CRYPTOGRAPHY
Lecture 2
Course structure
• Format: Part lecture, part group
activities
• HW:
– Daily assignments, some in-class and some
take home. Keep these in a portfolio.
– One 7-10 page essay on a related topic of
your choice. 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.
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#2a
1. Given the message
NNDATEAOIIOTINHRNNODTHSGAECSUIHEMENI
ECSTIWORSGAISYNOROINNETGREUNODNUILDS
CRCTP
with k=8: Decipher it.
HW#2a
2. Encipher 3 messages with with some 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 swap messages,
without sharing the value of k. Now decipher
the message . . .
Transposition Ciphers
A double transposition offers more
security:
rudnrudhmlerbsteokyhsdhwaeonadonteubryuhhmnecaeteesl
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
Transposition
How do you get back to where you started?
Reverse the process.
Secure transmission
Steganography
cryptography
Transposition
Substitution
HW #2b
• 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.
http://math.ucsd.edu/~crypto/java/EARLYCIPHERS/RectTran.html
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.