IPG OTM expansion

I have a guess as to IPG's "OTP" expansion algorithm.  The clue is the
prime wheels.  It reminded me of something I read in Kahn that was originally
done with paper tape.

Take two random streams, A and B.  Their lengths are relatively prime.  Let's
use 1000 and 999.  An expanded stream C is computed thus:

C[i] = A[i % 1000] ^ B[i % 999]

C thus does not repeat until 999000 values have gone past.  Using more than
two relatively prime wheels will produce very large streams.  The key,
of course, is that *the entropy does not increase*.  I am sure that this
sort of expansion is vulnerable to attack.  It certainly does not warrant
the name OTP.

Am I close, Ralph?

SINCLAIR DOUGLAS N writes:
> I have a guess as to IPG's "OTP" expansion algorithm.  The clue is the
> prime wheels.  It reminded me of something I read in Kahn that was originally
> done with paper tape.
> 
> Take two random streams, A and B.  Their lengths are relatively prime.  Let's
> use 1000 and 999.  An expanded stream C is computed thus:
> 
> C[i] = A[i % 1000] ^ B[i % 999]
> 
> C thus does not repeat until 999000 values have gone past.  Using more than
> two relatively prime wheels will produce very large streams.  The key,
> of course, is that *the entropy does not increase*.  I am sure that this
> sort of expansion is vulnerable to attack.

Indeed it is. It is fairly straightforward to crack this. If you read
the same chapter of "The Codebreakers" you will note that, in fact,
this same method was tried and broken way, way back.

> Am I close, Ralph?