CRYPTOGRAPHY
Lecture 1
3 week summer course
Course structure
• Format: Part lecture, part group activities
• HW:
– Daily assignments, some in-class and some take
home. Keep these in a portfolio.
– Weekly 7-10 page essays on history of
cryprography (topics not in book)
– Final project and presentation (you propose the
topic and format)
– Final grade will be determined by portfolio of work
including the above.
Expectations
• Most work should be typed. Even work
done in class should (usually) be typed
and added to portfolio.
• Attendance is mandatory.
• Respectful behavior to your peers.
• Your day is devoted to this class.
General Rules
• When decrypting or deciphering, all
tools are fair. You may do anything legal
to obtain the information you want.
• However, you must disclose the methods
you used. In unusual cases, you can keep
some technique secret from your peers,
with my approval, for a limited amount
of time.
Why we need secure means of
communication?
• Government: diplomacy is sometimes
better done quietly.
• Military: strategies often rely on the
element of surprise.
• Business: competitors will win if they
know your secrets.
• Love letters . . . Secret affairs . . .
History of secret writing I
• Herodotus chronicled the conflicts
between Greece and Persia in the fifth
century (499-472 BCE).
• Greece was organized into small,
disunited, independent city-states.
Persia was a large empire (and growing)
ruled by Darius, and later his son
Xerxes.
History of secret writing I
• The Persian rulers had a long history of feuds
with Athens and Sparta. Any minor problem
could spark a major war.
• When Xerxes built a new capital for his
kingdom (Persepolis), other countries sent
tributes and gifts, but Athens and Sparta did
not. Xerxes was upset by this lack of
respect, and began mobilizing forces to
attack the Greek city-states.
History of secret writing I
• The Persians spent 5 years building up their
forces. This was one of the largest fighting
forces in history. In 480 BCE they were
ready to attack.
• There was a Greek exile, Demaratus, who
lived in the Persian city of Susa and saw the
forces being built up for war with Greece. He
still felt a loyalty to his homeland, and
decided to send a message to warn the
Greeks of the impending attack. But how?!
History of secret writing I
• He scraped the wax off a pair of
wooden folding tablets, wrote on the
wood underneath, and covered over the
tablets with wax. The apparently blank
tablets got to Greece, where they
realized (how?) that there may be a
secret message in it, and found it. Now
the Persians lost the element of
surprise – and the war.
Steganography
• This is hidden writing or steganography.
Another example is the story of
Histaiaeus, who wanted to encourage
Miletus to revolt against the Persian
king. He shaved the head of his
messenger, wrote the message on his
scalp, and waited until the hair grew
back.
Steganography
• Other examples include
– The ancient Chinese would write messages
on fine silk, roll it into a tiny ball, coat it
with wax and swallow it . . .
– Secret ink: in the 1st century, Pliny the
Elder explained how the “milk” of the
thithymallus plant becomes transparent
after drying, but reappears upon heating.
(Many organic fluids behave this way, e.g.
urine)
Steganography
In the 16th century, the Italian scientist Giovanni
Porta described how to conceal a message in a
hardboiled egg by making ink from alum and
vinegar and writing on the shell. The solution
penetrates the shell, leaving its mark only on
the egg underneath!
During WWII, German agents in Latin America
would photographically shrink down a page of
text to a little dot, and hide it on top of a
period or dotted I on a page. A tip-off allowed
American agents to find this in 1941.
Steganography
Steganography suffers
from one problem: if it is
uncovered all is lost.
Cryptography
If we hide the message
but then make it difficult
to read if found, we have
an added level of
security.
Cryptography
The aim is to hide the
meaning of the message
rather than its presence.
This can be done by
scrambling the letters
around.
Transposition Ciphers
Make an anagram according to a
straightforward system (404 BCE):
The sender winds a piece of cloth or
leather on the scytale and writes the
message along the length of the
scytale. Then unwinds the strip,
which now appears to carry a list of
meaningless letters. The messenger
would take the leather strip
(sometime wearing it as a belt) and
when he arrives at his destination,
the receiver winds the strip back on
a scytale of the same diameter.
Transposition Ciphers
Rail fence transposition:
Round and round the mulberry bush the monkey chased
the weasel
r u d n r u d h m l e r b s t e o k y h s d h w a e
o n a d o n t e u b r y u h h m n e c a e t e e s l
Becomes:
rudnrudhmlerbsteokyhsdhwaeonadonteubryuhhmneca
eteesl
Simple Transposition
• Simple Columnar Transposition
• The key information is the number k of
columns.
• Encipherment: Plaintext is written in lines k
letters wide and then transcribed column by
column left to right to produce ciphertext.
This and the next few slides copied from:
http://www.rhodes.edu/mathcs/faculty/barr/Math103CUSummer04/TranspositionSlides.pdf
Simple Transposition: example
“April come she will
When streams are ripe and swelled
with rain”
Convert to a transposition cipher
using k=10
Simple Transposition: example
1234567890
APRILCOMES
HEWILLWHEN
STREAMSARE
RIPEANDSWE
LLEDWITHRA
IN
AHSRL
PEIIE
NIOWS
WRSNE
IPETI LNRWR
EDLLA AWCLM
DTMHA SHEER
EA
Simple Transposition
• Decipherment: If n is the length of the ciphertext,it is
written column by column left to right down in a k
×(n DIV k )rectangular array with a “tail ” of length n
MOD k as shown. Transcribing row by row produces
plaintext.
M E S S A G E
The message is n=37
A N D M O R E
letters long. It is set up
A
N
D
S
T
I
L
in k=7 columns. So there
L M O R E U N
are
T I L I T E N
37 DIV 7 = 5 rows
and the tail is
D S
37 mod 7 = 2
HW#1a
1. Given the message
NNDATEAOIIOTINHRNNODTHSGAECSUIHEMEN
IECSTIWORSGAISYNOROINNETGREUNODNUIL
DSCRCTP
with k=8: Decipher it.
HW#1a
2. Encipher a message with a given value of k. Now
the groups swap messages and are given the
value of k. Decipher the messages.
3. Encipher a message with a value of k between 2
and 10 and swap ciphers. Now decipher the
message . . .
Transposition Ciphers
A double transposition offers more
security:
Rudnrudhmlerbsteokyhsdhwaeonadonteubryuhhmnecaeteesl
Becomes
u n u h l r s e k h d w e n d n e b y h m e a t e l
R d r d m e b t o y s h a o a o t u r u h n c e e s
Becomes
unuhlrsekhdwendnebyhmeatelrdrdmebtoyshaoaoturuhncees
Column Transposition
A G A M E M N O N
1 4 2 5 3 6 7 9 8
key phrase
convert to numbers
ABCDEFGHIJKLMNOPQRSTUVWXYZ
AEGMNO delete the letters not used
134579 assign them numbers
2 68 according to how they appear
Example from http://hem.passagen.se/tan01/transpo.html
Column Transposition
A
1
s
r
e
r
G
4
e
e
a
s
A
2
n
d
d
j
M
5
d
c
q
*
E
3
a
a
u
*
M
6
r
r
a
*
N
7
m
t
r
*
O
9
o
o
t
*
N
8
u
h
e
*
key phrase
convert to numbers
The code is then
Srer-nddj-aau-eeas-dcq-rra-mtr-uhe-oot
Double Column Transposition
M
5
s
j
s
m
o
Y
7
r
a
d
t
t
C
2
e
a
c
r
E
3
r
u
q
u
N
6
n
e
r
h
A
1
d
e
r
e
E
4
d
a
a
o
key phrase
convert to numbers
The code is then
DEREE ACRRU QUDAA OSJSM ONERH RADTT
Transposition Grille
Example from http://hem.passagen.se/tan01/transpo.html
Transposition Grille
We need
more
machine
gun
ammunition
fast xx
Transposition Grille
Double column Transposition
How do you get back to where you started?
Reverse the process.
Secure transmission
Steganography
cryptography
Transposition
Substitution
HW #1b
• Use each of the transposition ciphers we
talked about today to encode your own
messages. Now swap them and (without
sharing the key, or even the method of
encryption) try to decipher them.
Don’t feel bad if you can’t decipher. It is hard, that’s the point!
• Look online for tools to help decipher
transposition cipher and use them.
• Read the code book’s introduction and
chapter 1 pages 1-14