From: norm@netcom.com (Norman Hardy)
Date: Thu, 21 Sep 95 20:18:02 PDT
To: cypherpunks@toad.com
Subject: Re: Patents and trade secrets was: Encryption algorithms used in PrivaSoft (fwd)
Message-ID: <ac87e6a600021004df72@DialupEudora>
MIME-Version: 1.0
Content-Type: text/plain


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.