Cryptography & Security

Intermediate

Brute-Force Time

Time to try every key at a given guess rate.

Formula

t = \frac{K}{r}

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Variables

tTime (s)

KKey space

rGuesses per second

Example

K=2^56, r=10^12/s: t ≈ 20 hours

Did You Know?

56-bit DES fell to brute force in 1998; today's hardware would crack it in seconds — hence the move to AES.

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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.

Password Entropy

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Key Space Size

Number of possible keys for a b-bit key.