4 Electronic-digital signature

The most essential application of public key cryptography domain are digital signatures. During many ages at the conduct of business correspondence, conclusion of contracts and registration of any other important papers a signature of responsible person or performer was the necessary condition of confession of his status or undeniable certificate his importance. A similar act pursued two purposes:

- guaranteing truth of letter by collation of signature with a present standard;

- guaranteing of authorship of document (from the legal point of view).

Implementation of these requirements is based on the followings properties of signature:

- a signature is authentic, i.e. it is possible to prove with its help the recipient of document, that it belongs to signing (in practice it is determined graphology examination);

- signature is unforged, i.e. serves as proof, what only a that man, whose autograph stands on a document, could sign this document and nobody other would be able it to do;

- signature are noncarred, i.e. it is of part of document and carrying it on other document is impossible;

- a document with a signature is unalterable, i.e. it is impossible to change of its after signing, leaving this fact unnoticed;

- a signature is unquestionable, i.e. man, signing a document, in the case of confession examination, that exactly he witnessed this document, can not contest the fact of signing;

- any person, having a standard of signature, can make sure of that this document is signed the proprietor of signature.

With passing to the nonpapered methods of transmission and storage of data, and also with development of the electronic translation of money facilities systems, in basis of which is an electronic analogue of paper payment, the problem of virtual confirmation of authenticness of document purchased the special sharpness.

Development of any similar systems now unthinkable without existence of electronic signatures under electronic documents. However much application and wide distribution of electronic-digital signatures (EDS) entailed a number of legal problems. So, EDS can be used on the basis of agreements into some group of users of the system of communication of data and, in accordance with an agreement into this group, must have legal force. But will there be an electronic signature to have evidential force in a court, for example at challenging of fact of transmission of payment? Yes, because in 2003 laws are accepted in Ukraine: “About electronic documents and electronic circulation of documens”, “About electronic-digital signature”.

Although EDS saved practically all of basic properties of ordinary signature, all the same some features of realization of electronic autograph do its separate class of signatures. Therefore the legal, legal and methodological aspects of application of EDS must take into account its specific.

There are a few methods of construction of charts of EDS, namely:

1 Cipherement of electronic document (ED) on the basis of symmetric algorithms. This chart foresees a presence in the system of the third person (arbiter), enjoying the confidence of participants of exchange by the electronic documents signed in like manner. Co-operation of users this system is made on the following algorithm:

- participant A encrypts a message on the secret key k_А, knowledge of which parts with an arbiter, the after ciphered message is passed to the arbiter with pointing of addressee of this message (information, identifying an addressee, is passed also in an in cipher kind);

- an arbiter decrypts received a message on the key k_А, makes necessary verifications and then encrypts on the secret key a participant В (k_в). An in further cipher message is sent a participant B together with information, that it came from a participant A;

- participant B decrypts this message and makes sure in that a sender is a participant A.

In this chart a fact of encryption ED by the secret key and transmission ciphered ED to the arbiter will be considered by authorizing of document. Basic advantage of this chart is a presence of the third party, eliminating some vexed questions between the participants of informative exchange, i.e. the additional system of arbitration of EDS is not required in this case. The lack of chart is a presence of the third party and use of symmetric algorithms of cipherement.

2 Cipherement ED with the use of asymmetric algorithms of cipherement. The fact of signing of document in this chart is encrypting of document on the secret key of his sender. This chart is also utillized enough rarely because of that length ED can appear critical. Application of asymmetric algorithms for the cipherement of messages of large length uneffective from point of speed descriptions. The presence of the third party is not required in this case, although it can play the role of certification organ of the opened keys of users.

3 Development of previous idea was become by the most widespread chart of EDs, namely: cipherement of final result of treatment ED by a hash-function through an asymmetric algorithm. The structure chart of such variant of construction of EDS is presented on a fig. 2.

Picture 2- Structure chart of construction of EDS

The generation of signature takes a place as follows:

1 Participant A calculates a hash-code from ED. The got hash-code passes procedure of transformation with the use of the secret key, whereupon got value (which is EDS) together with ED lea with EDS and certificated opened key of participant A, and then to make decryption on its ECP, ED is exposed to the operation of randomizing, whereupon results are compared and, if they coincide, EDS is acknowledged true, otherwise - false.

Firmness of this type of EDS is based on firmness of asymmetric algorithms of cipherement and applied hash-functions.

Except for considered there are “exotic” variants of construction of charts of EDS (group signature, uncontested signature, trusted signature and others). Appearance of these varieties is conditioned the variety of tasks, decided by electronic technologies of transmission and treatment ED.

In general case signed ED looks as a pair, consisting of binary lines (M, S), where M is ED, and S is a decision of equalization E_k(S) = М, where E_k is a function with a secret.

In connection with foregoing determination of EDS, it is possible to select followings its properties:

- it is uncounterfeited, as to decide equalization E_k(S) = М can only possessor of secret k;

- simply identifies an author, i.e. man, signing this document;

- verification of signature is made on the basis of knowledge of function E_k;

- it is unbearable on other ED; an exception is made by a case, when for an in-use hash-function found out collisions;

ED with EDS can be passed on the opened channals, as ED will bring any change over to that procedure of verification of EDS will expose this fact.