Cryptography/Key Lengths

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[edit] Key Length

Key length is directly proportional to security. In modern cryptosystems, key length is measured in bits (i.e., AES uses 256 bit keys), and each bit of a key increases the difficulty of a brute-force attack exponentially. It is important to note that in addition to adding more security, each bit slows down the cryptosystem as well. Because of this, key length -- like all things security -- is a tradeoff. In this case between practicality and security.

Furthermore, different types of cryptosystems require vastly different key lengths to maintain security. For instance, modulo-based public key systems such as Diffie-Hellman and RSA require rather long keys (generally around 1,024 bits), whereas symmetric systems, both block and stream, are able to use shorter keys (generally around 256 bits). Furthermore, elliptic curve public key systems are capable of maintaining security at key lengths similar to those of symmetric systems. While most block ciphers will only use one key length, most public key systems can use any number of key lengths.

As an illustration of relying on different key lengths for the same level of security, modern implementations of public key systems (see GPG and PGP give the user a choice of keylengths. Usually ranging between 768 and 4,096 bits. These implementations use the public key system (generally either RSA or ElGamal) to encrypt a randomly generated block-cipher key (128 to 256 bits) which was used to encrypt the actual message.

[edit] Entropy

Equal to the importance of key length, is entropy. Entropy, defined generally as "a measure of the disorder of a system" has a similar meaning in this sense: if all of the bits of a key are not securely generated and equally random (whether truly random or the result of a cryptographically secure PRNG operation), then the system is much more vulnerable to attack. For example, if a 128 bit key only has 64 bits of entropy, then the effective length of the key is 64 bits. This can be seen in the DES algorithm. DES actually has a key length of 64 bits, however 8 bits are used for parity, therefore the effective key length is 56 bits.