Improved Software Implementation for Montgomery Elliptic Curve Cryptosystem

The last decade witnessed rapid increase in multimedia and other applications that require transmitting and protecting huge amount of data streams simultaneously.For such applications,a high-performance cryptosystem is compulsory to provide necessary security services.Elliptic curve cryptosystem(ECC)has been introduced as a considerable option.However,the usual sequential implementation of ECC and the standard elliptic curve(EC)form cannot achieve required performance level.Moreover,the widely used Hardware implementation of ECC is costly option and may be not affordable.This research aims to develop a high-performance parallel software implementation for ECC.To achieve this,many experiments were performed to examine several factors affecting ECC performance including the projective coordinates,the scalar multiplication algorithm,the elliptic curve(EC)form,and the parallel implementation.The ECC performance was analyzed using the different factors to tune-up them and select the best choices to increase the speed of the cryptosystem.Experimental results illustrated that parallel Montgomery ECC implementation using homogenous projection achieves the highest performance level,since it scored the shortest time delay for ECC computations.In addition,results showed thatNAF algorithm consumes less time to perform encryption and scalar multiplication operations in comparison withMontgomery ladder and binarymethods.Java multi-threading technique was adopted to implement ECC computations in parallel.The proposed multithreaded Montgomery ECC implementation significantly improves the performance level compared to previously presented parallel and sequential implementations.

A Low-Cost and High-Performance Cryptosystem Using Tripling-Oriented Elliptic Curve

Developing a high-performance public key cryptosystem is crucial for numerous modern security applications.The Elliptic Curve Cryptosystem(ECC)has performance and resource-saving advantages compared to other types of asymmetric ciphers.However,the sequential design implementation for ECC does not satisfy the current applications’performance requirements.Therefore,several factors should be considered to boost the cryptosystem performance,including the coordinate system,the scalar multiplication algo-rithm,and the elliptic curve form.The tripling-oriented(3DIK)form is imple-mented in this work due to its minimal computational complexity compared to other elliptic curves forms.This experimental study explores the factors playing an important role in ECC performance to determine the best combi-nation that leads to developing high-speed ECC.The proposed cryptosystem uses parallel software implementation to speed up ECC performance.To our knowledge,previous studies have no similar software implementation for 3DIK ECC.Supported by using parallel design,projective coordinates,and a fast scalar multiplication algorithm,the proposed 3DIK ECC improved the speed of the encryption process compared with other counterparts and the usual sequential implementation.The highest performance level for 3DIK ECC was achieved when it was implemented using the Non-Adjacent Form algorithm and homogenous projection.Compared to the costly hardware implementations,the proposed software implementation is cost effective and can be easily adapted to other environments.In addition,the power con-sumption of the proposed ECC is analyzed and compared with other known cryptosystems.thus,the current study presents a detailed overview of the design and implementation of 3DIK ECC.

A trinomial type of σ-LFSR oriented toward software implementation

In this paper, we introduce a new type of feedback shift register based on words, called G-linear feedback shift register （σ-LFSR） which can make full use of the instructions of modern CPUs so that we can find good σ-LFSR with simple structure and fast software implementation. After analysis, we find a class of simple σ-LFSR with maximal period and give an algorithm of searching for those σ-LFSRs. As a result, we provide a new optional fast component in the design of modern wordbased stream ciphers.