[39823] in Cypherpunks
Re: Patents and trade secrets was: Encryption algorithms used in PrivaSoft (fwd)
daemon@ATHENA.MIT.EDU (Norman Hardy)
Thu Sep 21 23:20:14 1995
Date: Thu, 21 Sep 1995 20:17:37 -0800
To: iang@cs.berkeley.edu, cypherpunks@toad.com
From: norm@netcom.com (Norman Hardy)
At 9:47 PM 9/20/95, Ian Goldberg wrote:
....
> - Ian "I heard that 'x*y=[(x+y)/2]^2 - [(x-y)/2]^2' is a patented way
> to multiply numbers of the same parity. Can anyone verify this
> and/or produce a reference?"
....
That trick is probably at least 200 years old. There were once
"quarter square" tables published that started
i q(i)
000 000
001 000
002 001
003 002
004 004
005 006
etc.
i [1^2/4]
It works for all parities. ab = q(a+b) - q(a-b)
These tables were published in nautical navigation books.
Mechanical analog computers sometimes used this trick to
multiply shaft positions. There would be a cam that computed
the square of one angle, expressed as another angle.
