3 Secret communication systems
Secret communication systems are such transmission systems in which sense of transferrable information hides through cryptographic transformations, but the fact of information transmission is being hidden.
Task of information protection during transmission via its communication channels was first formulated by K. Shennon in September, 1945, and published in open view in 1949 in the technical magazine of Bell System Technical Journal. He offered a secret communication system, which is shown on a Fig. 3.
It is assumed that there are two information generators – source of messages Ті and source of keys Кj on a transmitter side. Thus, for both great numbers Т and К, distributions Р(Т) and Р(К) are set. It means that for any Ті є Т probability р(Ті) є Р(Т) is defined, and for any Кj є К probability р(Кі) є Р(К) is defined and rules are executed:
and
.
The key is formed on a side which transfer message with probability of р(Кі), is being transmitted on an opposite side via separate closed communication channel, to which a possible disturber must not have an access. A necessity of such channel is the serious disadvantage of the secret systems, because in networks with the large number of users their implementation requires too large resources.
1 Feistel Network and spn networks
Distinguish two types of construction of block algorithms of encipherement. One of them is built on the basis of chart (networks) of Feistel. To the number such algorithms belong, for example, a former standard of the USA - the DES algorithm and operating standard of Russia - ГОСТ 28147-89.
Other algorithms are built on appearance and similarity networks of SPN (Substitution-permutation-network). To the number such algorithms the new standard of the USA belongs, for example, - AES.
The most widespread method of construction of iterative block ciphers is a construction which carries the name of Feistel.
Chart of Feistel, or a network of Feistel is a variety of block cipher. At the decryption block of plaintext is divided into two equal parts - right and left. Thus, initial length of block of data must be even. In every loop one of parts is exposed to transformation through the F function and subkey - K1, got from the initial secret key - K. The result of operation is added up on the module 2 (operation of XOR) with other part. Then left and right parts switch places. The general view of one cycle of encipherement algorithm, built on the chart of Feistel, is presented on fig.1.
Transformations to every cycle are identical, but on the last cycle transposition is not executed. Procedure of decryption is analogical procedure of encryption, but the subkeys of Ki get out upside-down. If at encrypyion transposition was executed in the last loop, it is necessary to begin decryption with transposition of left and right part of data block.
Basic advantage of such structure of cipher is that procedures of encryption and decryption coincide, with that exception, that key information at a decryption is utillized upside-down. It allows during physical realization of block cipher to utillize identical blocks in the chains of encryption and decryption.
Lack is that on every iteretion only the half of block of the processed text changes. It results to necessity to increase the number of iteretion for achievement of a required firmness.
Crypanalitical firmness of algorithm of encipherement, built on the chart of Feistel depends from three basic parameters:
- numbers of rounds of cipherement;
- type of F function;
- algorithm of keys calculation.
It was already marked that to the cipherement algorithms, wich built on the Feistel chart are refer such as DES and ГОСТ 28147-89. Besides foregoing algorithms, there is quite a few other such, as, for example Lucifer, FEAL, Khufu, Khafre, LOKI, COST, Blowfish, wich also built on a chart of Feistel. A block algorithm of cipherement, utillizing the described construction, is convertible and guarantees possibility of renewal of input data of F function in every loop.
It is necessary also to mark that dividing of initial cipher by two parts can be transferable a division on four, eight and more than parts. Such algorithms of cipherement are named derivative from the chart of Feistel. Some modern ciphers have such structure. For example, algorithm of cipherement of CAST or algorithm of cipherement of Skipjack closed till recently.