An Efficient Representation of Scalars for Simultaneous Elliptic Scalar Multiplication

Yasuyuki SAKAI  Kouichi SAKURAI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E86-A   No.5   pp.1135-1146
Publication Date: 2003/05/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
elliptic curve cryptosystems,  scalar multiplication,  

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The computational performance of cryptographic protocols using an elliptic curve strongly depends on the efficiency of the scalar multiplication. Some elliptic curve based cryptographic protocols, such as signature verification, require computation of multi scalar multiplications of kP+lQ, where P and Q are points on an elliptic curve. An efficient way to compute kP+lQ is to compute two scalar multiplications simultaneously, rather than computing each scalar multiplication separately. We introduce new efficient algorithms for simultaneous scalar multiplication on an elliptic curve. We also give a detailed analysis of the computational efficiency of our proposed algorithms.