Download - Rail-Fence Cipher Presentation

The Rail-Fence Cipher

Matt BremsMelissa Hannebaum

Franklin College

Cryptology

Matt Melissa

Be Rational.

Get Real.

Methods of Character Encryption

Substitution Transposition

FRANKLIN

PQLUFITU

Plaintext

Ciphertext


Substitution

FRANKLIN

PQLUFITU

Plaintext

Ciphertext

Plaintext

Ciphertext

Part Of Key


Transposition

FRANKLIN

NILKNARF

Plaintext

Ciphertext

Transposition Cipher• Columnar• A method of encryption in which the plaintext

is shifted according to a regular system, so that the ciphertext constitutes a permutation of the plaintext.

Function

Columnar Transposition As A Function

f(x)=y

f(x) = y


Transposition Cipher

f(plaintext)=ciphertext

Plaintext

Ciphertext


• The columnar transposition cipher uses a bijective (one-to-one and onto) function to encrypt the text and an inverse function to decrypt the text.

f (ciphertext)=plaintext-1

f(plaintext)=ciphertext

Columnar Transposition

• Three ColumnsC = 3

COLUMNARC O L

U M N

A RCUAOMRLN

Rail-Fence Cipher

• Two Columns• C = 2

COLUMNARC

U

A

O

MR

LN

CLMAOUNR

Rail-Fence Cipher

• C = 2

C A

RN

M

U

L

OCLMAOUNR

COLUMNAR

Selected Formulas

Rail-Fence Cipher

S M I T HS I H M TS H T I MS T M H IS M I T H

Rail-Fence Cipher

• 4 permutations• Conjecture: Length n

implies order (n-1)

S M I T HS I H M TS H T I MS T M H IS M I T H

Rail-Fence CipherF R A N K L I N C O L L E G E M A T H A N D C O M P U T I N G !

F A K I C L E E A H N C M U I G R N L N O L G M T A D O P T N !

F K C E A N M I R L O G T D P N A I L E H C U G N N L M A O T !

F C A M R O T P A L H U N L A T K E N I L G D N I E C G N M O !

F A R T A H N A K N L D I C N O C M O P L U L T E I G N E G M !

F R A N K L I N C O L L E G E M A T H A N D C O M P U T I N G !

Order = 5

Rail-Fence Cipher

• Length of plaintext = 5• Cycles of characters• Can be numerous cycles

in one encryption

S M I T HS I H M T

0 1 2 3 4

0 1 2 3 4

(0) (1, 3, 4, 2)

Trivia

l Cycl

e Initial Cycle

Length = 16F R A N K L I N C O L L E G E !F A K I C L E E R N L N O L G !

(0) (1-8-4-2) (3-9-12-6) (5-10) (7-11-13-14) (15)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Length = 16

1

8

4

2

3

9

12

6

7

11

13

14

5

10

(0) (1-8-4-2) (3-9-12-6) (5-10) (7-11-13-14) (15)

F R A N K L I N C O L L E G E !F A K I C L E E R N L N O L G !

Length Cycle

2 1

3 2

4 2

5 4

6 4

7 3

8 3

9 6, 2

10 6, 2

Length Cycle

11 10

12 10

13 12

14 12

15 4, 2

16 4, 2

32 5

49 21

64 6

Length of 2 = n-cycle n


F A K I C L E E A H N C M U I G R N L N O L G M T A D O P T N !

F K C E A N M I R L O G T D P N A I L E H C U G N N L M A O T !

F C A M R O T P A L H U N L A T K E N I L G D N I E C G N M O !

F A R T A H N A K N L D I C N O C M O P L U L T E I G N E G M !


Primes

Length = 32 = 2 5 5-Cycle

General Rules

Answered Questions

• What are the fixed points in a RFC?

• What are the fixed points in a general CTC?

• Can we tell when the RFC has a k-cycle?

Unanswered Questions

• Simple way to calculate length of initial cycle?

• Can we tell when the CTC has a k-cycle?

• How much of this works if C > 2?

Questions?