Fwd: Re: Fwd: Re: FH radios [Dave Emery] [Vaughan Pratt]

[stig@hackvan.com (Stig)]

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I forwarded a cypherpunks message to technomads, where it got a killer
response, so I'll bounce it back to Cypherpunks...

    Stig
    

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From: Vaughan Pratt <pratt@cs.stanford.edu>
To: technomads@UCSD.EDU
Subject: Re: Fwd: Re: FH radios [Dave Emery] 
Sender: pratt@cs.stanford.edu
Date: Tue, 26 Dec 1995 12:00:43 -0800
Message-Id: <199512262000.MAA23334@Coraki.Stanford.EDU>
In-reply-to: Your message of "Tue, 26 Dec 1995 07:07:00 PST."
             <m0tUayp-0006F0C@hackvan.com> 


>>> Thus in a frequency-hopping radio you can push the retuning (read RF
>>> phase-locked loop) technology to its limit and build transmitters and
>>> receivers around them. These typically hop in the order of 100 times a
>>> second. The adversary has to find the uncorrelated signal very quickly
>>> indeed *and* have PLL technology at least as good as yours to recover
>>> anything from it. Finding the signal generally means listening to all
>>> frequencies at once, requiring huge amounts of hardware parallelism and/or
>>> realtime computing power. Once you throw ten or so radios onto the same
>>> band, it's no longer any use looking for the strongest signal, making that
>>> approach useless.
>> 
>> This is nowhere near the limit of the technology.  15 years ago, I was
>> working on PLLs that would stabilize within a couple degrees of final
>> phase within 3.5 microseconds.  That permits you to do useful work at
>> 100,000 hops per second.
>> 
>	There is also a newer technology called direct digital synthesis
>or DDS that works by accumulating phase (adding to the previous value) 
>each tick of a high frequency clock in a register at a rate determined
>by the contents of another register (the value here sets the frequency)
>with the upper bits of the accumulated phase being used to address a
>sine/cosine lookup table rom which in turn feeds digital output values
>into a D/A converter.  The output of the D/A converter is a sampled 
>approximation of a sine or cosine wave at a frequency set by the
>increment register.  The sample rate is set by the high frequency clock
>rate.

This is all wishful thinking.  A 26-MHz wide channel such as 902-928MHz
has a channel capacity of 2*26 Mbs or 6.5 megabytes/sec.  So if someone
can tell *that* you are transmitting somewhere within that channel then
they simply record *everything* at that data rate in the entire
channel, your transmission and everyone else's, for the necessary
time.  A $600 3.5Gb Sequel drive can record a ten-minute transmission;
then the eavesdropper can use one Pentium or two dozen, budget
permitting, to extract your message from that data.  If all you are
doing is frequency hopping or spread spectrum, reconstruction is a very
undemanding algorithmic task, and one Pentium should be able to
reconstruct your signal the same day, two dozen the same hour.

>But to get back to the original point of this thread - while
>such techniques are possible (as is full hard encryption), it is my
>understanding that actual conusmer 900 mhz digital cordless phones
>that use frequency hopping use a very limited set of frequencies
>and a small set of fixed hopping patterns and don't hop very fast. 

Hopping speed is almost completely irrelevant to the computational
complexity of this problem.

>When the brand of cordless phones that most emphasizes security
>from eavesdropping in its point of sale advertising display is the one that
>uses open FM with simple speech inversion you know there is something
>wrong, particularly when the company that makes it is a pioneer in
>really secure digital speech over handheld radios (and a big governmeent
>contractor).

To put it mildly.

You can never overestimate the cost of decryption.  What looks
expensive enough today to decrypt can plummet by orders of magnitude on
alarmingly short notice.  We used to think TCP was mildly secure until
easily installed sniffers became freely available on the internet that
would reconstruct a telnet connection and print out the first 100
characters, making it child's play to extract passwords.

If you think that you are secure because the effort of an attack seems
on the high side, bear in mind that the tasks in a systematic attack can
by definition of "systematic" be programmed, greatly easing the
attacker's task.  And once programmed, the program can be distributed to
all and sundry on the internet.

If a given level of cryptographic strength seems adequate for a message,
add several orders of magnitude and maybe you'll be lucky.  

I know of only two really satisfactory places to hide information worth
hiding: combinatorial search space (read: real encryption such as DES
or RSA, with a hefty key), and the real world, which as a search space
is approximately the size corresponding to a combinatorial space
encrypted with a 256-bit key (i.e. the world seems bigger than 128 bits
and smaller than 512).  The latter is distributed in space-time and
frequency (momentum-energy); if you consider only space-time or only
frequency the universe looks like only a 128-bit hiding place in either
case.  Both together give you 256 bits (very approximately, that's a
very round binary number).

Vaughan Pratt
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