Mohamad Rushdan Md. Said

Password Authentication Based on Fractal Coding Scheme

Password authentication is a mechanism used to authenticate user identity over insecure communication channel. In this paper, a new method to improve the security of password authentication is proposed. It is based on the compression capability of the fractal image coding to provide an authorized user a secure access to registration and login process. In the proposed scheme, a hashed password string is generated and encrypted to be captured together with the user identity using text to image mechanisms. The advantage of fractal image coding is to be used to securely send the compressed image data through a nonsecured communication channel to the server. The verification of client information with the database system is achieved in the server to authenticate the legal user. The encrypted hashed password in the decoded fractal image is recognized using optical character recognition. The authentication process is performed after a successful verification of the client identity by comparing the decrypted hashed password with those which was stored in the database system. The system is analyzed and discussed from the attacker’s viewpoint. A security comparison is performed to show that the proposed scheme provides an essential security requirement, while their efficiency makes it easier to be applied alone or in hybrid with other security methods. Computer simulation and statistical analysis are presented.

An even and odd situation for the multiplier of scalar multiplication with pseudo τ-adic non-adjacent form

An algorithm was developed for elliptic scalar multiplication (SM) on Koblitz curve where the multiplier of SM is in the form of Pseudo τ-adic Non-Adjacent Form (pseudoTNAF). This expansion is equivalent to τ-adic Non-Adjacent Form (TNAF) and Reduced τ-adic Non-Adjacent Form (RTNAF) that was produced by Solinas in the year 1997 and 2000 respectively. Some properties for the multiplier of SM was proposed in order to guess the secret message. For the same reason, the objective of this paper is to give five new properties for such multiplier.

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.

Improved digital signature protocol using iterated function systems

In this paper, a novel digital signature protocol is proposed. It is based on the iterated function system attractor, which is regarded as an emerging method. The idea behind our proposed method is based on selecting a known fractal set and then finding the attractor of the affine transformation functions. The attractor is then used in the encryption and decryption of a hash function to ensure the protection of the document from eavesdropping and integrity during the transmission. The properties and software implementation of the proposed protocol are discussed in detail. A comparison is made with the Rivest, Shamir, and Adleman cryptosystems, which shows that it performs better.

An efficient computation technique for Cryptosystems based on Lucas Functions

Lucas Functions is a special form of second order linear recurrence relation. This function has been used in the LUC Cryptosystems. The encryption process of this system is the computations of V(e), while the decryption process is done by the computations of V(d). The V(e) and V(d) are both Lucas Function. The performances of computations of LUC are influence by the size of e and d. It is also depends on the size of message, M and two primes p and q. In the case of e, d, M, p and q are in a large number, we are sure that the existing algorithm would suffers a huge computations time and spaces. In this paper, we are presenting a new and efficient computations algorithm for LUC Cryptosystems. We have found that the binary sequence used in a new algorithm is shorter than a special sequence used in an existing algorithm. Once we get a generated binary sequence, we shall use this sequence to perform the LUC computations. We are examining the efficiency of this new algorithm by comparing the computation time with an existing algorithm.

Chaotic Pseudorandom Sequences and the Security of Cryptosystems

The generation of pseudo-random numbers (bits) plays a critical role in a large number of applications such as statistical mechanics, numerical simulations, gaming industry, communication or cryptography. The choice of secret keys for cryptographic primitives largely depends on the quality of random numbers used. These random numbers are fundamental tools in the generation of secret keys and initialization variables of encryption for cryptographic application, masking protocols, or for internet gambling. Chaotic Pseudorandom numbers were found to be very efficient in this aspect. The relevance of chaotic pseudorandom sequences in ensuring security in cryptosystems is considered, at the same time reviewing statistical tests required to make such sequences cryptographically secure. This paper intends to review the development of chaotic pseudorandom number generators through the years and the statistical tests they are required to pass as a measure of their randomness.

A New Direction in Utilization of Chaotic Fractal Functions for Cryptosystems

Ever since Baptista in 1998 introduced his cryptographic scheme utilizing the only in online version. ergodic property of chaotic maps which is able to produce different cipher values for the same plaintext within the same message, intense scrutiny has been given upon the design. The capability to do the above mentioned output is akin to the Vigenere cipher and thus has the capacity to render an attacker with infinitely many choices (theoretically speaking) or in cryptographic terms would render an attacker to have a set off possible ciphertexts that could all have the possibility to just be mapped to a unique plaintext. This makes it computationally infeasible for the attacker to re-construct the correct plaintext. The Baptista design has been attacked and repaired many times. Alvarez noticed the characteristic of the cryptosystem that generates a sequence which can be exploited by an attacker. The attack which is dubbed the one-time pad attack is akin to an attack upon a One-Time-Pad (OTP) cryptosystem that reuses its key. Since then, attempts were made to redefine the cryptosystem such that it would be resistant towards the attack. Most of the attempts failed due to either the repaired cryptosystem still generates an exploitable sequence or it is not invertible. In this work we pair the Baptista design with a concept taken from the Iterated Function Systems (IFS). Although we did not encompass the whole concept of iterating the IFS, it could be seen that this could be easily done with the same desirable results. Four main outcomes are discussed. Beginning with the discussion on the infeasibility of Alvarez’s one-time pad attack on the design, we then discuss the quantitative properties of the design in discussing its cryptographic properties namely the Maximum Deviation Factor (MDF), Correlation Coefficient Factor (CCF) and the Strict Avalanche Criterion (SAC). Each experimental result shows promising results for this new design.

An improvement of LUC 2 cryptosystem algorithm using Doubling with Remainder

The major factor that influences the performance of the LUC public-key cryptosystem is the computation of Ve and Vd, a public and private key, respectively. Its involve a huge steps of computations for large values of e and d. We concentrated our discussion on how to utilize and manipulate the doubling step technique for an efficient LUC2 computation. Therefore, we proposed the so-called doubling with remainder technique. It shows a better performance in LUC2 computations and also a great reductions of time consume for computations. The experimental results for sequential, doubling steps and doubling with remainder are also included.

Synchronization between two discrete chaotic systems for secure communications

In this article, we have investigated synchronization phenomenon between two discrete chaotic systems. A general scheme for synchronization between two discrete maps with adaptive coupling has been studied analytically. The scheme can be successfully implemented for generalized synchronization between two chaotic maps. Conditional Lyapunov exponents (CLE) and Transverse Lyapunov exponents (TLE) can quantifies the robustness of synchronization. A secure communication scheme based on synchronization between two Logistic maps is also demonstrated. Numerical results show the effectiveness of our proposed scheme.

An explicit estimation of p-adic sizes of common zeros of partial derivative polynomials associated with a complete quartic form

In this paper we obtain an estimation of p-adic sizes of common zeros of partial derivative polynomials associated with a complete quartic polynomial by applying the Newton polyhedron technique. Such estimates are obtained by examining indicator diagrams associated with the Newton polyhedra of partial derivatives polynomials considered and applying new conditions to improve the results of earlier researchers.