Cryptography & Security

Intermediate

Password Entropy

Bits of security from password length and character-set size.

Formula

H = L \log_2 R

Variables

HEntropy (bits)

LPassword length

RSize of character set

Example

12 chars from 95 printable: H = 12 log2(95) ≈ 78.8 bits

Did You Know?

Every extra random character adds about 6.6 bits — length beats complexity for strong passwords.

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More in Cryptography & Security

Modular Exponentiation

Core operation of RSA encryption — raise a message to a power, modulo n.

RSA Decryption

Recovers the message using the private exponent d.

Euler's Totient

Counts integers below n coprime to it, for n = pq — used to make RSA keys.

Shannon Entropy

Average information content — and the theoretical strength of a random source.

Key Space Size

Number of possible keys for a b-bit key.

Birthday Bound

Collisions become likely after about √ of the hash space.