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MODEL OF E-MAILING SYSTEM USING POLYNOMIALS OVER NONCUMMUTATIVE DIVISION SEMIRING

Deo Brat Ojha*1, Abhishek Shukla2 and Meenu Sahani3
  1. Department of Mathematics, R.K.G. Institute of Technology, Ghaziabad, U.P. INDIA -201003
  2. (Research Scholar Singhania Univ., Jhunjhunu, Rajsthan) College of Computer Application,R.K.G. I.T., Ghaziabad ,U.P. INDIA-201003
  3. Department of Mathematics, Bhagwati Institute of Technology & Science, Ghaziabad, U.P. INDIA-201002
Corresponding Author: Deo Brat Ojha, E-mail: [email protected]
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Abstract

In this paper we show a model of e-mailing system using polynomials over non-commutative Division semiring for internet communication. It is the model of a real-life secure mailing system. In this model, a sender can send a secret message even to a unacquainted person in an anonymous way. The users of this model are assumed to be may or may not be the members of a closed organization.

Keywords

Stegnography, Symmetric key, Semirings , Encryption / Decryption, Mailing System

INTRODUCTION

Human beings have long hoped to have a technique to communicate with a distant partner anonymously but later on distinctive and must be secure. We may be able to realize this hope by using stegnography. Modern steganography has a relatively short history because people did not pay much attention to this skill until Internet security became a social concern. Most people did not know what stegnography was because they did not have any means to know the meaning. Even today ordinary dictionaries do not contain the word “stegnography.” Books on stegnography are still very few [1], [2]. The most important feature of this stegnography is that it has a very large data hiding capacity [3], [4]. It normally embeds 50% or more of a container image file with information without increasing its size. Stegnography can be applied to variety of information systems. Some key is used in these systems when it embeds/extracts secret data. One natural application is a secret mailing system [7] that uses a symmetric key. Another application pays attention to the nature of stegnography whereby the external data (e.g., visible image data) and the internal data (any hidden information) cannot be separated by any means. We will term this nature as an “inseparability” of the two forms of data. For more details [5,6,8,9,10,11,12]. In the present paper we will show our basic model of emailing system using polynomials over non-commutative division semiring. The structure of the present paper is as follows. In Section 1.1, we will make a short discussion on the problem of an encrypted mailing system. Section 2.1 describes the scheme of the e-mailing system using polynomials over non-cummutative division semiring.

PROBLEMS OF AN ENCRYPTED MAILING SYSTEM

There are two types of cryptography scheme: Symmetric key schemes and asymmetric key schemes.
In a symmetric system a message sender and receiver use a same encryption/decryption key. In this scheme, however, the sender and the receiver must negotiate on what key they are going to use before they start communication. Such a negotiation must be absolutely secret. They usually use some second channel (e.g., fax or phone). However, the second channels may not be very secure. There is another problem in this situation in that if the sender is not acquainted with the receiver, it is difficult to start the key-negotiation in secret. Furthermore, the more secure the key system is, the more inconvenient the system usage is. An asymmetric system uses a public key and a private key system. The public key is open to the public, and it is used for message encoding when a sender is sending a message to the key owner.

MATERIAL AND METHODS

A Model of e-mailing system using polynomials over noncommutative division semirings
We do not intend to develop a new “message reader-andsender” or “message composer”, but we are developing three system components that make e-mailing system using polynomials over non-commutative division semirings (EPNCDS) A message sender inserts (actually, embeds) a secret message in an envelope using steganography and sends it as an e-mail attachment. The receiver receives the attached envelope and opens it to receive the message. An “envelope” in this system is actually an image file that is a container, vessel, cover, or dummy data in the terminology of steganography. This system can solve all the problems mentioned above.
The following items are the conditions we have set forth in designing the system. 1.The name of the message sender may or may not be anonymous, as depends upon their wish. 2.The message is hidden in the envelope and only the designated receiver can open it.
3.Sender can send a secret message even to an unaccustomed person. 4.It is easy to use for both sender and receiver.

BACKGROUND OF PUBLIC KEY INFRASTRUCTURE AND PROPOSALS BASED ON COMMUTATIVE RINGS

There is no doubt that the Internet is affecting every aspect of our lives; the most significant changes are occurring in private and public sector organizations that are transforming their conventional operating models to Internet based service models, known as eBusiness, eCommerce, and eGovernment. Public Key Infrastructure (PKI) is probably one of the most important items in the arsenal of security measures that can be brought to bear against the aforementioned growing risks and threats. The design of reliable Public Key Infrastructure presents a compendium challenging problems that have fascinated researchers in computer science, electrical engineering and mathematics alike for the past few decades and are sure to continue to do so.

BUILDING BLOCKS FOR PROPOSED SCHEME

INTEGRAL CO-EFFICIENT RING POLYNOMIALS:
image

SEMIRING

A semiring R is a non-empty set,on which the operations of Addition and multiplication have been defined such that the Following conditions are satisfied
(i) (R,+) is a commutative monoid with identity element “0”
(ii). (R,•) is a monoid with identity element 1.
(iii).Multiplication distributes over addition from either Side
(iv). 0• r = r • 0 for all r in R
Note:
1. A Semiring without zero divisors is called Entire semiring.
2. A Semiring R is Zerosumfree semiring if and only
image

DIVISION SEMIRING

An element r of a semiring R, is a “unit” if and only if there exists an element 1 r r1 of R satisfying
image
Note:
1. A commutative division semiring is called a semifield.
2. A Semiring R is Zerosumfree semiring if and only
image

POLYNOMIALS ON DIVISION SEMIRING

Let ( R, +, •) be a non-commutative division semiring. Let us consider positive integral co-efficient polynomials with semiring assignment as follows. At first, the notion of scale multiplication over R is already on hand. For 0 k Z> Î &
image

RESULTS AND DISCUSSION

PROPOSED SCHEME
Our scheme contains the following main steps.
Initial setup:
Suppose that (S, +, ) is the non commutative division semiring & is the underlying work fundamental infrastructure in which PSD is intractable on the noncommutative group
( S,  ). Choose two small integers m n Z.
image
Key Generation:
EPNCDSfirst wants to sign and send a message M
to sec EPNCDS ond for verification. First EPNCDSfirst selects two random elements p, qÎS and a random
image
image
image
Following the above mentioned notations, we describe the EPNCDS below. The protocol works in the following steps.
image
image
image

COMPONENT OF THE SYSTEM

EPNCDS is a steganography application .It makes use of the inseparability of the external and internal data. The system can be implemented differently according to different programmers or different specifications. Different EPNCDS’ are incompatible in operation with others.
An EPNCDS consists of the three following components.
1. Envelope Producer (EP)
2. Message Inserter (MI)
3. Envelope Opener (EO)
In this scheme we have two communicating parties first and second. We denote first’s EPNCDS as EPNCDSfirst So, it is described as EPNCDS , , first first first first = EP MI EO .
image
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References

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