote down vote A Bitcoin private key is a random 256-bit number.However, the public key reveals some information about the private key.The best known algorithms for breaking ECDSA require O(sqrt(n)) operations.That means 2^128 operations would be needed to break a Bitcoin account.The largest ECDSA key broken to date of the type that Bitcoin uses was 112 bits long.A Bitcoin account is more than 4,000 billion billion times harder to break.The only realistic risk would be quantum computing.up vote 1 down vote A Bitcoin private key (ECC key) is an integer between one and about 10^77.This may not seem like much of a selection, but for practical purposes it's essentially infinite.If you could process one trillion private keys per second, it would take more than one million times the age of the universe to count them all.Even worse, just enumerating these keys would consume more than the total energy output of the sun for 32 years.This vast keyspace plays a fundamental role in securing the Bitcoin network.

up vote 0 down vote 2^256 = 1.1x10^77 = number of key combinations 2^128 = 3.4x10^38 = the average number of guesses needed /wiki/TOP500, the fastest supercomputer is the K computer which has 10.51 petaflops.bitcoin offline backupA petaflop is 10^15 FLOPS, floating point instructions per second.litecoin boxSo far so good, but I need to know how many FLOPS are needed per guess?bitcoin visual studio 2012[I will venture a guess:] Between 1,000 and 10,000 FLOPS (or integer equivalents) per guess.bitcoin isin10.51x10^15 ops/second / 1000 to 10000 ops/guess) = 10.51x10^12 to 10.51x10^11 guess/second.bitcoin node raspberry pi

3.4x10^38 guesses/crack / 10.51x10^12 guess/second = 3.2x10^25 seconds.3.2x10^25 seconds / 60 seconds/minute / 60 minutes/hour / 24 hours/day / 365.25 days/year = 1.01x10^18 years 1.01x10^18 years / 1x10^9 / 1x10^9 = 1.014 to 10.014 billion billion years.litecoin default locationSo the computers on the Bitcoin network are twice as fast as the single largest laboratory computer.bitcoin live wettenup vote down vote The fastest computer is 150 Petraflops FPC per sec not 10 ... Try and keep up with the times (NV Link and Volta HCP Cards on IBM power processors) ... you can read or watch more at team green's website or the 2015 Conference vids on U tube.valor da bitcoin hojeSince the general answer seems to be based on 10 Petraflops as the worlds fastest computer ...bitcoin valor hoje

You should be clearly able to see how quickly the FPC per sec can change , The Department of Energy is planning a 300P system already based on the same technology.The point Is that your bitcoin folks telling you how secure it is based on 10P already have the basic math wrong by 15-30 times because they evidently don't know as much as they think.The improvements are not dependent on Moore's Law either , the recent advancements and present limitations have to do with an entirely different Law which is what NV Link solved as best it could and improved computing time so well , This is just today's example of how their theory of a billion billion years is already wrong by a factor of 15-30 and will continue to become wrong each year at a much higher rate than they assume.In 30 years or less bitcoin at it's present level will be easily cracked by anyone who has 40 to 50,000 dollars to spend (in todays money) or can use any number of University or Corporate Supercomputers.Anyone who actually believes that 50 year old technology is going to keep something digitally secure 50 years later is frankly not the kind of person you should be paying ANY attention to at all ... Does that mean bitcoin is dangerous today ?