Nadia M. G. Al-Saidi

Towards enhancing of fractal image compression performance via block complexity

Fractal image coding technique is considered as very effective for a higher compression ratio. Despite this method had received much attention because of its high resolution and fast decoding and many other advantages, but it has not been used widely because it requires high computation time for the encoding process. This defect is considered as one of the drawbacks of fractal image coding technique. However, many solutions have been proposed to facilitate the encoding time and optimize the computational time and resolution. In this paper, we proposed a new technique based on a fractal dimension that represents image complexity to be used as an index for the domain blocks in order to facilitate the searching process for each range block. In comparing to the original technique, the experiment shows that the encoding time is improved with a percentage of 30%, and the compromise between image quality and image compression is achieved.

Perfect secret sharing scheme based on vertex domination set

Due to the fast development in data communication systems and computer networks in recent years, the necessity to protect the secret data has become extremely imperative. Several methods have been proposed to protect the secret data; one of them is the secret sharing scheme. It is a method of distributing a secret K among a finite set of participants, in such a way that only predefined subset of participant is enabled to reconstruct a secret from their shares. A secret sharing scheme realizing uniform access structure described by a graph has received a considerable attention. In this scheme, each vertex represents a participant and each edge represents a minimum authorized subset. In this paper, an independent dominating set of vertices in a graph G is introduced and applied as a novel idea to construct a secret sharing scheme such that the vertices of the graph represent the participants and the dominating set of vertices in G represents the minimal authorized set. While most of the previous schemes were based on the principle of adjacent vertices, the proposed scheme is based upon the principle of non-adjacent vertices. We prove that the scheme is perfect, and the lower bound of the information rate of this new construction is improved when compared to some well-known previous constructions. We include an experiment involving security threats to demonstrate the effectiveness of the proposed scheme.

A comparative performance analysis of NTRU and its variant cryptosystems

With the fast developing of computer hardware, many problems which are previously considered hard, will be solved practically. Number of theoretical problems that form the core of many public key cryptosystems are such of them. Therefore, new cryptosystems which are designed based on other mathematical techniques are of great demands. NTRU which is based on the hardness of lattice problems is one of such cryptosystems. In previous works, we designed three cryptosystems alternatives to NTRU, called HXDTRU, PQTRU, and BITRU they are based on high dimensional algebra. We proved that, they performed better than NTRU. For practical use, a comparative performance between the aforementioned cryptosystems and NTRUforms the core of this work.

An interactive proof via some generalized reduced rings

Algebra is one of the important fields of mathematics. It concerns in the study and manipulates of mathematical symbols. It also concerns with study of abstractions such as groups, rings and fields. Ring theory is the most attractive category of algebra in the area of cryptography. Recently, many algebraic cryptosystem protocols based on non-commutative algebraic structures such as; authentication, key exchange, and encryption-decryption processes are adopted. In this paper, we employ the algebraic structure called nil Armendariz (NA) rings to design a neoteric algorithm for zero knowledge proof. The proposed protocol is implemented and illustrated through numerical example, and its soundness and completeness are proved.

BITRU: Binary Version of the NTRU Public Key Cryptosystem via Binary Algebra

New terms such as closest vector problem (CVP) and the shortest vector problem (SVP), which have been illustrated as NP-hard problem, emerged, leading to a new hope for designing public key cryptosystem based on certain lattice hardness. A new cryptosystem called NTRU is proven computationally efficient and it can be implemented with low cost. With these characteristics, NTRU possesses advantage over others system that rely on number-theoretical problem in a finite field (e.g. integer factorization problem or discrete logarithm problem). These advantages make NTRU a good choice for many applications. After the adaptation of NTRU, many attempts to generalize its algebraic structure have appeared. In this study, a new variant of the NTRU public key cryptosystem called BITRU is proposed. BITRU is based on a new algebraic structure used as an alternative to NTRU-mathematical structure called binary algebra. This commutative and associative. Establishing two public keys in the proposed system has distinguished it from NTRU and those similar to NTRU cryptosystems. This new structure helps to increase the security and complexity of BITRU. The clauses of BITRU, which include key generation, encryption, decryption, and decryption failure, are explained in details. Its suitability of the proposed system is proven and its security is demonstrated by comparing it with NTRU.

Crowding Optimization Method to Improve Fractal Image Compressions Based Iterated Function

Fractals are geometric patterns generated by Iterated Function System theory. A popular technique known as fractal image compression is based on this theory, which assumes that redundancy in an image can be exploited by block-wise self-similarity and that the original image can be approximated by a finite iteration of fractal codes. This technique offers high compression ratio among other image compression techniques. However, it presents several drawbacks, such as the inverse proportionality between image quality and computational cost. Numerous approaches have been proposed to find a compromise between quality and cost. As an efficient optimization approach, genetic algorithm is used for this purpose. In this paper, a crowding method, an improved genetic algorithm, is used to optimize the search space in the target image by good approximation to the global optimum in a single run. The experimental results for the proposed method show good efficiency by decreasing the encoding time while retaining a high quality image compared with the classical method of fractal image compression.