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~ This paper proposes extensions for the RSA cryptosystem and digital SignaNre schemes to the domain of Gaussian integers. The required arithmetic and the use of it in the proposed extensions are illustrated. Also, numerical examples are given. The proposed extensions have many advantages over the classical RSA cryptosystem and digital signature.

In this study, a new array pattern synthesis approach using a genetic algorithm (GA) is proposed. The proposed approach has a unique set of objectives to be achieved by exploiting the GA optimisation capabilities. These objectives are: (i) steering the pattern main lobe in the direction of the signal of interest, (ii) minimising the side lobes level, (iii) steering pattern nulls in the directions of jammers and interferers, (iv) forcing the pattern nulls to have prespecified values in order to insure sufficient elimination of jammers and interferers and (v) the whole pattern synthesis will be done by changing the amplitudes and phases of the array elements' complex weights without any physical changes in the array; thus the method will be suitable for adaptive processing applications in which the array pattern will be dynamically adapted to the environments. Numerical examples will be used to demonstrate the effectiveness of the proposed array pattern synthesis approach using a uniform linear array of isotropic elements. Finally, the effect of changing the array number of elements and the weighting factor will be investigated using numerical examples.

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This paper presents a proposed algorithm for power control in CDMA system that is based on the powerful optimization technique known as Particle Swarm Optimization (PSO). The algorithm finds a suitable power vector, i.e. the power levels that are determined in the base station and told to the mobile units so that if the mobile units adjust their transmitting levels to these power levels, they will fulfill the objectives of the power control problem. The proposed algorithm is based on a similar idea to the one presented in [1] and called 'Genetic Algorithm for Mobiles Equilibrium' (GAME). So, a detailed discussion of GAME is given then the proposed algorithm is presented. The application of the algorithm to the problem is investigated via testing the algorithm on a hypothetical CDMA network model. To illustrate its effectiveness, the proposed algorithm is then compared to the application of Genetic Algorithms (GA) to the same problem. Finally, a detailed example is studied considering a cell of 20 users that are allowed to update their positions and fading conditions.

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Signcryption is a cryptographic primitive which simultaneously provides both confidentiality and authenticity in a single logical step. In a proxy signature scheme, an original signer delegates his signing power to a proxy agent, who signs a message on behalf of him. This paper introduces a new proxy signcryption scheme based on the Discrete Logarithm Problem (DLP) with a reduced computational complexity compared to other schemes in literature. In this proposed scheme, the receiver is the only one who can verify the origin of the ciphertext. Moreover, in this scheme, an authorized proxy signcrypter can create valid proxy signatures after verifying the identity of the original signcrypter. The proposed scheme achieves the various desirable security requirements. An elliptic curve based version of the proposed proxy signcryption scheme has been implemented using Mathematica for realistic (256-bit) parameters to emphasize the ease of its practical use.