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by bspammer 1645 days ago
> A private key is basically just a number between 1 and 2^256

It's like saying "I'm gonna pick a random number between 1 and a trillion", and then picking 999,999,999,995. Probably not a smart idea given that you don't want anyone else to be able to guess your number.
1 comments
grumple 1645 days ago
But the values are generally generated pseudo randomly by machine. This seems similar to the birthday problem, where the odds of encountering a value in a given range is higher than you'd expect.
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FabHK 1645 days ago
1. yes, generally and ideally the private key is generated pseudo randomly. But at the beginning or for testing, people might have manually picked a private key.

2. the birthday problem basically halves the exponent security wise. The rule of thumb: If you have N possible outcomes, then after around sqrt(N) guesses the probability of a collision approaches 0.5. So, for birthdays, it's 365 outcomes, so with 19 or 20 people your risk of collision already approaches a half. For BTC private keys, there are 2^256 possible, so with 2^128 guesses you'd approach a likely collision. Fortunately, that's still 1e38, so if you check 1e10 per second, you'd still need 1e20 years to get there.

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bspammer 1645 days ago
The birthday problem means that the number of values you have to choose to have a 50% chance of a collision scales approximately with the square root of the size of the space. [0]

2^(256/2) is way, way bigger than the number of used bitcoin addresses, which is about 33 million according to this csv [1].

[0] https://en.wikipedia.org/wiki/Birthday_attack#Mathematics

[1] https://bitkeys.work/download.php

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