uplinks:: Probability Public-key Cryptography
tags:: #lang/en #type/faq

Probability of someone generating the same private key

Assuming that the private Key Space is nn bits long, a total of 2n2^n private keys can be generated. Therefore, the probabiity of someone generating the exact private key equals to 12n\frac{1}{2^n}

Did You Know

The size of bitcoin’s private key space, (22562^{256}) is an unfathomably large number. It is approximately 107710^{77} in decimal. For comparison, the visible universe is estimated to contain 108010^{80} atoms.
— Mastering Bitcoin

References

See Also