Eddie Shahril Ismail

The multistage variational iteration method for a class of nonlinear system of ODEs

This paper implements the multistage variational iteration method (MVIM) to solve a class of nonlinear system of first-order ordinary differential equations (ODEs). The domain of validity of the solutions via the standard variational iteration method (VIM) is extended by the simple multistage strategy. Comparisons with the exact solution and the fourth-order Runge–Kutta (RK4) method show that the MVIM is a reliable method for nonlinear equations.

Secure Key Authentication Scheme Based on Discrete Logarithm and Factoring Problems

Protecting public key from being forged or misused by enemies is very important in public key cryptosystems. Thus, key authentication process must be done to ensure that no intrusion occurred. Most researchers develop the key authentication scheme based on a single problem such as factoring, discrete logarithm, elliptic curve discrete logarithm or knapsack. Although some of these systems look secure, but due to technological advancement nowadays, it is possible that intruders can solve the single problem easily. Hence, in this paper we develop a key authentication scheme based on multiple problems; discrete logarithm and factoring problems. This research proposes a scheme with two phases; user registration phase and key authentication phase. The efficiency performance of this scheme requires \(1442T_{\text{mul}} + T_{h} + T_{\text{qrt}}\) for user registration phase and \(481T_{\text{mul}}\) for key authentication phase. Security of the scheme was proven mathematically in the security analysis and it is more secure compared to the scheme that is based on a single problem. This scheme is developed as an alternative to existing key authentication schemes and can contribute towards the development of the cryptography system based on multiple problems.

A New Threshold-Authenticated Encryption Scheme

An authenticated encryption scheme is a message recovery scheme that provides the authenticity property. In an authenticated encryption scheme, the recipients not only verify the message authentication, but they also could recover the message. In this paper, we propose a new authenticated encryption scheme based on two hard number theoretical problems: factoring and discrete logarithm. In our new scheme, t out of n signers/senders are required to sign and at the same time encrypt a message, while k out of l recipients cooperate to verify and recover the original message. We also show that our scheme is secure against some cryptographic attacks and requires reasonable number of operations in both signature/encryption and verification/decryption phases.

Threshold cryptosystem based on factoring and discrete logarithm problems

Recently, the development of cryptosystem based on two problems has increased, since it is proved that the cryptosystem based on two problems is more secure than the cryptosystem based on single problem. Meanwhile, the concept of group-oriented cryptography, known as threshold cryptography, gave a new dimension in development of cryptosystems. In this paper we propose a new threshold cryptosystem based on two number theoretical problems; factoring and discrete logarithms. Other than the scheme, we also show that our cryptosystem is secure against some possible attack and requires reasonable time in encryption and decryption phases.