Welcome to the resource topic for
**2002/179**

**Title:**

Parallel Algorithm for Multiplication on Elliptic Curves

**Authors:**
Juan Manuel Garcia Garcia, Rolando Menchaca Garcia

**Abstract:**

Given a positive integer n and a point P on an elliptic curve E, the computation of

nP, that is, the result of adding n times the point P to itself, called the

\emph{scalar multiplication}, is the central operation of elliptic curve cryptosystems.

We present an algorithm that, using p

processors, can compute nP in time O(\log n+H(n)/p+\log p), where H(n) is

the Hamming weight of n. Furthermore, if this algorithm is applied to Koblitz curves,

the running time can be reduced to O(H(n)/p+\log p).

**ePrint:**
https://eprint.iacr.org/2002/179

See all topics related to this paper.

Feel free to post resources that are related to this paper below.

**Example resources include:**
implementations, explanation materials, talks, slides, links to previous discussions on other websites.

For more information, see the rules for Resource Topics .