Cryptography & Security

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Shannon Entropy

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

Formula

H = -\sum_i p_i \log_2 p_i

Variables

HEntropy (bits)

p_iProbability of symbol i

Example

Fair coin: H = -2(0.5 log 0.5) = 1 bit

Did You Know?

Claude Shannon coined the term 'bit' and founded information theory in a single 1948 paper.

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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.

Password Entropy

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

Key Space Size

Number of possible keys for a b-bit key.

Birthday Bound

Collisions become likely after about √ of the hash space.