Shorter addition-subtraction chain with signed composition method

M.A., Mohamed and A., Ahmad and R.R., Mohamed and M.R.M., Said (2017) Shorter addition-subtraction chain with signed composition method. International Journal of Engineering and Technology, 9 (2). pp. 299-308. ISSN 2319-8613

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Abstract

Addition chain is considered as the solution to large number operation of scalar multiplication in elliptic curve cryptosystem. Recently, a decomposition method was introduced as a new technique to generate addition chain with minimal possible terms. The method which is based on prime power input form was shown to outclass previous methods under certain condition. An earlier study shows that this method can also be used with non-prime integer such that found in composition method. As a result of no extra cost for point negation on elliptic curve, subtraction operation can be included during the generation of the chain as we found in signed decomposition method. As an alternative, in this paper, we proposed a signed composition method. Using this method, we study the properties of the chain against those generated by prime power equivalent. The comparative result between signed composition method against signed decomposition method shows that by allowing a subtraction information into the chain, the resulting chains are nearly of equal length which is very different from the unsigned case, where original decomposition method is by far has outperformed the composition method.

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