MC14562B 128 bit static CMOS shift register

[Magnus Danielson]

From: "Theo" <t.hogers at home.nl>
Subject: Re: MC14562B 128 bit static CMOS shift register
Date: Thu, 6 Apr 2000 11:44:24 +0200

> Not completly sure about this, but I've just checked on some examples of
> other shiftregister noise makers.
> They all have one thing in common: the shift register is a "prime" steps
> long.
> (eg. 31 steps and not 32)
> Seems like the MC14562B does not match that criteria.

Naturally I need to respond to this with a bunch of counter examples:

m  n  Length
4  3  15
6  5  63
9  5  511
10 7  1023
18 11 262143
28 25 268435455
36 25 68719476735

Further, if you have more taps you can find other values as well

m  Taps     Length
8  4,5,6    255
16 4,13,15  65535
24 17,22,23 16777215

However, primes does have something to do with it, you will notce that the
given values x^m + x^n + 1 is really a prime number and thus from a Galois
field with the length of 2^m-1. You can also find that other polynoms may be
related.

Since there is plenty of primes of various lengths you should be able to find
a bunch of them of the length 128 bits.

If you want to check weither a certain m and n combination forms a prime there
are reliable and fast primality checks to use which are feasable for 128 bit
numbers. Such checks is being used in RSA key generation.

Cheers,
Magnus