Cryptographic Randomness & Information Entropy
In information theory and cyber security, the strength of a credential is measured in Shannon entropy, represented in bits. Entropy measures the measure of uncertainty or unpredictability in a random variable.
Calculating Password Entropy
For a randomly generated password of length \(L\) selected from an unbiased character pool of size \(N\), the entropy \(H\) in bits is computed as:
H = L * log2(N)
When using all 94 printable ASCII characters across a 16-character string, the entropy reaches:
H = 16 * log2(94) = 16 * 6.55 = ~104.9 bits of entropy
A space of \(2^{105}\) possibilities would require modern supercomputers billions of years to exhaustively brute-force, ensuring impenetrable credentials for your essential online accounts.