In the contemporary world, the security of data and privacy policies are major concerns in cloud computing. Data stored on the cloud has been claimed to be unsafe and liable to be hacked. Users have found it difficult to trust their data in the cloud. Users want to know that their data is accessible from anywhere and that an unauthorized user will not be able to access it. Another area of concern is the authentication of users over the cloud. There are a number of security concerns with Cloud Computing which include Distributed Denial of Service, Data leakage, and many more, just to mention a few. In this paper, an Elliptic Curve Cryptography (ECC) algorithm is used for the encryption and decryption of the information stored on

            The widespread use of the Internet of things (IoT) in different aspects of an individual’s life like banking, wireless intelligent devices and smartphones has led to new security and performance challenges under restricted resources. The Elliptic Curve Digital Signature Algorithm (ECDSA) is the most suitable choice for the environments due to the smaller size of the encryption key and changeable security related parameters. However, major performance metrics such as area, power, latency and throughput are still customisable and based on the design requirements of the device.

The present paper puts forward an enhancement for the throughput performance metric by p

The Elliptic Curve Cryptography (ECC) algorithm meets the requirements for multimedia encryption since the encipher operation of the ECC algorithm is applied at points only and that offer significant computational advantages. The encoding/decoding operations for converting the text message into points on the curve and vice versa are not always considered a simple process. In this paper, a new mapping method has been investigated for converting the text message into a point on the curve or point to a text message in an efficient and secure manner; it depends on the repeated values in coordinate to establish a lookup table for encoding/ decoding operations. The proposed method for mapping process is&

Plane cubics curves may be classified up to isomorphism or projective equivalence. In this paper, the inequivalent elliptic cubic curves which are non-singular plane cubic curves have been classified projectively over the finite field of order nineteen, and determined if they are complete or incomplete as arcs of degree three. Also, the maximum size of a complete elliptic curve that can be constructed from each incomplete elliptic curve are given.

   The aim of this paper is to construct the (k,r)-caps in the projective 3-space PG(3,p) over Galois field GF(4). We found that the maximum complete (k,2)-cap which is called an                       ovaloid  , exists in PG(3,4) when k = 13. Moreover the maximum (k,3)-caps, (k,4)-caps and   (k,5)-caps. 

Let R be a ring with 1 and W is a left Module over R. A Submodule D of an R-Module W is small in W(D ≪ W) if whenever a Submodule V of W s.t W = D + V then V = W. A proper Submodule Y of an R-Module W is semismall in W(Y ≪_S W) if Y = 0 or Y/F ≪ W/F ∀ nonzero Submodules F of Y. A Submodule U of an R-Module E is essentially semismall(U ≪es E), if for every non zero semismall Submodule V of E, V∩U ≠ 0. An R-Module E is essentially semismall quasi-Dedekind(ESSQD) if Hom(E/W, E) = 0 ∀ W ≪es E. A ring R is ESSQD if R is an ESSQD R-Module. An R-Module E is a scalar R-Module if, ∀ , ∃ s.t V(e) = ze ∀ . In this paper, we study the relationship between ESSQD Modules with scalar and multiplication Modules. We show that

Let be a ring with 1 and D is a left module over . In this paper, we study the relationship between essentially small quasi-Dedekind modules with scalar and multiplication modules. We show that if D is a scalar small quasi-prime -module, thus D is an essentially small quasi-Dedekind -module. We also show that if D is a faithful multiplication -module, then D is an essentially small prime -module iff is an essentially small quasi-Dedekind ring.

  The purpose of this work is to study the classification and construction of (k,3)-arcs in the projective plane PG(2,7). We found that there are two (5,3)-arcs, four (6,3)-arcs, six (7,3)arcs, six (8,3)-arcs, seven (9,3)-arcs, six (10,3)-arcs and six (11,3)-arcs.         All of these arcs are incomplete.         The number of distinct (12,3)-arcs are six, two of them are complete.         There are four distinct (13,3)-arcs, two of them are complete and one (14,3)-arc which is incomplete.         There exists one complete (15,3)-arc.
 

  In this work, we construct and classify the projectively distinct (k,3)-arcs in PG(2,9), where k ≥ 5, and prove that the complete (k,3)-arcs do not exist, where 5 ≤ k ≤ 13. We found that the maximum complete (k,3)-arc in PG(2,q) is the (16,3)-arc and the minimum complete (k,3)-arc in PG(2,q) is the (14,3)-arc. Moreover, we found the complete (k,3)-arcs between them.

MDS code is a linear code that achieves equality in the Singleton bound, and projective MDS (PG-MDS) is MDS code with independents property of any two columns of its generator matrix.   In this paper, elementary methods for modifying a PG-MDS code of dimensions 2, 3, as extending and lengthening, in order to find new incomplete PG-MDS codes have been used over . Also, two complete PG-MDS codes over  of length  and 28 have been found.