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Introduction to
Cryptology I
Cryptography
&
Cryptanalysis
M. Meyer
Bridges To Computing
2010
Table of Contents
•
•
•
•
Resources
Defined
History of Cryptography & Cryptanalysis
Computers and Cryptography
Resources
• For detailed information:
o An Overview of Cryptography - by Gary C. Kessler:
http://www.garykessler.net/library/crypto.html
o Wikipedia actually has a good entry for
cryptography: http://en.wikipedia.org/wiki/Cryptography
o Free PGP software can be gotten from the GNU-PG:
http://www.gnupg.org/
• Limited but easier/fun resources:
o Build some secret coding devices:
http://www.unmuseum.org/excoded.htm
o Creating & breaking substitution ciphers:
http://www.physicspost.com/articles.php?articleId=174
Definitions
• Cryptography: (from the Greek kryptos, "hidden,
secret"; and gráphō, "I write") the practice and study of
hiding information.
• Cryptanalysis: the study of methods for obtaining the
meaning of encrypted information.
• Cryptology: ... basically, the study of both of the items
above.
• Code: An alternate expression of some unit of
information, designed to condense and/or obfuscate
that information.
• Cipher: An algorithm used to encode information.
SPARTA!!!
• One of the earliest encryption devices was the Spartan
Scytale (c 500 B.C.) which consisted of a ribbon
wrapped around a dowel of a particular diameter and
length.
• The secret message was written on the ribbon while the
ribbon was wrapped on the dowel.
• The ribbon was then removed and transported to the
other field commander who had an identical dowel.
• If the ribbon was intercepted it look like jumble of
letters.
• Officially this kind of encryption would be called a
"transposition" cipher.
THIS IS A SCYTALE!!!
Cryptanalysis - 1
• Question 1: If you didn't have the dowel and intercepted
the message, could you still break the code? How?
• Question 2: What were (and are) the limitations of the
Scytale cipher?
• More information on (and examples of) transposition ciphers
can be found here:
• http://www.counton.org/explorer/codebreaking/transpositi
on-ciphers.php
• NOTE: A Russian spy ring, broken up in 2008 was sending
messages embedded in letters (first letter of each row) using
a form of transposition cipher (rail-fence).
Hail Caesar!!!
• One of the simplest examples of
a substitution cipher is the Caesar
cipher, which is said to have
been used by Julius Caesar.
• Caesar decided that shifting
each letter in a message would
be his standard algorithm, and so
he informed all of his generals of
his decision, and was then able
to send them secured messages.
Caesar Cipher
Using the Caesar Shift (3 to the right), the message,
"RETURN TO ROME"
would be encrypted as,
"UHWXUA WR URPH"
• Technically the Caesar cipher is a shift cipher, since
the cipher-text is derived from the plain-text
alphabet by shifting each letter a certain number
of spaces.
• Other substitution ciphers such as the St. Cyr Cipher
are also substitution ciphers.
Cryptanalysis (2)
• Question 1: If you don't have the "shift" and
intercepted the message, could you still break the
code? How?
• Question 2: How could the Caesar cipher be made
stronger?
Brute Force
• The Caeser cipher was successful because it was
used in a time when most people couldn’t read
regular text, much less understand the concept of
encoded text.
• Question: Given an message, how many different
encodings are possible using the Caeser cipher
(hint how many letters are in the alphabet).
• Break this code if you can: FG EGJW LZSF LOWFLQ
XANW LJAWK SJW FWUUWKSJQ
• http://www.secretcodebreaker.com/caesarcipher.html
Letter Frequency
• Heuristics refers to experience-based techniques
for problem solving and discovery.
• In most languages certain letters are used far more
frequently than other letters.
• For English letters (most too least common):
e t a o i nsrhldcumfpgwybvkxjqz
• You can use letter frequency to help you crack a
Caesar Ciphered message by counting the
frequency of encrypted letters.
• The most popular encrypted letter is likely to
translate to 'e' 't' or 'a'.
Word Frequency
• Just as certain letters are more popular then other
letters in a given language, certain words are more
likely to appear than other words.
• For example the top 20 most common words in the
English Language are:
The of and a to in is you that it
he was for on are as with his they I
• If a coded message still has spaces in it word frequency
is especially easy to use!!
Example: VLR XKA F HKLT QEB PBZOBQ.
• Note: Another “frequency heuristic” is repeated letter
frequency: KWW TWW TGGC ZGGC
Organized Cryptanalysis
• In the 9th century a Muslim scholar
named Al-Kindi wrote his "Manuscript for
the Deciphering of Cryptographic
Messages",
• Among his many contributions was the
observation that the frequency of the
letters in languages, make most
substitution ciphers a very weak form of
encryption.
• In his book he also described a wide
variety of cryptanalysis techniques,
including some that could be used for
polyalphabetic ciphers.
Polyalphabetic ciphers
• From the 9th century on, most serious cryptography
attempts moved into the realm of polyalphabetic
ciphers.
• A polyalphabetic cipher is any cipher based on
substitution, using multiple substitution alphabets.
• Polyalphabetic ciphers were used as far back as
the 8th century and were in widespread use well
into the 1960’s.
• The Enigma machine a famous cryptographic
device used by the Nazi’s in WWII was a very
complex machine but still fundamentally at its core
it used a polyalphabetic substitution cipher.
Vigenère cipher
• The Vigenère cipher is probably the best-known
example of a polyalphabetic cipher, though it is a
simplified special case.
• Just like a Caesar cipher I am going to shift letters. But
for each letter, I might use a different shift. Example:
Vigenere cipher with shift keys (1,2,3)
DOG
becomes:
EQJ
• Rather than using numbers (like 1,2,3) Vigener ciphers
often used a “key phrase” that is a word or phrase that
was used to make the shift, letter by letter.
Vigenère Table
Vigenère Example
S E C R E TME S S AG E
K E Y PHRA S E K E Y P
C I A G L K MWW C E E T
•
•
•
•
First line is the original message.
Second line is the cipher key phrase.
Third line is encrypted message.
Online Resource:
http://sharkysoft.com/misc/vigenere/
Cryptanalysis (3)
• For many years the Vigenère Cipher was
considered unbreakable!
• It was finally cracked by the British cryptographer
Charles Babbage in 1854.
• You may remember Babbage from the lecture on
the History of Computer Science.
• Babbage identified a series of steps that could be
taken to break a message encoded using a
Vigenère cipher, provided that:
1. The key use was shorter than the message enciphered!
2. The message itself is long enough that the key is used repeatedly (even
better would be multiple message encoded with they key)!
Babbage's Method
1. Search for sequences of letters that appear more
than once in the encoded text.
o
The most likely reason for such repetitions is that the same sequence of
letters in the plaintext has been enciphered using the same part of the
keyword.
2. Graph all of the repeated letter sequence by how
many letter separate the repetition.
3. Try and find the least common denominators
(factors) used by the repeated sequences.
4. Find the most common factor among all repeated
sequences.
5. This is most likely the length of the key used to
encode the message!!!
Babbage's Method (2)
Babbage's Method (3)
• With the key length in hand the message can be
broken up into columns the width of the key.
• Letter frequency analysis can then be applied to
each column!
• With a little bit of work the message can be
translated and then the key itself can be derived
for future use.
• Resource Link:
http://www.simonsingh.net/The_Black_Chamber/cr
acking_example.html
Babbage's Method (4)
One Time Pass
• But what about Vigenère Ciphers that don't repeat
their keys (where key is as long as the message)?
• Believe it or not, such ciphers, (provided that the
key is random, the same length as the message,
and never used again) ARE unbreakable.
• The one time key, or one time pass, cipher is
unbreakable because you can, with time, find a
key for such a message that will generate any
phrase that you wish.
• Example: The coded text-> optsqkles
Could mean ->
surrender
Or ->
attacknow
Enigma
• During WWII Alan Turing
helped create a
electromechanical
machine (computer) to
help break Enigma codes.
• The computer age
completely changed our
approach to cryptology.
"Nazis. I hate these guys."
- Indiana Jones
Computer Cryptography
• "The development of digital computers and electronics
after WWII made possible much more complex ciphers.
• In a standard alphabetic cipher each letter can be
transformed into one of 25 possible other characters,
while a computer can represent 109,000 characters
using Unicode.
• Furthermore, computers allow for the encryption of any
data representable in binary format, unlike classical
ciphers which only encrypted written language texts."
• Computer use has thus supplanted linguistic
cryptography for cipher design.
Computer Cryptanalysis
• Modern cryptanalysis is also computer driven.
• Computers can test billions of possible cipher
solutions (brute force attack) in a matter of
minutes.
• Online tools exists for breaking Caesar and
Vigenere ciphers:
•
•
http://www.secretcodebreaker.com/caesar-cipher.html
http://sharkysoft.com/misc/vigenere/
The End