The fact is that the text letter can have the most different size - from the empty communication (incomprehensibly, true, why necessary it to sign) to the volumetric file and furthermore which includes to graph, and the algorithms ETSP are intended for the signature of the communications of the specific length, in particular, THE ALL-UNION STATE STAN. Therefore the task of hash- function consists in to calculate the digital sequence of standard size, let us say from the letter of arbitrary volume, the same 32 bytes, equal to 256 bits. Hash- function possesses or, at least, it must possess the following properties.

communication (hash - the result of the work of hash- function) it must unambiguously correspond to it and change with its modification.

Hash- function must be unidirectional. Then, in the first place, even knowing hash h(.M), it is not possible to calculate communication itself M and, in the second place, for each piece of information M it is not possible to select such communication M ', for which would be satisfied the condition:

h(.M) = h(.M ').

The no fulfillment of the second condition would allow criminal to substitute letters, leaving the signature in them of accurate. Furthermore, in many communications hash is identical, since, as they speak mathematics, many permissible letters (their quantity is practically limitlessly) substantially more than the set of the hash- values, whose maximally possible number in all 2256. But now, being expressed by the language of cryptography, let us otherwise formulate the conditions given above: the "laboriousness for the successful calculation of communication M ' on already known hash h(.M), which satisfies condition h(.M ') = h(.M), must not be less than the labor expense of the straight sorting of communications".

Let us note that the hash- functions also widely are used for authorization of users and appeared the mass of the cryptographic protocols, based on their application.

In the preparatory stage of two friends, for example, create two pairs of the keys: secret and opened for the asymmetric coding, and also secret and open keys ETSP. They are exchanged the open keys, and then one sends the communication, signed by its secret key, to another.

Then the first friend generates the random key of the symmetrical coding K, by which the sent letter ciphers, moreover only this.

Further so that it would be possible to decipher the communication, it codes key K (but in the open form to send the key of symmetrical coding in no case inadmissibly) on the open key of the asymmetric coding of its friend is added it to the encoded letter.

The second friend, after obtaining the encoded communication, deciphers by his secret key of asymmetric coding key K, by which then deciphers letter itself.

And finally, it checks with the aid of the open key of the friend of his ETSP in this letter even it is convinced, that it arrived precisely from its friend and in the unchanged form.

To here cavil in practice to nothing - with the competent use a similar system will leave to the hacker of no chances to the success. True, can seem by inconvenient that is necessary to make too many keys. For the solution of this problem is provided the algorithm the open key is calculated from the secret:

Kp = aKs mod p,

where a and p - some well-known large numbers (they can take values to 21024, and this great significance). Let us assume that to eat users 1 and 2, generated its secret keys and calculated of them opened:

Kp1 = aKs1 mod p;

Kp2 = aKs2 mod p.

After the exchange of the open keys in each of them the pair of the keys appeared: his secret and strange opened, i.e. subscriber 1 has keys Ks1 and Kp2, and subscriber 2 - Ks2 and Kp1. Now let us recall mathematics (be glad schoolboys and students, who know mathematics by heart,!) and let us represent that it will be, if to subscriber 2 suddenly decides to elevate into the degree of its secret key the open key of subscriber 1:

(Kp1)Ks2 = (aKs1)Ks2

mod p = (aKs2)Ks1 mod p = (Kp2)Ks1 = Kc.

Does impress you a similar result? Indeed came out the same, which would leave, if subscriber 1 wanted to make analogous with those available to it by the open key of subscriber 2 and his secret key! It means, there is a key Kc, usually called the "key of paired connection", which subscribers 1 and 2 with the use of the keys available to them can calculate only, since the criminals do not have Ks1 or Ks2, and therefore they will not know how to determine Kc. Then with the aid of pass key Kc it is possible rapidly to symmetrically encode communications on the standard ALL-UNION STATE STAN. 28147 - 89. Beauty! And do not be frightened all these complex formulas, I will again recall that all calculations are produced automatically, it is worthwhile to only give indications to program, that also for whom to cipher and to sign.