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I'm making an informational video about how unlikely it is for an attacker to successfully brute force a specific bitcoin address. Obviously, it will deal with impossibly huge numbers ("not in earth's lifetime with today's technology"), but I would like to include the number of trials required for an attacker to gain 1%, 50% and 90% confidence of success.

Normally I can get away with using Excel for statistical problems. However, Excel doesn't do really big numbers so I'm unable to calculate.

If I were to use Excel, I would use the below formula that tells me the chance of getting 0 successes in ???? trials. I would subtract the result from 1 and that % represents the possibility of success.

=1-BINOM.DIST(0,????,2^-160,TRUE)

For a simplified example of what I'm looking for: If I were to play a game with a 1% chance of winning, I would have about a 90% chance of 1 or more successful efforts after 250 trials, 50% chance after 70 trials, and 1% chance after 1 trial.

91.89%=1-BINOM.DIST(0,250,0.01,TRUE)

50.52%=1-BINOM.DIST(0,70,0.01,TRUE)

1.00%=1-BINOM.DIST(0,1,0.01,TRUE)

Can anyone calculate how many trials would be needed for 90%, 50%, and 1% possibility of success against a single bitcoin address? The possibility of landing the address correctly is 1 out of 2^160.

Kudos if you can do the math in your head.

pgSystemTester
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1 Answers1

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Since nobody replied, I posted this on the Math Stack Exchange and quickly got an answer.

For anyone that's interested, using a formula from R we get the following values:

pbinom(0,3.365231884e48,2^(-160), FALSE)   = 0.9000000000339017
pbinom(0,1.0130357393e48,2^(-160), FALSE)  = 0.5000000000001161
pbinom(0,1.46885823057e46,2^(-160), FALSE) = 0.01000000000005571
pgSystemTester
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