Greetings all.
Does anyone have a clue how to use Ruby to do modular exponentiation
using the binary left-to-right method? I looked through the
documentation and searched the forums and found the String.each_byte
method. However I had no luck finding anything showing how one might
manipulate bits of bytes.
Below is an example of what I am talking about.
The calculation a = b^e mod n (or in Ruby: a = (b ** e).modulo(n) )is
known as modular exponentiation. One efficient method to carry this out
on a computer is the binary left-to-right method. To solve y = x^e mod n
let e be represented in base 2 as
e = e(k-1)e(k-2)…e(1)e(0)
where e(k-1) is the most significant non-zero bit and bit e(0) the
least.
set y = x
for bit j = k - 2 downto 0
begin
y = y * y mod n /* square /
if e(j) == 1 then
y = y * x mod n / multiply */
end
return y
Thanks for looking,
Doug