Transcript Welcome to Cryptology - Science and Mathematics Academy

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
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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
4
d = _________
(4, 1, 2, 3)
f = ____________________
Plaintext
This is an example → this isan exam plex
________________________________________
Ciphertext
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
Plaintext: This is an
example of a
column
permutation
cipher.
Key: break
Key: (2,5,3,1,4)
HAMFURTIXIXEOPT
NEXINPAMMIPXTS
AOLEACRSELCNUO
HX
1 22 33 44 55
t
hh ii ss ii
s aa nn ee xx
a m
m pp ll ee
o ff aa cc oo
l
uu m
m nn pp
e rr m
m uu tt
a tt ii oo nn
c ii
pp hh ee
r xx xx xx xx
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
EEADU
RTCPJ
TSDDS
SOSYS
INR
LTDSR
OUUFI
AOEGE
OEOAC
TNNCG
TSSTF
RRRRS
WNLHO
EHNTL
EMETT
MDCET
NEROT
EPMWA
HFLAU
YDYRR
DRHXS
CFIEM
WERUV
RAEEN
NEOOE
WHOHO
EDSHA
AAINA
OTOTS
RESTH
(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
Plaintext: This an example of a turning grille cipher
Ciphertext: HSNEMTIIE AXLFRGGLX IPANLCIHR
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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.