Laura Tinney
Dr. Greg Boudreaux
1
Outline

 Some definitions and background
 Trifid Cipher
 What does it look like?
 How does it work?
 Research Project
 What is being done to attack this cipher?
2
Some Definitions

 Cipher: a method of transforming a text in order to
conceal its meaning
 Encipher: to convert a message into cipher
 Decipher: to convert into intelligible form.
 Cryptography: the enciphering and deciphering of
messages in secret code or cipher
3
Some Background

 Felix Delastelle
 1840-1902
 Published 1902
 Traité Élémentaire de Cryptographie
“Delastelle invented a fractionating system of considerable
importance in cryptology”
David Kahn
4
The Trifid Algorithm

1
1
2
2
3
1
3
2
3
1
1
1
1
2
2
2
3
3
3
2
3
5
The Trifid Algorithm

1
1
2
3
J
K
L
1
2
M
N
O
3
P
Q
R
1
2
3
1
A
B
C
1
2
D
E
F
3
G
H
I
M
A
T
2
1
3
2
3
S
T
U
2
V
W
X
3
Y
Z
!
H
Layer
Column
Row
6
The Trifid Algorithm

1
1
2
3
J
K
L
1
2
M
N
O
3
P
Q
R
1
2
3
1
A
B
C
1
2
D
E
F
3
G
H
I
M
Layer
2
Column
1
Row
2
A
T
2
1
3
2
3
S
T
U
2
V
W
X
3
Y
Z
!
H
7
The Trifid Algorithm

1
1
2
2
3
J
K
L
1
2
M
N
O
3
P
Q
R
1
2
3
1
A
B
C
1
2
D
E
F
3
G
H
I
M
A
T
H
Layer
2
1
3
1
Column
1
1
2
2
Row
2
1
1
3
1
3
2
3
S
T
U
2
V
W
X
3
Y
Z
!
8
The Trifid Algorithm

1
1
2
2
3
J
K
L
1
2
M
N
O
3
P
Q
R
1
2
3
1
A
B
C
1
2
D
E
F
3
G
H
I
M
A
T
H
Layer
2
1
3
1
Column
1
1
2
2
Row
2
1
1
3
1
2
3
2
3
S
T
U
2
V
W
X
3
Y
Z
!
1
2
9
The Trifid Algorithm

1
1
2
2
3
J
K
L
1
2
M
N
O
3
P
Q
R
1
2
3
1
A
B
C
1
2
D
E
F
3
G
H
I
1
3
2
3
S
T
U
2
V
W
X
3
Y
Z
!
M
A
T
H
Layer
2
1
3
1
2
1
2
1
Column
1
1
2
2
1
1
3
2
Row
2
1
1
3
1
1
2
10
3
The Trifid Algorithm

1
1
2
2
3
J
K
L
1
2
M
N
O
3
P
Q
R
1
2
3
1
A
B
C
1
2
D
E
F
3
G
H
I
1
3
2
3
S
T
U
2
V
W
X
3
Y
Z
!
M
A
T
H
J
Layer
2
1
3
1
2
1
2
1
Column
1
1
2
2
1
1
3
2
Row
2
1
1
3
1
1
2
11
3
The Trifid Algorithm

1
1
2
2
3
J
K
L
1
2
M
N
O
3
P
Q
R
1
2
3
1
A
B
C
1
2
D
E
F
3
G
H
I
1
3
2
3
S
T
U
2
V
W
X
3
Y
Z
!
M
A
T
H
J
A
O
H
Layer
2
1
3
1
2
1
2
1
Column
1
1
2
2
1
1
3
2
Row
2
1
1
3
1
1
2
12
3
A little about the project

 Cryptology Class
 The Team
 The Programmer
 The Analyzer
 As a group
13
Specifics/Assumptions
of the Project

14
Specifics/Assumptions
of the Project

Chosen plaintext attack: assumes the attacker has the ability to choose whatever
text they want to be encrypted, submit that material and receive the corresponding
cipher text. (Encryption here is applying the Trifid Algorithm)
15
Recall the grid…

Text
Layer
Column
Row
16
Recall the grid…

Text
Layer
0
1
2
Column
3
4
5
Row
6
7
8
17
Recall the grid…

Text
Layer
0
1
2
Column
3
4
5
Row
6
7
8
Layer
0
3
6
Column
1
4
7
Row
2
5
8
Text
18
Recall the grid…

Text
Layer
0
1
2
Column
3
4
5
Row
6
7
8
Layer
0
3
6
Column
1
4
7
Row
2
5
8
Layer
0
1
2
Column
3
4
5
Row
6
7
8
Text
Text
19
0 1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16 17
18 19 20 21 22 23 24 25 26
-----------------0 9 18 1 10 19 2 11 20
3 12 21 4 13 22 5 14 23
6 15 24 7 16 25 8 17 26
-----------------0 3 6 9 12 15 18 21 24
1 4 7 10 13 16 19 22 25
2 5 8 11 14 17 20 23 26
------------------
0 1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16 17
18 19 20 21 22 23 24 25 26
20
21
22
23
24
25
Conjecture

0 1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16 17
18 19 20 21 22 23 24 25 26
-----------------0 9 18 1 10 19 2 11 20
3 12 21 4 13 22 5 14 23
6 15 24 7 16 25 8 17 26
-----------------0 3 6 9 12 15 18 21 24
1 4 7 10 13 16 19 22 25
2 5 8 11 14 17 20 23 26
-----------------0 1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16 17
18 19 20 21 22 23 24 25 26
26

 T = the Trifid Algorithm
 i= the row
 j= the column
 n= the number of columns (or length of message)
 Recall:
 mod is remainder
 div is quotient
27

n=3
0,0
0,1
0,2
1,0
1,1
1,2
2,0
2,1
2,2
28

n=3
0,0
0,1
0,2
1,0
1,1
1,2
2,0
2,1
2,2
0,0
29

n=3
0,0
0,1
0,2
1,0
1,1
1,2
2,0
2,1
2,2
0,0
1,0
30

n=3
0,0
0,1
0,2
0,0
1,0
2,0
1,0
1,1
1,2
0,1
1,1
2,1
2,0
2,1
2,2
0,2
1,2
2,2
31
st
1 ,
Proof that
middle, and
last don’t move

We want to find all (i,j)  W x W that are fixed by T,
where T(i,j)= (ni + j)mod3, (ni+j)div3.
32
st
1 ,
Proof that
middle, and
last don’t move


33
st
1 ,
Proof that
middle, and
last don’t move

0,0
0,1
0,2
1,0
1,1
1,2
2,0
2,1
2,2
And everything else moves!!
34
Conjecture

The order of the
Trifid
Permutation
where n=number
of columns=3k,
k N is k+1.
0 1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16 17
18 19 20 21 22 23 24 25 26
-----------------0 9 18 1 10 19 2 11 20
3 12 21 4 13 22 5 14 23
6 15 24 7 16 25 8 17 26
-----------------0 3 6 9 12 15 18 21 24
1 4 7 10 13 16 19 22 25
2 5 8 11 14 17 20 23 26
-----------------0 1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16 17
18 19 20 21 22 23 24 25 26
35
0 15 30 1 16 31 2 17 32 3 18 33 4 19 34
5 20 35 6 21 36 7 22 37 8 23 38 9 24 39
10 25 40 11 26 41 12 27 42 13 28 43 14 29 44
------------------
0 5 10 15 20 25 30 35 40 1 6 11 16 21 26
31 36 41 2 7 12 17 22 27 32 37 42 3 8 13
18 23 28 33 38 43 4 9 14 19 24 29 34 39 44
-----------------0 31 18 5 36 23 10 41 28 15 2 33 20 7 38
25 12 43 30 17 4 35 22 9 40 27 14 1 32 19
6 37 24 11 42 29 16 3 34 21 8 39 26 13 44
-----------------0 25 6 31 12 37 18 43 24 5 30 11 36 17 42
23 4 29 10 35 16 41 22 3 28 9 34 15 40 21
2 27 8 33 14 39 20 1 26 7 32 13 38 19 44
36
T(i) = ni mod(3n-1), 0<i<3n-1

37
T(i) = ni mod(3n-1), 0<i<3n-1

0
1
0
2
2
3
4
1
4
5
3
5
38
T(i) = ni mod(3n-1), 0<i<3n-1

0
1
0
2
2
3
4
1
4
5
3
5
0, 1, 2, 3, 4, 5
39
T(i) = ni mod(3n-1), 0<i<3n-1

Recall:
n = message length
i = location
0
1
0
2
2
3
4
1
4
5
3
5
0, 1, 2, 3, 4, 5
0, 1, 2, 3, 4, 5
T(0) = 2(0)mod(3*2-1)≡0mod5
40
T(i) = ni mod(3n-1), 0<i<3n-1

Recall:
n = message length
i = location
0
1
0
2
2
3
4
1
4
5
3
5
0, 1, 2, 3, 4, 5
0, 1, 2, 3, 4, 5
T(0) = 2(0)mod(3*2-1)≡0mod5
T(1) = 2(1)mod5 ≡ 2mod5
T(2) = 2(2)mod5 ≡ 4mod5
T(3) = 2(3)mod5 ≡ 1mod5
T(4) = 2(4)mod5 ≡ 3mod5
41
In addition …

Tk(i) = (nki)mod(3n-1)
Calculates the ith location in the kth
permutation.
42
Theorem

The order of the Trifid Permutation
where n=number of columns=3k,
and k  N is k+1.
43
Proof

Unfortunately,
not enough
time…
44
A Big Question…

What is the order of a Trifid
permutation for an arbitrary
number of columns, n?
45
Theorem

The order of the Trifid permutation for n columns is a
divisor of φ(3n-1), where φ is the Euler Phi function.
46
Theorem

The order of the Trifid permutation for n columns is a
divisor of φ(3n-1), where φ is the Euler Phi function.
Corollary:
If we are using the chosen plaintext attack, we can
apply the Trifid Algorithm φ(3n-1) times and the message
will be automatically decrypted.
47
Resources

 Bowers, W. M. (1961). Practical ctyptanalysis. (Vol. 3).
American Cryptogram Association.
 http://cryptogram.org/cdb/aca.info/aca.and.you/c
hapter_09.pdf#TRIFID
 Kahn, David, The Codebreakers
48