Scalar Multiplication on Kummer Surface Revisited

Qiping LIN  Fangguo ZHANG  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E95-A   No.1   pp.410-413
Publication Date: 2012/01/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E95.A.410
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Cryptography and Information Security
Kummer surface,  scalar multiplication,  genus 2 curves,  Euclidean addition chains,  

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The main benefit of HECC is that it has much smaller parameter sizes and offers equivalent security as ECC and RSA. However, there are still more researches on ECC than on HECC. One of the reasons is that the computation of scalar multiplication cannot catch up. The Kummer surface can speed up the scalar multiplication in genus two curves. In this paper, we find that the scalar multiplication formulas of Duquesne in characteristic p > 3 on the Kummer surface are not correct. We verify and revise the formulas with mathematical software. The operation counts become 29M + 2S for new pseudo-addition formulas and 30M + 10S for doubling ones. And then we speed up the scalar multiplication on the Kummer surface with Euclidean addition chains.