Cryptography/Key Lengths

Key Length
Key length is directly proportional to security. In modern cryptosystems, key length is measured in bits (e.g. 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.

Entropy
Equal to the importance of key length is information entropy. Entropy, defined generally as "a measure of the disorder of a system", implies randomness. i.e. 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 lacks entropy and is much more vulnerable to attack. For example, if a 128-bit key has only 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, the effective key length is 56 bits because 8 bits are used for parity.

Common Mistakes
The fundamental deficiency in advantages of long block cipher keys when compare it to short cipher keys could be in difficulties to screening physical random entropy in short digits. Perhaps we can't store screening mechanism of randomness in secret, so we can't get randomness of entropy 2^256 without energy, which will be liner to appropriate entropy. For example, typical mistake of random generator implementation is simple addiction of individual digits with probability 0.5. This generator could be easy broken by bruteforce by neighbor bits wave functions. In this point of view, using block ciphers with large amount of digits, for ex. 10^1024 and more have a practical sense.

Other typical mistake is using public key infrastructure to encrypt session keys, because in this key more preferable to use Diffie-Hellman algorithm. Using the Diffie-Hellman algorithm to create session keys gives "forward secrecy".