Hailiza Kamarulhaili

Data organization for broadcasting in mobile computing

The rapidly expanding technology of cellular communications, wireless LAN (local area network), wireless data networks and satellite will give mobile users capability of accessing information anywhere and anytime. One of the important components of this environment is the server with broadcasting capabilities. Data are fetched from the server and being broadcast to the air. Mobile users keep listening within the air and catch those data that interest him. In one of the work known as the Acharya algorithm (Acharya et al., 1995) has focused on developing algorithm for arranging the sequence order of data to be broadcasted. The work has generated the sequence of data to be broadcast with the policy of broadcasting more popular data compare to the less popular one. However, the work does not covers the overhead issue incurred by the disk during actual data retrieval task in order to satisfy the broadcasting order. In this paper, we present a data organization called sequence to be used as a data storing method in the server to support broadcasting environments. Our scheme, the sequence order of data to be stored on physical disk, is basically similar in pattern to the sequence order of data to be broadcasted. Having this approach the servers disk incurs less overhead (seek and latency). We show by simulation result that our scheme has reduced the overhead of Acharya scheme by average 60%. We also work on multiple disks with the same speed and configuration as opposed by the Acharya scheme, which used different disk speed and configuration.

Digital video watermarking based on 3D-discrete wavelet transform domain

One of the significant problems in video watermarking is the Geometric attacks. The DWT (discrete wavelet transform) domain is used for proposed a novel algorithm to place invisible watermark in a video frame based on a three-level DWT using Haar filter. The proposed algorithm is robust against JPEG compression, geometric attacks such as Downscaling, Cropping, and Rotation. It is also robust against Image processing attacks such as low pass filtering (LPF), Median filtering, and Weiner filtering. Furthermore, the algorithm is robust against Noise attacks such as Gaussian noise, Salt and Pepper attacks. The embedded data rate is high and robust. The experimental results show that the embedded watermark is robust and invisible. The watermark was successfully extracted from the video after various attacks.

Data storage and retrieval for video-on-demand servers

Video on demand (VOD) is a system that provides a service to users to browse and watch videos within a computer network. One of the most challenging aspects in such system is to have a VOD server with a capability of retrieving and transmitting different blocks of videos simultaneously. A part from this the VOD server should also capable of producing high number of simultaneous streams with a low average waiting time. In this paper we present a new data storage scheme employed by the VOD server to eliminate latency and hence producing maximum number of simultaneous streams. In this scheme the disk is divided into regions and blocks of video are scattered within the regions based on the residual theory rule. We also developed a stream caching technique for reducing the average waiting time of the system.

On the distribution of scalar k for elliptic scalar multiplication

In this study, we introduce the probability distribution of the elliptic curve scalar multiplication through finding the probability distribution of the secret key, namely, the scalar k of the scalar multiplication kP of a point P which has a large prime order n lying on elliptic curve group E(Fp) over a finite prime field Fp. To determine this distribution of k, we use the integer sub-decomposition (ISD) approach that inspired from Gallant, Lambert and Vanstone (GLV) idea. In ISD approach, the distribution of the values of scalars k lie outside the range ±n on the interval [1, n − 1]. This distribution determines the successful rate to compute a scalar multiplication kP, on ISD approach, in comparison with the original GLV method. The conception of the ISD approach depends on the sub- decomposition of the scalar k to compute the scalar multiplication kP which uses efficiently computable endomorphisms Ψ1 and Ψ2 of elliptic curve E over Fp. The ISD sub-decomposition can be defined by kP=k11P+k12ψ1(P)+k21P+...

The computational complexity of elliptic curve integer sub-decomposition (ISD) method

The idea of the GLV method of Gallant, Lambert and Vanstone (Crypto 2001) is considered a foundation stone to build a new procedure to compute the elliptic curve scalar multiplication. This procedure, that is integer sub-decomposition (ISD), will compute any multiple kP of elliptic curve point P which has a large prime order n with two low-degrees endomorphisms ψ1 and ψ2 of elliptic curve E over prime field Fp. The sub-decomposition of values k1 and k2, not bounded by ±Cn, gives us new integers k11, k12, k21 and k22 which are bounded by ±Cn and can be computed through solving the closest vector problem in lattice. The percentage of a successful computation for the scalar multiplication increases by ISD method, which improved the computational efficiency in comparison with the general method for computing scalar multiplication in elliptic curves over the prime fields. This paper will present the mechanism of ISD method and will shed light mainly on the computation complexity of the ISD approach that will b...

Application of message embedding technique in ElGamal Elliptic Curve Cryptosystem

The use of elliptic curve for public key cryptosystem has been developed almost twenty years ago. The strength of the elliptic curve cryptosystem relies on the elliptic curve discrete logarithm problem (ECDLP). In this paper, a method of embedding plaintexts to points on the elliptic curve is proposed. The method deploys elliptic curve based on encryption and decryption processes by using the two protocols, the ElGamal Elliptic Curve Cryptosystem. Maple 10 is used to determine and compute points on the elliptic curves as well as to compute the addition and scalar multiplication operations using the proposed method.

Elliptic Curve Cryptography and Point Counting Algorithms

Elliptic curves cryptography was introduced independently by Victor Miller (Miller, 1986) and Neal Koblitz (Koblitz, 1987) in 1985. At that time elliptic curve cryptography was not actually seen as a promising cryptographic technique. As time progress and further research and intensive development done especially on the implementation side, elliptic curve cryptography is now being implemented widely. Elliptic curves cryptography offers smaller key size, bandwidth savings and faster in implementations when compared to the RSA (Rivest-Shamir-Adleman) cryptography which based its security on the integer factorization problem. The most interesting feature of the elliptic curves is the group structure of the points generated by the curves, where points on the elliptic curves form a group. The security of elliptic curves cryptography relies on the elliptic curves discrete logarithm problem. The elliptic curve discrete logarithm problem is analogous to the ordinary algebraic discrete logarithm problem, l = gx, where given the l and g, it is infeasible to compute the x. Elliptic curve discrete logarithm problem deals with solving for n the relation P = nG. Given the point P and the point G, then it is very hard to find the integer n. To implement the discrete logarithm problem in elliptic curve cryptography, the main task is to compute the order of group of the curves or in other words the number of points on the curve. Computation to find the number of points on a curve, has given rise to several point counting algorithms. The Schoof and the SEA (Schoof-Elkies-Atkin) point counting algorithms will be part of the discussion in this chapter. This chapter is organized as follows: Section 2, gives some preliminaries on elliptic curves, and in section 3, elliptic curve discrete logarithm problem is discussed. Some relevant issues on elliptic curve cryptography is discussed in section 4, in which the Diffie-Hellman key exchange scheme, ElGamal elliptic curve cryptosystem and elliptic curve digital signature scheme are discussed here accompanied with some examples. Section 5 discussed the two point counting algorithms, Schoof algorithm and the SEA (Schoof-Elkies-Atkin) algorithm. Following the discussion in section 5, section 6 summaries some similarities and the differences between these two algorithms. Section 7 gives some brief literature on these two point counting algorithms. Finally, section 8 is the concluding remarks for this chapter.

Quadrant interlocking factorization of hourglass matrix

This paper presents hourglass matrix, a dense square matrix which is obtained from Quadrant Interlocking Factorization (QIF) of nonsingular matrix. We discuss the condition to generate its nonzero entries and formulate its total number of zero and nonzero entries. Furthermore, the determinant of even and odd order of the matrix as well as the eigenvalue of the odd order of the matrix are examined. In all, we give some deductions to differentiate between hourglass matrix and classical Z-matrix.

On Determinant of Laplacian Matrix and Signless Laplacian Matrix of a Simple Graph

In a simple graph, Laplacian matrix and signless Laplacian matrix are derived from both adjacency matrix and degree matrix. Although, determinant of Laplacian matrix is always zero, yet we express it using only the adjacency matrix and square of its adjacency matrix. Likewise, we express the determinant of signless Laplacian matrix using only the diagonal elements provided the signless Laplacian matrix is equal to the square of its adjacency matrix.

Mathematical analysis of the computational complexity of integer sub-decomposition algorithm

In this paper, the computational complexity to compute a scalar multiplication on classes of elliptic curve over a prime field that have efficiently-computable endomorphismsis analyzed mathematically. This scalar multiplication is called integer sub-decomposition (ISD) method, which is based on the GLV method of Gallant, Lambert and Vanstone that was initially proposed in the year 2001. In this work, the mathematical proof of the computational cost of ISD implementation is presented. The computational cost of ISD algorithm has been proven based on the operations counting. Two types of the operations are used, namely, elliptic curve operations represented by elliptic curve point addition A and elliptic curve point doubling D and finite field operations represented by field inversion I, field multiplication M and field squaring S that design the computation of the running time of ISD scalar multiplication.