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 5t h i s is a n e xa 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: breakKey: (2,5,3,1,4)HAMFURTIXIXEOPTNEXINPAMMIPXTSAOLEACRSELCNUOHX

1tsa

o

l

e

a

c

r

2ham

f

u

r

t

i

x

3inp

a

m

m

i

p

x

4sel

c

n

u

o

h

x

5ixe

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.