When we use a block cipher to encrypt a message of arbitrary length, we use techniques that are known as modes of operation for the block cipher. Modes must be at least as secure and as efficient as the underlying cipher. Modes may have properties in addition to those inherent in the basic cipher. The standard DES modes have been published in FIPS PUB 81 and as ANSI X3.106. A more general version of the standard generalized the four modes of DES to be applicable to a block cipher of any block size. The standard modes are Electronic Code Book (ECB), Cipher Block Chaining (CBC), Cipher Feedback (CFB), and Output Feedback (OFB).
The Cipher Feedback (CFB) mode and the Output Feedback (OFB) mode are two more standard modes of operation for a block cipher.
In CFB mode, the previous ciphertext block is encrypted and the output produced is combined with the plaintext block using exclusive-or to produce the current ciphertext block. It is possible to define CFB mode so that it uses feedback that is less than one full data block. An initialization vector or value c0 is used as a "seed" for the process.
Due to shortcomings in OFB mode Diffie has proposed an additional mode of operation, termed the counter mode. It differs from OFB mode in the way the successive data blocks are generated for subsequent encryptions. Instead of deriving one data block as the encryption of the previous data block, Diffie proposed encrypting the quantity i + IV (mod 264) for the ith data block, where IV is some initialization vector.
Intuitively, we might expect that by encrypting a message twice with some block cipher, either with the same key or by using two different keys, then we would expect the resultant encryption to be stronger in all but some exceptional circumstances. And by using three encryptions, we would expect to achieve a yet greater level of security. While there are some more complicated issues to consider, this is pretty much the case, and triple-DES has been used for a considerable time as a more secure cipher for protecting the keys used with single-DES. However, there are some surprising results when we consider exactly how much additional protection is provided by using double and triple encryption.
LUC is a public-key cryptosystem developed by a group of researchers in Australia and New Zealand. The cipher implements the analogs of ElGamal, Diffie-Hellman, and RSA over Lucas sequences. LUCELG is the Lucas sequence analog of ElGamal, while LUCDIF and LUCRSA are the Diffie-Hellman and RSA analogs. Lucas sequences used in the cryptosystem are the general second-order linear recurrence relation defined