Re: One time pads and randomness?

[Bill Stewart <stewarts@ix.netcom.com>]

Welcome!  You've asked a Frequently Asked Question, so you're obviously 
new here, but you're also thinking, so we'll cut you some slack :-)
A good book on cryptography that you should read is Bruce Schneier's
"Applied Cryptography", which talks about both math and practical issues.

At 09:51 AM 1/18/97 -0500, AaronH4321@aol.com wrote:
>I want to use a one time pad pased crypto system. I understand that the
>randomness of the pad genorator is key to security (other than lossing 
>the keys).  What I want to know is if I use a psuedo-RNG that ....

Pseudo-Randomness isn't Real Randomness, and OTPs need Real Randomness.
[Von Neumann said that anyone using mathematical methods to generate
random numbers "is, of course, in a state of sin."]
If you've got a Pseudo-RNG, your random number generator has some state
at step 1 that totally determines the output at steps 2...infinity.
This means that anybody who can determine the state of the PRNG at
step n can decode all messages for steps n+1, n+2, ...., and often
for steps 1....n-1 as well (depending on the particular PRNG.)
If you're got Real Randomness*, even if you know the value of the
pad at step n, it tells you entirely nothing about any other step.
	
To make it worse, the popular PRNGs turn out to be annoyingly easy
to crack, i.e. to determine the state from a small number of samples.

>Say I create a 1 million character one time pad that passes all of the
>randomness tests.  It is "truely random". 

Unfortunately, passing randomness tests doesn't tell you a pad is
"truly random" - it just eliminates the blatantly easy stuff.
For instance, x[n+1] = Hash( x[n] ) or X[n+1] = Encrypt( x[n] )
for a cryptographically strong hash function or encryption like 
MD5 or SHA or 3-DES will pass randomness tests just fine,
but it's still totally deterministic.  Still not a OTP.

However, say you create the pad from really random sources like
flipping lots of coins or counting gamma rays, and haul it to your
computers by well-armed guys with briefcases handcuffed to their wrists.

>"A" grabs a chunk of the one time pad  starting at a random point and 
>encrypts it....There "B" moves to the random point and begins decryption.

If the pad is _really_ random, and you're sure nobody's seen any of it,
then there's no difference between starting at a random point and
starting at the beginning, and the bookkeeping is much cleaner.

>During to process both computers mark that section of the OTP used so 
>that they don't retransmit with it.  I realize this has a limited amount 
>of messages before it is used up.  But would this be secure?

Yeah, you've got it (once you remember to use a really random pad
so there's entirely no relationship between bits n and n+1.)
And you've also hit one of the basic difficulties with using OTPs,
which is making sure you only use the once, and that this means
that sometimes you run out AND YOU STILL CAN'T USE THE PAD AGAIN.

	[*Some philosophers will argue that there isn't any
	Real Randomness, that there's just a deterministic
	State Of The Universe that's more complex than you happen to know,
	and some will rant about Quantum Mechanics, and others who
	actually have some clue about Quantum will tell you that it 
	doesn't get you off the hook; in any case, as long as the universe
	is messy enough it's be close enough for government work.]

The NSA was able to crack a bunch of Russian OTP transmissions back
in the 50s (the project name was Venona, and it was recently announced)
because the Russians did two major things wrong: They used pads more
than once when they were sloppy or out of new pads, and they didn't
use very good randomness - clerks banging "randomly" on typewriters
generate data with more correlation and less even distribution than
they'd expect, and in nearly-pre-computer days they weren't able

#			Thanks;  Bill
# Bill Stewart, +1-415-442-2215 stewarts@ix.netcom.com
# You can get PGP outside the US at ftp.ox.ac.uk/pub/crypto/pgp
#     (If this is a mailing list, please Cc: me on replies.  Thanks.)