Day 13 Classical Transposition Ciphers
Dec 29, 2015
Day 13
Classical Transposition Ciphers
Objectives
Students will be able to…
…understand what transposition ciphers are and how they are implemented.
…encrypt and decrypt using classic transposition ciphers.
…create and use transposition ciphers of their own.
Transposition ciphers
Rearrange the existing letters in the plaintext.
Rail-Fence cipher
This is an example
t i e p
h s s n x m l
i a a e
tiephssnxmliaae
Permutation cipher
Key (d, f)
d is a fixed length
f is a permutation function
Example if d = 4 then f could be (4, 2, 1, 3)
Break the plaintext up into blocks of length d.
Shuffle each block according to d.
Permutation: Example
d = _________
f = ____________________
Plaintext
________________________________________
Ciphertext
________________________________________
4
This is an example
(4, 1, 2, 3)
→ this isan exam plex
sthi nisa mexa xple → STHINISAMEXAXPLE
Column permutation cipher
Select keyword
Determines the number of columns
Determines the order of the columns
Column permutation cipher: Example
1 2 3 4 5
t h i s i
s a n e x
a m p l e
o f a c o
l u m n p
e r m u t
a t i o n
c i p h e
r x x x x
Plaintext: This is an example of a column permutation cipher.
Key: break
Key: (2,5,3,1,4)
HAMFURTIXIXEOPTNEXINPAMMIPXTSAOLEACRSELCNUOHX
1
t
s
a
o
l
e
a
c
r
2
h
a
m
f
u
r
t
i
x
3
i
n
p
a
m
m
i
p
x
4
s
e
l
c
n
u
o
h
x
5
i
x
e
o
p
t
n
e
x
Column permutation cipher: cryptanalysis
Determine possible underlying rectangles. How?
Discover which of the possible rectangles is correct (Note: vowels account for about 40% of characters.)
Determine the column order. How?
Column permutation cipher: cryptanalysis – centiban
weight
Which columns are matched?
U.S. government studied a collection of 5000 digrams
Calculated a value called a centiban weight, for each digram
Columns that produced a sum total of centiban values from the digrams that are greater then other columns have a higher probability of being the correct column.
Column Cipher: Example
NETEF LTDSR TSSTF MDCET DRHXS WHOHO EEADU OUUFI RRRRS NEROT CFIEM EDSHA RTCPJ AOEGE WNLHO EPMWA WERUV AAINA TSDDS OEOAC EHNTL HFLAU RAEEN OTOTS SOSYS TNNCG EMETT YDYRR NEOOE RESTH INR
(Spillman, 2005, p. 91)
Double-Transposition Cipher
Perform a column transposition cipher twice. You can use the same keyword.
Makes it more difficult for cryptanalysis.
Can be broken when you have multiple ciphertext documents.
History of Transposition Ciphers
Used by Greeks
Used by the U.S. during the Civil war
Used by the Germans in WWI (Turning grille)
Turning grille
t h i s a n
e x a m p l
e o f a t u
r n i n g g
r i l l e c
i p h e r x
Plaintext: This an example of a turning grille cipherCiphertext: HSNEMTIIE AXLFRGGLX IPANLCIHR
TAEOUNREP
Transposition Assignment
Parts of this assignment are independent and parts require a partner.
Review
What is the principle behind transposition ciphers?
Classically what was an important skill for breaking a transposition cipher?
How can mathematics be used to break a column transposition cipher.