Algorithm Of The Electronic Digital Subscript On The Basis Of The Composition Of Computing Complexities

In article the new algorithm of a digital signature in composition of the existing difficulties is developed: discrete logarithming in a final field, decomposition of rather large natural number on simple multipliers, additions of points with rational coordinates of an elliptic curve. On the basis of a combination of difficulties of discrete logarithming on a final field with the characteristic of large number, decomposition of rather large odd number on simple multipliers and additions of points of an elliptic curve develops algorithm of a digital signature for formation. The conventional scheme (model) of a digital signature covers three processes: generation of keys of EDS; formation of EDS; check (authenticity confirmation) of EDS. The idea of a design of the offered algorithm allows modifying and increasing crypto stability with addition to other computing difficulties. It is intended for use in systems of information processing of different function during forming and confirmation of authenticity of digital signature.

The American Journal of Engineering and Technology (ISSN -2689-0984

INTRODUCTION
The electronic digital subscript in the electronic document, received because of special transformations of the information of the given electronic document with usage. Of the closed key of an electronic digital subscript and allowing by means of an open key of an electronic digital subscript establishes the lack of distortion of the information in the electronic document and identifies the owner of the closed key of an electronic digital subscript.
Existing algorithms of an electronic digital subscript is developed based on one of computing complexity: expansions on prime factors, a discrete taking the logarithm, and addition of points of an elliptic curve and [1][2][3][4][5].

PROBLEM STATEMENT
In this article on the basis of a combination of complexities of the discrete logarithm on the final field with the great number, expansions of enough big odd number on prime factors and additions of points of an elliptic curve develops Algorithm of the Electronic Digital Subscript (АEDS) for shaping and acknowledgement of authenticity of an electronic digital subscript (EDS) under the set message (the electronic document), transmitted on not protected telecommunication channels of the general use [8-9]. The conventional scheme (model) of an electronic digital subscript envelops three processes [6-7]:  Generation of keys of EDS;  Shaping EDS;  Check (authenticity acknowledgement) EDS. The basic mathematical definitions and the requirements superimposed on plants of algorithm of a digital subscript are given below.

SOLUTION OF STATEMENT OF A PROBLEM
For a subscript of message M, the signing by generating keys: e-opened and d-confidential of comparison de1  mod (n) where the great number suffices n=p1q1, p1q1 -unknown prime numbers (satisfying to conditions p1>2512, q1>2512), (n) -Euler's function, for accuracy p1>q1, let gets out a random number k and x, and 1kq, q -a prime number and qq1, 1<x<q and NOD (x, n)=1, the parameter g<n gets out on condition NOD(q, n)=1 and g q modn ≠ 1, and also q is not a divider (n). The prime number q is opened and can be the general for group of users.
Processes of shaping of an electronic digital subscript under the message of the user and authenticity acknowledgement.
For realization of the given processes, it is necessary, that to all users parameters of algorithm of an electronic digital subscript were known. Besides, each user to have closed key of EDS (d, x) and open key of EDS (e, y, Q).
For creation of an electronic digital subscript under the M message, it is necessary to fulfil following operations (pitches).

ALGORITHM SUBSCRIPT GENERATION
Input data: message M, initial parameters, confidential and discovery keys.

CORRECTNESS OF АEDS
For the correctness proof it is necessary to show to justice equality: Really, from expression We discover: Then: 2 1  .
On the other hand: Thus, the algorithm correctness is proved.

THE ANALYSIS OF OUTCOMES
Crypto stability existing АEDS it is based on one of having computing complexities. In offered AEDS, its cryptographic firmness is based on several complexities: evaluations of a discrete taking the logarithm in a final field, solutions of a problem of expansion of enough big odd number to prime factors, realizations of addition operation of points of the elliptic curve set in a final field. It considerably raises crypto stabilities.

CONCLUSION
The idea of a design of offered algorithm allows modifying and raising crypto stabilities with adding of other computing complexities. It is intended for use in data reduction systems of different function at shaping and acknowledgement of authenticity of an electronic digital subscript.