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Cryptography
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Cryptography: A History and Explanation


Information Security

K. Crum

February 2008




Brian J. Harman



Cryptography
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When we are young we are told that secrets don’t make friends and friends don’t make
secrets.
This statement works well in the logic of
all humans however there are certain
circumstances where it would be mutually beneficial for a bit of information to not be heard by
a certain individual or individuals. Take this scenario: If there are three kids, say Bobby, Susie,
and Patty, and both Pa
tty and Susie like Bobby and Bobby ended up kissing Susie one could say
that if Patty found out she might cause harm to either Susie, Bobby, or both. In this case it
would be beneficial for Bobby and Susie to not allow Patty to find out.


There are other
such scenarios that have much greater weight and are most notably
found in times of war. War in
-
fact has been the most influential breeding ground for keeping
secrets, though, not always for the benefit of all parties involved. Some of the greatest
disco
veries in the art of secrets
, and secret
-
keeping

have

been on the account o
f wartime
strategy. One prime example is the famous Enigma machine from World War II.


The problem
, though,

with keeping
these
secrets is that it is extraordinarily hard to
make su
re that the secret is kept. Looking back at the above example we can put a fairly
high

probability
on the event
that Patty will find out about the kiss; with the way people talk and
through mutual friends it is almost inevitable that Patty will find out a
bout Susie’s kiss with
Bobby.


Also,
in

this example no lives would likely be lost over the secret’s discovery

but, as it
turns out,

there are m
any

examples where there would be bloodshed
if

the secret
were to be

heard by the wrong party
. Since
a lot of

secrets are kept from enemies during times of war

it
would be inevitable for lives to be lost if a secret were to be
rev
e
aled
. One of the first
, and a
Cryptography
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prime example

of this took place around 480 B.C. at
the

time Xerxes
was planning to invade
Greece.


The

Beginnings of Cryptography

Persia was rapidly expanding and when Xerxes sought to add Greece to the Persian
Empire he was not welcomed by the Greeks and so he began to form an extensive army to take
Greece by force.
A

man by
t
he name of Demaratus witness
ed the Persian military being
compiled and still holding his loyalty to Greece
,

even
after being exiled
,

he
decided

to warn
them against the coming invasion.


The problem that Demaratus faced was how send a message to the Greeks without the
Persians find
ing the message and destroying it.
H
is solution

was to scrape the wax off a
wooden writing tablet and
write

the Pers
ian’s intent on the wood itself,

then covering the
message back up with wax. This way the guards along the road would see only the apparen
tly
blank
tablets and not confiscate them, thus allowing
the message
to
be sent to Greece.


Upon receiving the tablets the king of Sparta did nothing with them, it was his wife who
actually noticed the writing underneath the wax and not
ified him of the hid
den message. And,
w
ith this information the king prepared an army to combat the Persians and when they arrived
the Spartans were able to
greatly weaken the Persian army. Without the information from
Demaratus the Greeks would have been slaughtered.


This type of “hidden message” is referred to as steganography. Another form of
steganography that arrived about two

centuries later was the scytale which involved words
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written on a strap of leather that was wrapped around a piece of wood of a certain dia
meter.

People could use the leather strap
as a belt and even if the strap was
found to contain a message it
would be unreadable by anyone
who didn’t have the appropriate
diameter scytale to wrap the
leather around.


Another way people hid messages was to

write them on a messenger’s head after it had
been shaved and then allowed to grow back to conceal the message. Once the messenger
made it to the intended recipient he would shave his head allowing the message to be read.


The Growth of Crypto
-
Systems

Th
ese types of secret keeping are all good ways of hiding messages but like in the
example of the shaved head they require a lot of patience on the part of the recipient and once
the method of hiding is found they can no
-
longer be used.


This problem was
c
onquered

mid
-
first
-
century B.C. by Julius Caesar when he created
what we now call the Caesar
-
Cipher. The cipher involves using two alphabets, the plain
alphabet and the cipher alphabet. The cipher alphabet
he used
was the same as the regular
alphabet
with each letter moved up

three, thus C
a
=P
a
+3(mod 26), therefore the word “CAT”
would have each character substituted using the cipher alphabet to become “FCW”.

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This was the first instance of what we now call a substitution cipher or in more exact
terms a

monoalphabetic substitution cipher. It is an extremely formidable cipher because there
are so many different ways to form the cipher alphabet. Not only can the cipher alphabet be a
shifted form of the regular alphabet it can also have letters swapped ou
t at random, in
-
fact,
being that there are 4.0E
26

different ways to rearrange the alphabet it was once conceived that
this form of cipher could never be broken, and, for years to come this was the case.


It was not until around 800 A.D. that the first sign
s of a solution to the monoalphabetic
cipher came about



nearly a millennia had gone by. It was the
Arabs

during
the

enormously
prosperous period that followed Muhammad’s meeting with the archangel Gabriel that the
threads of the monoalphabetic cipher be
gan to fray.


What they discovered was that one did not have to go through every rearrangement of
the alphabet to come up with what is commonly refered to as the plain
-
text message, but,
rather use a system of
analyzing

the frequency of letters and comp
aring the
m with the natural
relative frequencies
. By using this technique one can decrypt a message that would have taken
centuries in the time it takes to do
a crossword puzzle.


It would not suffice to just
say this. The technique is really
quite gen
ius. If there is a message
that is a few sentences long you
can start by jotting down the
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frequencies of the encrypted letters. From there you cannot
simply
assume that the frequency
matches exactly to the graph above but there will be a few two and thre
e
-
letter words that can
be used to figure out what the letters E
,
T
,
A
,
O
,I,N,S,R, and H

represent in the ciphertext. After
these are plugged in the next step is to see if any sense can be made of other words in the text,
for example the word “aQQ” (where th
e capital letters are from the ciphertext and the
lowercase letters are fro
m the decrypted text) would

be the word “all”, and the word “eneKL”
would most likely be “enemy”
.

The rest is just piecing together the remaining letters using
context and logic.


From this, the cracking of the monoalphabetic cipher, history was forced to come up
with other measures to make the transportation of confidential messages secure. Two things
happened to bring about stronger encryption. One was the introduction of null c
haracters

(meaningless characters entered into a text to fool people trying to break the encryption)

into
the ciphertext and another strategy was the use of codes. Codes are a different type of
strategy altogether but in the famous example of Mary Queen of Scotts secret messages to
overthrow Queen Elizabeth it was a conjunction of the two that she thoug
ht would void her
chance of being caught.


The problem was that her messages were not only being intercepted but the art of
decryption was becoming a very fashionable thing at the time and Mary’s messages didn’t have
a chance against the
English cryptograp
hers. After she was found and tried she was beheaded
for the attempted assassination of the queen.

Cryptography
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It was to her disadvantage that the next big breakthrough in cryptography was just
being developed. A man by the name of Vigenere had come up with a new w
ay to encrypt
messages that still used the technique of the cipher alphabet but it used more than one. It is
referred to as a polyalphabetic
cipher and it consists of a codeword
and a “vigenere square”.


The codeword is used to
pick what line of the
sq
uare to use
for each letter of the plaintext.
Now, b
ack to our “cat” example… If
we had the codeword “dog” and
the plaintext “cat” what we would
do is replace the “c” in cat with
whatever “c” represents in the row
of “d”, so “c” would be changed to “F”.
Next we would take the letter “a” and put it though
with the line that corresponds to the next letter in the codeword, “o”. So “a” would be
changed to “O”. Last we would take the next letter “t” and filter it using the “g” line to get “Z”.
So the word “
cat” has now been encrypted to read “FOZ”.



What this does is make it so a frequency analysis will not show what common letters
represent because the letters are constantly switching. This type of cipher is monumentally
stronger that the monoalphabetic
cipher that was broken many years prior. Also, just like the
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way monoalphabetic ciphers can use a random arrangement of the letters so can the square
used to do the encryption. As long as both parties know the code and both parties use the
same square it

requires an enormous amount of work to break the encryption, and again, it was
thought to be an impossible feat.


The polyalphabetic cipher came about around 1600 and the world of cryptography at
that time was expanding quickly. After about 100 years we
started to see “Black Chambers”
where there would be rooms of people all working to decrypt a message. Although some of the
available cryptography at the time was unbreakable most messages didn’t use it and the men in
these black chambers would be given a

message and as quickly as they could get it decrypted
they would send it out.


It wasn’t until about 150 years later, around 1850 that the Vigenere cipher was cracked
by an

eccentric man by the name of Charles Babbage. He broke the cipher by realizing th
at
although there is an alphabet
-
switch every letter there is a codeword of limited length,
therefore making the decryption possible by finding the codeword length and then using logic
to determine letters of the codeword. Once that step has been accompli
shed the remainder of
the problem is just plugging in the letters and if the square had been changed it still will only
take the use of frequency analysis to do the rest.


Modern Cryptography


From this point on in history there was a change in the way we
utilized encryption
techniques. The telegraph saw its first signs around 1844 and shortly after its invention came
Morse code and then after that came Marconi and his wireless telegraphy in the early 1900s.
Cryptography
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With these great technologies came the need for

new forms of encryption and also as history
has taught us the breaking of these forms of encryption.


Duri
ng World War I an ambitious man by the name of Arthur Zimmerman devised a way
to send communications securely via a collaboration of codebooks. For
each codebook there
was an answer
-
key that sorted the codes numerically. Because there was no use of
cryptography and there were only two codebooks it was thought that this would be a sure way
to eliminate any possibility of breaking the codes.


Again, th
e thought was not warranted. It did not take long for messages to be decoded.
The problem that was found to be wrong with the use of codes and codebooks was that they
took so long to create and distribute that they were used for extended periods of time


so
much time that the interceptors of the messages could piece together their own codebooks.
Also,

since the codebooks were used for such a long period, the pieced
-
together codebook
would work for months before a new one had to be made.


The Second Wo
rld War the Germans came up with a much better plan, albeit one that
still didn’t pan out. Arthur Scherbius created a machine that would encrypt a message using a
team of three rotors and electronic signals. It was the famous Enigma machine and the way i
t
worked was via a group of three rotors and electronic signals it would take a typed letter and
display the cipher text. It was an elaborated version of the Vigenere cipher in that it would
change based on each letter typed. The machine was genius becau
se of the way it was set. The
three rotors were set daily based on tables that only lasted for two weeks. This way if an
enemy captured the list of tables it would only do them good for a short time.

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The main problem that the Enigma had was that it had
a few flaws including that it
never encrypted the same letter as the
plaintext letter, but more importantly was that it was up
against one of the greatest men in the history of cryptography, Alan Turing.


At his post in Bletchley Park, Britain’s black cham
ber of the 1900s Alan Turing devised
ways of utilizing the weaknesses of the Enigma machine to his advantage and created a
machine called a “bombe” to run through the settings that matched his constraints within a
couple of hours. With the “bomb” breaking

the Enigma the Second World War
was shortened
by nearly three years (Singh), and saved hundreds of lives.
Alan’s life was one with great
promise that ended in great tragedy. The best representation I have seen is from Simon Singh’s
“The Science of Secre
cy”:


Alan Turing was another cryptanalyst who did not live long enough to receive any public
recognition [Babage was the other]. Before the war Turing had shown himself to be a mathematical genius,
publishing work that laid down the ground rules for comp
uters and computing. At Bletchley Park he turned
his mind to cracking Enigma, arguably making the single most important contribution to finding the flaws in
the German cipher machine. After the war, instead of being acclaimed a hero, he was persecuted fo
r his
homosexuality. In 1952, while reporting a burglary to the police, he naively revealed that he was having a
homosexual relationship. The police felt they had no option but to arrest and charge him with ‘Gross
Indecency contrary to Section 11 of the
Criminal Law Amendment Act 1885’. The newspapers reported the
subsequent trial and conviction, and Turing was publicly humiliated.


Turing’s secret had been exposed, and his sexuality was now public knowledge. The British
Government withdrew his security

clearance. He was forbidden to work on research projects relating to the
development of the computer. He was forced to consult a psychiatrist and to undergo hormone treatment,
chich made him impotent and obese. Over the next two years he became severel
y depressed, and on 7
June 1954 he went to his bedroom, carrying with him a jar of cyanide solution and an apple. He dipped the
apple in the cyanide and took several bites. At the age of just forty
-
two, one of the true geniuses of
cryptanalysis committed

suicide.”




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Cryptography Today

The last few breakthroughs in cryptography involve a different methodology.
Computers came into play along with ARPANET and what is now the internet. Using the
computer we can use a different type of encryption that
involves codewords (or keys as they
are referred to now) that are of an exceedingly long length. The computer can use these to
produce an encrypted message that would take such a long time to figure out that it would
span the life of the universe or as St
eve Gibson put it on his podcast “Security Now” there are
“more possible keys than atoms in the known universe.”


The problem that was solved most recently was the problem of getting the key to the
recipient without having to personally give it to them an
d it was solved by Whitfield Diffie and
Ralph Merkle. What they discovered was the idea of “public key” cryptography. It is a way of
allowing a message to be encrypted by one person but in such a way that it cannot be
unencrypted in the same way it was d
ecrypted.

The trio that are credited for the discovery of how to create such a function are Rivest,
Shamir, and Adleman (RSA), although there were actually two men back in Britain
working for
the Government Communications Headquarters (formed from the remi
nisce of Bletchley Park)
who made the discovery about ten years earlier, James Ellis and Clifford Cocks.

The way that it works is by taking two exceedingly large prime numbers, multiplying
them together you have the public key. When a person sends you a m
essage using your key
and the encryption method because of the use of modulus to encrypt the message there is no
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way to undo the encryption


unless you have the two numbers that were multiplied together
to get the key.

This way the message cannot be dec
rypted by anyone and the person receiving the
message does not have to find a way to meet up to be told the key. All a person needs to do is
create their public key and put it out for people to use.

Cryptography in the Future

The forms of encryption in us
e today are extremely strong and no
body in the world of
academia has been able to find a way to quickly find prime factors of really large numbers in
such a way that would make it worthwhile to use brute force to decrypt a message, but
because history has
always proven us wrong when we think we have something unbreakable
there is now a new type of cryptography on the horizon. Quantum cryptography is the next
wave of cryptological methodologies and as of now it is still in early stages of development but
it

involves using the distortion of how we perceive things to encrypt messages. The
mathematics involved make it quite difficult to understand and will therefore have to be
explained by someone with a greater understanding than myself.