Novel Access Control Mechanism Based New Chinese Remainder Theorem II (New Crt II)

Security is a very vital concern in information system in this modern day. The protection of confidential files and integrity of information kept in the database are also of great important, the security model play an important role in protecting the privacy and integrity of messages in the database from unlawful users is a formal method to verify and describe intricate information system. An access Control mechanism is a main strategy for prevention and protection of the classified files in a database; this is carried out by restricting rights of access for different approved users of these files. This paper proposes a novel access control mechanism based on Chinese remainder theorem II which implements a single-key-lock system to encrypt one key called a secret key which is used for both encryption and decryption in the electronic information system for accessing the database. The key to be used in the decryption process must be exchanged between the entities in communication using symmetric encryption for the users to have access to the database. This method represents flocks and keys which is highly efficient and proficient. Also, this implementation can be achieved using the Chinese remainder theorem which executes faster operations and enables simpler construction of keys and locks to be provide for user to have access to control.


Introduction
Data can be allocated to different users in the database in a time sharing system at a different time. Thus, the major unease task is to maintain the content of the file in the database by the database system chic [1][2][3]. Information stored in the database need to be protected from being damage, change or distorted without been notice by the database chic. The system supervisor needs to guarantee each user of the database, the use of the database resources in conformity with the policies of the system administrators. Information newly generated can be distributed across an extensive network for many users in the database environment; the safety of independent data becomes a heightened concern [4]. Cloud computing allows data sharing amid distinctive users of the database, which can be achieved with various degree of receptive means. As a result, controlling access system and stout isolation would be required.
Information fortification can be accomplished by means of an access control method. Once demand is made to access a file, it is interrupted by the control system to check for the validation before access can be given to the user [5]. The emergence of multimedia knowledge and distributed systems, has introduced the sharing of digital information across distinct users in unambiguous system or institution. These include video duplicates or digital audio, personnel data, commercial specifications, and digital books, which is stored in a universal database. Digital files are tremendously useful and must be confidentially reserved; to safeguard the content of the files from illegal access is a focus of eminent attention in the discipline of information security. The security of files during information accessing, is determined by an access control system employed to permit or hinder the access rights of distinct authorized users, i.e., to determine the degree of access distinct users have to the classified digital files. Therefore, the intrinsic purpose of the access control system is to avoid an unapproved users from viewing modifying and damaging the digital files [6].
Therefore, an access control mechanism is a technology to secure the privileged files stored in a database by limiting the access rights of distinct authorized users of the files. [6].
An access control method is an assembly of components and methods that decide the order of admission by rightful users to activities determined by predefined access authorization and privileges defined in the access security strategy [7]. The elementary objective of this access control method is to regulate the user privileges and secure information from illegitimate access [8].
The residue number system (RNS) is a number system for representing integers which is capable of supporting parallel, high-speed arithmetic. This system also presents some valuable properties for error detection, error correction, and fault tolerance. It has several applications in computationintensive digital signal processing (DSP) operations, like Fast Fourier Transform,, Discrete Fourier Transform, direct digital frequency synthesis, digital filtering, convolution, correlation etc [9].
Addition, subtraction, and multiplication, are arithmetic operations that can be performed independently and parallel in various residue channels more effectively than in the conventional binary systems. The adoption of RNS has offered notably effective improvements for distinct types of DSP applications [10].

Data Conversion
The forward conversion can be express as the execution of a forward converter which decomposes a weighted binary number into a residue represented number with regards to a moduli set, this implies the conversion from a conventional representation to a residue one by dividing the number X by each of the identified moduli and then collect their remainder [11]. For instance, given moduli set {3, 4, 5}, the number 4 can be represented in RNS as: Thus, the RNS representation of 4 is(1, 0, 4) ( , , ) . The basic technique in converting binary to RNS was presented by [11,12].
New CRTII: To determine the correct decimal representation of the RNS number X with residue representation ( , , … ) with respect to { , , , , }is The difference between CRT II and the CRT is noticeable. CRT II does not have big modulo operations as compare to CRT, New CRTII is bounded by size √$ [13].
Illustration: Given that { , , , , }are set of relatively co-prime . The decimal equivalent of residue representation of { , , , } of an integer X is given as such that Given the set of 4moduli set of Demonstrating example:

Proposed Scheme
Given a moduli set { , , , -, its equivalent weighted number X can be transformed from the residue representation ( , , , )by the definition of Divide and Conquer Techniques we have as follows: Such that And also, | | " = 1 Theorem 1:    We begin by explaining the component of the outcome from the New CRT II method, which is based on A, B and C. As it can be seen from equation 13 A, B and C are generated by Carry Save Adders (CSAs) with end around carries (EACs) taking the values 1 2 3 , , x x x and 4 x . These values must be added modulo 2 1 2 1 n+ − in order to derive A, i.e., with a one's complement adder, namely a Carry Propagate Adder (CPA) with EAC. Bits easily derived by concatenating the operand x with the n-bit left shift of A. This concatenation does not require any additional hardware. The operands B required 2n bit which concatenation of which does not required any additional hardware also. And finally, C required 2n-1 bits moduli adder and also concatenation last three and four moduli of the set.
Residue are obtained by nominally dividing X by i m , the residue 3 x is the easiest to compute. The 2n least significant bits constitute the remainder when X is divided by the least significant 2n bits of X. these bits are obtained by nominally shifting to the right by 2n bits.

An Application of New Chinese Remainder Theorem II to Access Control Method
The information protection system is employed to secure the access right of the information saved in the computer [14].  Table 1, above shows an access control with four user and files, where 8 and 9 are denoted as user i and j, for users and files respectively. First, the system assigns four relatively prime locks : = 10, : = 17, : = 21 ;<= : = 15 to the files 9 , 9 , 9 ;<= 9 respectively. These lock to control by the access rights for each file. Then, the system computes four keys by using forward conversion ? , ? , ? ;<= ? by New CRT II for the four users8 , 8 , 8 ;<= 8 , respectively.

Performance Analysis
This segment considers some issues about the proposed access control methods, as well asthe computational complexity related with the construction of the keys and the storage requirement for the keys and locks. The implementation of the proposed mechanism is based on below equation.
and the hardware complexity are n-bit 1's complement operation and n-bit multiplication and n-bit 1's complement operation. The proposed scheme required 0(logn) for the time complexity and five n-bit for the hardware (area) complexity. GCRT 0(< A ) 0(m+n) [6] mechanism GART 0(nA ) 0(m+n) Our proposed mechanism CRT11 0(logn) 0(logm+n) So, 0(log m + n) form keys and n locks thus avoiding the overflow problem.

Conclusion
The efficient access control method proposed is predicated on the concept of the single key lock method, based on forward conversion and Chinese remainder theorem II (CRTII) for both key and lock respectively. The proposed method utilized an effective technique to produce keys for users. First, choosing n pairwise co-prime integers : @ for 1 ≤ j ≤ n as the keys of the n files and determing the access right ; @ of distinct user 8 to each digital file 9 @ in the invisible access control matrix. The key ? for distinct user 8 can be generated easily by the locks, : , : , … . . : , 8 's rights CRTII. We examined the time complexity of the CRTII and determined that the method are more efficient than [1].