Algorithm 8.2 The di-subgraph signed digit representation of the positive integers

Input: A directed graph G(V, E), where V = (v1, v2, …, vl) and E = (e1, e2, …, em). Output: The SDRsubgraph(v).

1. Determine (v1, v2, …, vk) and (e0, e1,…, em � 1) in any subgraph H of G.

 2. i 0.



Table 4.

The experimental results for sign digit representing l-tuple of the scalars using the subgraphs.


Table 5.

The experimental results for computing l-tuple of the scalar multiplications based on using the subgraphs.

The computationalresults based on Figure 5 and using Algorithm (8.2) are given in Table 4. With the signed digitrepresentations which are given in Table 4, the l-tuple of the scalar multiplications on elliptic curve E defined over a prime field Fp can be computed. Some experimentalresultsfor computing the l-tuple of the scalar multiplications based on using the directed subgraphsto represent the scalars are given in Table 5.
