Elliptic Curve Scalar Point MultiplicaliOll Algorithm Using Radix-4 Booth's Alg
| Paper File | Download Paper File | | Appear In | ECTI Transaction CIT (ECTI Transaction CIT) | | Publication Date | 01/05/2005 - 31/05/2005 | | Volume | 1 | | Pages | 3 - 8 | | No | 1 | | Author 1 | Sangook Moon |
Abstract
The main back-bone operation in elliptic curve
cryptosystems is scalar point multiplication. The
most frequently used method implementing the scalar
point multiplication, which is performed in the topmost
level of GF multiplication and GF division, has
been the double-and-add algorithm, which is being
recently challenged by NAF (Non-Adjacent Format)
algorithm. In this paper, we propose a more efficient
and novel approach of a scalar multiplication
method than the double-and-add by applying redundant
recoding which originates from the radix-4 modified
Booth’s algorithm. We call the novel algorithm
quad-and-add. After deriving the algorithm, we created
a new GF operation, named point quadruple,
and verified with calculations of a real-world application
to utilize it. Derived numerical expressions were
verified using both C programs and HDL (Hardware
Description Language). Proposed method of elliptic
curve scalar point multiplication can be utilized in
many elliptic curve security applications for handling
efficient and fast calculations. |
