Triple-base number systems are mainly used in elliptic curve cryptography to speed up scalar multiplication. We give an upper bound on the length of the canonical triple-base representation with base {2, 3, 5} of an integer x, which is O( log x log log x ) by the greedy algorithm, and show that there are infinitely many integers x whose shortest triple-base representations with base {2, 3, 5} h...

One the challenging in hardware performance is to designing a high speed calculating unit. The higher of calculations speeds in a computer system  will be pointed out in terms of performance. As a result, designing a high speed calculating unit is of utmost importance. In this paper, we start design whit this knowledge that one multiplier made of several adder and one divider made of several su...

Elliptic curves scalar multiplication over some …nite …elds, attractive research area, which paid much attention by researchers in the recent years. Researchs still in progress to improve elliptic curves cryptography implementation and reducing it’s complexity. Elliptic curve point-halving algorithm proposed in [11] and later double-base chain [3] and step multi-base chain [19] are among e¢ cie...

-----------------------------------------------------------------------ABSTRACT---------------------------------------------------------The fast implementation of elliptic curve cryptosystems relies on the efficient computation of scalar multiplication. As generalization of double base number system of a number k to multi-base number system (MBNR) provides a faster method for the scalar multipl...

In this paper we present the theoretical base for some modifications in interval multiplication algorithms. A diversity of proposed implementation approaches is summarized along with a discussion on their costefficiency. It is shown that some improvements can be achieved by utilizing some properties of interval multiplication formulae and no special hardware support. Both conventional and exten...

The technique for hardware multiplication based upon Fourier transformation has been introduced. The technique has the highest efficiency on multiplication units with up to 8 bit range. Each multiplication unit is realized on base of the minimized Boolean functions. Experimental data showed that this technique the multiplication process speed up to 20% higher for 2 − 8 bit range of input operan...

A new and highly efficient architecture for elliptic curve scalar point multiplication is presented. To achieve the maximum architectural and timing improvements we have reorganized and reordered the critical path of the Lopez-Dahab scalar point multiplication architecture such that logic structures are implemented in parallel and operations in the critical path are diverted to noncritical path...

In the current work we propose two efficient formulas for computing the 5-fold (5P ) of an elliptic curve point P . One formula is for curves over finite fields of even characteristic and the other is for curves over prime fields. Double base number systems (DBNS) have been gainfully exploited to compute scalar multiplication efficiently in ECC. Using the proposed point quintupling formulas one...

Corresponding Author: Mohsen Bafandehkar Department of Computer Science, University Putra Malaysia, Selangor, Malaysia Email: [email protected] Abstract: The most expensive and time-consuming operation in Elliptic curve cryptosystem is scalar multiplication operation. Optimization of scalar multiplication will substantially enhance the ECC performance. Scalar multiplication can be improved ...

The fast implementation of elliptic curve cryptosystems relies on the efficient computation of scalar multiplication. Based on the double-base chain representation of scalar using powers of 2 and 3, we propose a new representation with powers of 1⁄2 and 3 instead. Thus the efficient point halving operation can be incorporated in the new double-base chain to achieve fast scalar multiplication. E...