this is for holding javascript data
Scott Fluhrer edited untitled.tex
almost 9 years ago
Commit id: 34880f51fee69a891e34565cfea589bd396cab5f
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and then perform the computation:
$$kG = d_0G + b \cdot ( d_1 G + b \cdot (d_2 G + ... + b \cdot(d_{i-1}G + b \cdot (d_i G)))...)))$$
In the straight-forward way, this takes $b-2$ additions to evaluate the values $(0G, 1G, 2G, ..., (b-1)G)$, and then $i$ cycles of multiplying by the small integer $b$ and adding the next digit. Of course, there are a number of variants to this approach, both to try to achieve constant time, and to reduce the number of additions required (for example, by using the digits in the range $(-b/2, b/2)$, taking advantage of the fact that
with Elliptic Curves, computing we can compute the inverse $-G$
is cheaply within an
easy operation). Elliptic Curve group).
The obvious choice is to make $b$ a power of two (so $b = 2^m$); this yields two immediate advantages: