day 13 classical transposition ciphers. objectives students will be able to… …understand what...

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

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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

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t

n

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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.