For Full-Text PDF, please login, if you are a member of IEICE,|
or go to Pay Per View on menu list, if you are a nonmember of IEICE.
Efficient Scalar Multiplication on Montgomery-Form Elliptic Curves
Yuichi FUTA Motoji OHMORI
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2004/08/01
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Information Security
elliptic curve, Montgomery-form elliptic curve, scalar multiplication, fixed point,
Full Text: PDF(503.6KB)>>
Montgomery-form elliptic curves have the advantage of faster arithmetic than Weierstrass-form elliptic curves. The dominant operation of the Elliptic Curve Cryptosystem (ECC) is scalar multiplication of points on an elliptic curve, and it usually includes scalar multiplication of a fixed base point of ECC. For Weierstrass-form elliptic curves, accelerating methods of scalar multiplication by using a pre-computed table of the fixed point have been widely studied. However, such methods cannot naturally expand to Montgomery-form elliptic curves. In this paper, we propose a fast scalar multiplication method on Montgomery-form elliptic curves by using a pre-computed table for the first time. Our method is 1.6 times as fast as the known method for Montgomery-form elliptic curves under the practical conditions that the size of the definition field is 160 bits and the memory size used for the pre-computed table is 3.2 KB.