Presented by Matthew Brems and Melissa Hannebaum, students at Franklin College, documenting results of summer research under the direction of Dr. Robert Talbert, PhD.

1. The Rail-Fence Cipher
Matt Brems
Melissa Hannebaum
Franklin College

2. Cryptology
Be
Rational.
Get
Real.

3. Methods of Character Encryption
Substitution Transposition
Plaintext
Ciphertext

4. Methods of Character Encryption
Substitution
Plaintext
Ciphertext
Part
Of
Key

5. Methods of Character Encryption
Transposition
Plaintext
Ciphertext

6. 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.

7. Columnar Transposition As A Function
f(x) = y

8. Columnar Transposition As A Function
Transposition Cipher
Plaintext
Ciphertext

9. Columnar Transposition As A Function
• 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.

10. Columnar Transposition
• Three Columns
C = 3

11. Rail-Fence Cipher
• Two Columns
• C = 2

12. Rail-Fence Cipher
• C = 2

13. Selected Formulas

14. Rail-Fence Cipher

15. Rail-Fence Cipher
• 4 permutations
• Conjecture: Length n
implies order (n-1)

16. Rail-Fence Cipher
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 !
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 !

17. Rail-Fence Cipher
• Length of plaintext = 5
• Cycles of characters
• Can be numerous cycles
in one encryption
0 1 2 3 4
0 1 2 3 4

18. Length = 16
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 !
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

19. Length = 16
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 !

20. Length = 16
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 !

21. Length = 16
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 !

22. Length = 16
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 !

23. Length = 16
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 !

24. 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

25. 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 !
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 !
Primes

26. General Rules

28. 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?

29. 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?

30. Questions?