Efficient Arithmetic on Koblitz Curves

It has become increasingly common to implement discrete-logarithm based public-key protocols on elliptic curves over finite fields. The basic operation is scalar multiplication: taking a given integer multiple of a given point on the curve. The cost of the protocols depends on that of the elliptic scalar multiplication operation. Koblitz introduced a family of curves which admit especially fast elliptic scalar multiplication. His algorithm was later modified by Meier and Staffelbach. We give an improved version of the algorithm which runs 50% faster than any previous version. It is based on a new kind of representation of an integer, analogous to certain kinds of binary expansions. We also outline further speedups using precomputation and storage.

• Type: Journal
• Year: 2000
• Where: DCC
• Authors: Jerome A. Solinas
• Keywords: Computer Graphics, DCC 2000, Elliptic Scalar Multiplication, Scalar Multiplication, Scalar Multiplication Operation