Remember the play about 6 degrees of separation? The thesis is
that many or most people are connected with almost anyone else
through just a few links. Any reader of Brian”s week in review
column knows of his views on Bill Clinton. Well, my wife
pointed out to me that Bill and Hill attended a fund raising party
for her New York Senate campaign at the home of Frank Biondi
in Edgartown, Massachusetts a week or so ago. In the article,
Biondi was identified as a Viacom executive but, unless rehired,
he hasn”t been CEO at Viacom since 1996 and was more recently
CEO of Universal Studios and I believe is now a consultant for
King World. It happens that Frank Biondi”s father, also Frank
Biondi, was my director for several years at Bell Labs. Brian”s
parents purchased young Frank”s youth bed for Brian to sleep in
as a young lad and today Brian”s nephew sleeps in that very bed.
I don”t know how to count them, but I think this means that Brian
is only separated from the Clintons by 2 or at the most 3 degrees
of separation. I hope it doesn”t ruin his day! [Editor: It did.]
When not commenting on Clinton, Brian has written a good deal
about spying and espionage, with emphasis on China and its
(our?) nuclear weapons and missile technology. I also wrote
about espionage in the World War II-Korea eras in an earlier
column. The subject naturally brings to mind messages written
in invisible ink or encoded in microdots like the period at the end
of this sentence. Today, the coding of messages and data is a
matter of great concern to all of us, not just those employed by
the CIA. The Internet, with its huge number of transactions
ranging from my first Internet purchase of a CD of Dick
Wellstood”s stride piano artistry from Amazon.com to the
transfer of billions of dollars in financial transactions, demands
that privacy be guaranteed. The manner in which encryption of
messages on the Internet is carried out is the subject of vigorous
debate. In particular, law enforcement agencies are rightfully
concerned about losing one of their most potent weapons against
crime and terrorism, the Internet equivalent of the wiretap.
Should, for example, the FBI have the keys to crack the Internet
codes under restrictions similar to those now governing
permission to wiretap?
The encoding of communication has been going on for quite a
while now. I read a book review in the May 23 NY Times and
found that 2000 years ago Aristotle characterized the “eidos” as
the essence that shapes the embryo. He said this eidos
“contributes nothing to the material body of the embryo but only
communicates its program of development.” The book”s author
pointed out that it would be hard to come up with a better
definition of DNA. Indeed, DNA has been encrypting
information for a couple billion years or so and the decoding of a
human gene is not too far from completion.
Encryption of communications by us humans is done by all kinds
of fancy mathematical devices such as factoring very large
numbers, the use of public and private “keys” and other means
which I must admit boggles my brain. While researching
material for this piece I accidentally ran across one of many pi
websites. Pi, the ratio of the circumference of a circle
to its diameter, is a fascinating number and apparently can lead to
addiction. Pi never ends but goes on forever in non repeating
sequences 3.1415926……… Someone reportedly has memorized the first
42,000 digits of pi and only takes 9 hours to recite them! I didn”t
find out if there was anyone who listened to the recitation, let
alone checked the accuracy! Presumably, a coded message could be
based on keying the message to a number or sequence of numbers in
pi. But now some bright guys have come up with a formula for
calculating any digit in pi. In this formula you just plug in, say
200 trillion and you get the 200trillionth digit, without knowing any
of the surrounding digits. If you”re ever in a bind and want to know
the value of pi I highly recommend the website
www.cecm.sfu.ca/pi/pi.html When I logged on, a gentleman was
continuously reciting (in French!)the value of pi while a running
tabulation of pi appeared on the screen. You”re right, I need to get
a life!
Another book review in the same issue of the Times also dealt
peripherally with encoding of a simpler nature during World War
II. The language of the Navajo Indians (Native Americans
today) was understood only by a small number of non-Navajos.
None of these were Japanese. So, the US Marine Signal Corps
simply used Navajos talking openly on the airwaves to each
other to send messages in a secure fashion that couldn”t be
decoded by the enemy. On the other hand, the cracking of the
Japanese code by the Allies played a major role in the naval
engagements of that war. One of the biggest naval battles was at
Midway in the Pacific. In a letter in the August issue of the
National Geographic, which had run an article on war in the
Pacific, one Mitsuharu Ito wrote that he was a university student
in Tokyo during World War II. Ito was drafted into the Imperial
Navy to join a code breaking team trying to crack the U.S.
Navy”s “strip ciphers”. Although the team was successful in
cracking some aircraft codes, they couldn”t manage the strip
ciphers and a Japanese mathematics professor at the Japanese
Naval Staff College proved theoretically that they couldn”t be
broken. The strip ciphers were apparently a poor man”s version
of the more complex cipher machines used by our military at the
time.
Not as crucial to world history was my own experience with
coded messages. As a child, I was a faithful listener (no TV) to
such radio shows as the Lone Ranger, Buck Rogers and Little
Orphan Annie. I believe it was the latter show that had this
fabulous offer. By sending in the metal foil seal on a can of
Ovaltine (it only took a 3 cent stamp in those days), one would
receive in return a shiny copper-colored, round decoder badge.
This sophisticated “badge”, about the size of a silver dollar, but
thicker, had dials that permitted a variety of settings. I will never
forget sitting breathlessly, taking down the numbers read by the
announcer with the first secret message, 1, 13, 4, 22, … and the
appropriate “key” setting. To this day I remember the essence of
the message, “BIG NEWS COMING”! I can”t recall ever
decoding another message. Guess I became more mature and
graduated to listening to The Shadow, Jack Benny and Fred
Allen shows.
Today, things are a little more complex. You have a choice of at
least a couple of systems, the public key or the secret-key
system, or a combination of both. The degree of security
provided by either system is based on the computing power and
time available (more accurately, unavailable) to a potential
eavesdropper to figure out the key. The only perfectly secure
key would seem to be a “one-time” secret key that would consist
of a random key exactly as long as the message. In all the
literature I”ve seen, it seems that only people named “Bob” and
“Alice” are interested in sending each other messages. To send
Alice a message, Bob would add each bit of the key to the
corresponding bit of the message (see below for my
interpretation of this strategy). At the receiving end, Alice would
subtract the key to obtain the original message. To be absolutely
certain that nobody could intercept the message, however, Bob
and Alice would have to meet personally to exchange the secret
key or transmit it to each other over an absolutely secure
channel. I would guess that the secret key could actually be
made longer than any anticipated message and that a programmer
would be able to handle the lack of an exact match in the number
of bits in the key and the message. As an example, let”s assume
that Bob and Alice are lovers and that Bob wants to send the
following message encoded in the secret key abdfeccade:
Message: I love you (Here I”ve assumed a=1, b=2, c=3
Secret key: abdfeccade etc. and a space =0 and added
Coded message: jbprahczpz the corresponding no. of letters
of the alphabet)
This is my impression of how it works. It”s pretty simple but the
result should be awfully hard to figure out without the key.
For the public key option, Bob and Alice each have their own
“public” keys, as well as their “private” keys, which they”ve
shared with each other in some secure way. To send a message
to Alice, Bob gets her public key from a “trusted” source. This
trusted source has a bunch of public keys for lots of people and
distributes them on request. Bob now encodes his message
using her public key. Alice receives the message and decodes it
using her private key. In one system the private key is based on
a couple of “prime” numbers, numbers such as 3, 5, 7, 11, 13,
17, 23 etc., which can”t be factored. In this system the public
key is the product of two large prime numbers. By making the
prime numbers very large, the computer time to arrive at the
private key can be so long as to be impractical for Eve, the
eavesdropper. This method depends on the fact that there is no
known neat way to factor very large numbers derived in this
way. If, however, someone has been bright enough to solve this
problem, like the guys who figured out how to calculate any
number in pi, the security is shot!
Now suppose Alice is suspicious and questions whether the
message is really from Bob and not someone else who has her
public key. To reassure her, Bob could then encrypt the message
first with Alice”s public key, then with his private key. Alice in
turn would have to first decode it with Bob”s public key, then
with her private key. If someone other than Bob had sent the
message, the result would be gibberish and Alice would know
her suspicions were correct. If this sounds complicated, it is.
The computer time for all this coding and decoding can be quite
large. So, Bob may just use this approach to send a “secret” key
that Alice will recognize as coming from Bob. He may then
encode his message in this secret key which Alice can decode
using the secret key. If this sounds complex, the public/private
key method(s) are child”s play compared to what could become
the encryption gold standard of the 21st century, “quantum
encryption”.
You must have noticed that I haven”t yet mentioned Einstein,
who seems to worm his way into the majority of my columns.
Well, just as with the concept of black holes, Einstein did not
think quantum encryption could exist and even called it spooky.
And spooky it is! The crux of the matter is that photons, or even
atoms, can become “entangled” and, once entangled, what
happens to one of the photons can affect the state of the other
photon. This may not seem strange to you, especially since you
don”t know what “entangled” means, but what about this? The
other photon may be miles or possibly even billions of miles
away from the other and still be affected! And that ain”t all. You
can introduce a third photon, let it get together with one of the
two entangled photons and the other entangled photon way out
there will end up looking just like that 3rd photon. It”s very
much like the “Beam me up, Scotty” of Star Trek. The third
photon disappears and the distant entangled photon looks like its
twin.
In the past few years, various groups have demonstrated this
spooky “action at a distance” over distances of at least 30 – 40
miles. I should stress that not every photon sent through the
experimental setup to entangle the photons participates in this
phenomenon and that it takes statistical treatment of the data to
extract the spooky result. Part of the difficulty lies in the
equipment for detecting the photons and part due to the
probability of a given photon becoming entangled is only 25% in
one type of transmission. If Bob tries to contact Alice using
quantum encryption, any attempt to eavesdrop by Eve would be
readily detected as loused up statistics.
Incidentally, don”t you count on being teleported any time soon.
You would have to dissected atom by atom and the amount of
information needed for reassembling you would be quite
outrageous! I haven”t attempted to describe the entanglement
and “action at a distance” details here. Even one of the
investigators who proved the effect says he doesn”t understand it.
I personally think it must be related to the “strings” that I
discussed earlier since they”re just as spooky!
Although the experimenters have only proved these peculiar
effects over a distance of miles to date, it seems that action at a
distance should in principle hold over unlimited distances.
Perhaps linking Brian to the Clintons by only 2 or 3 degrees of
separation isn”t so far fetched after all!
Allen F. Bortrum
