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To randomly guess a single key from a 128-bit key space has a chance of 1 divided by the number of elements or $\frac{1} {2^{128}}$ where $2^{128}$ is the number of keys possible. To get ballpark figures to convert between base 2 exponents and base 10 exponents you can use the following trick: Because $2^{10} = 1024 \approx 10^3$ you can easily count the ...


See https://en.wikipedia.org/wiki/RSA_%28cryptosystem%29 Under Key Generation: Compute n = pq. n is used as the modulus for both the public and private keys. Its length, usually expressed in bits, is the key length.


The size of the public key depends on the elliptic curve used. Any private key will produce a point on the curve, which is the same size – approximately 256 bits for 256-bit curves, for example. Random numbers from a small range could be insecure, however. The secure way to generate the private key is to take it from the range $[1, l-1]$, where $l$ is the ...

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