Post on 20-Jun-2015
description
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
Methods of Character Encryption
Substitution
FRANKLIN
PQLUFITU
Plaintext
Ciphertext
Plaintext
Ciphertext
Part Of Key
Methods of Character Encryption
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
Columnar Transposition As A Function
Transposition Cipher
f(plaintext)=ciphertext
Plaintext
Ciphertext
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.
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 = 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 = 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 = 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 = 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 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
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?