An Efficient Modification to Playfair Cipher

Abstract

Playfair is one of the best-known traditional ciphers but it is limited from different aspects. This paper deals with some of its limitations and extensibilities. Proposed modification uses a 7 × 7 matrix with a matrix randomization algorithm to extend the data holding capability and security at the same time. Some limitations like I/J inconsistency and padding character ambiguity is eliminated. According to the performed cryptanalysis, this modification is stronger than playfair.

Full text

ULAB JOURNAL OF SCIENCE AND ENGINEERING VOL. 5, NO. 1, NOVEMBER 2014 (ISSN: 2079-4398) 26
An Efficient Modification to Playfair Cipher
1Md. Ahnaf Tahmid Shakil and 2Md. Rabiul Islam
1 Department of Computer Science & Engineering, University of Information Technology and Sciences,
Bangladesh, at.shakil@yahoo.com
2 Department of Computer Science & Engineering, Rajshahi University of Engineering & Technology,
Rajshahi-6204, Bangladesh, rabiul_cse@yahoo.com
Abstract— Playfair is one of the best-known traditional ciphers but it is limited from different aspects. This paper deals with
some of its limitations and extensibilities. Proposed modification uses a 7  7 matrix with a matrix randomization algorithm to
extend the data holding capability and security at the same time. Some limitations like I/J inconsistency and padding character
ambiguity is eliminated. According to the performed cryptanalysis, this modification is stronger than playfair.
Keywords— Algorithm Enhancement and Optimization, Classical Cryptography, Computational Algorithm, Cryptography,
Polyalphabetic Cipher, Private-key Encryption
 University of Liberal Arts Bangladesh
All rights reserved.
Manuscript received on 19 July 2014 and accepted for publication on 24 August 2014.
1 INTRODUCTION
RYPTOGRAPHY is the study of mathematical tech-
niques related to aspects of information security
such as confidentiality, data integrity, entity authen-
tication, and data origin authentication [1]. It discusses
about a set of techniques, Encryption is one of them. One
of the primitive purposes of data and information is to
interact with it via various communication channels. The-
se channels are not always authentic. Information or data
must be masked before the communication is initiated to
assure confidentiality. The process of masking data before
transmission through communication channel is encryp-
tion, though purposes of encryption may differ. Most of
the cryptosystem follows a generic structure to encipher
and decipher data. It involves plaintext, ciphertext, en-
cryption algorithm, decryption algorithm and key [2].
Figure 1: General structure of cryptography.
According to the structure, encryption and decryption
uses two different algorithms which may use either iden-
tical or different keys. Based on the usage of key, encryp-
tion may be categorized into two distinct sections – sym-
metric or private key encryption and asymmetric or pub-
lic key encryption [3]. Symmetric encryptions can be
block ciphers or stream ciphers.
2 THE PLAYFAIR CIPHER
Playfair is a symmetric polyalphabetic encryption system
that uses block substitution. It was invented by Charles
Wheatstone in 1954 but implementation was popularized
by Lord Playfair [4], [5]. This cipher was also used as a
British field cipher [6]. Playfair cipher uses a 5  5 matrix
which is shown in table 1.
TABLE 1
A PLAYFAIR MATRIX
K E Y W O
R D A B C
F G H I/J L
M N
P Q S
T U V X Z
The matrix is constructed by choosing a keyword from
which duplicate characters are removed and placed in the
matrix. Then the rest of the empty spaces are filled with
remaining characters by following an alphabetic order.
Consistency with English alphabet is kept by putting any
two characters in a single entry (Traditionally, these char-
acters are I and J). Then plaintext is considered as a con-
struction of two character blocks. A plaintext with odd
length is normalized by appending a padding character at
the end. Each block is substituted by following the rules
below:
• If both characters are same, a filler character e.g., x
is added after the first character.
C

27 ULAB JOURNAL OF SCIENCE AND ENGINEERING VOL. 5, NO. 1, NOVEMBER 2014 (I SSN: 2079-4398)
• If both characters are on the same row of the ma-
trix, they are replaced by their immediate next
with the first element of the row circularly follow-
ing the last.
• Two characters that are on the same column are
replaced by the character beneath them with the
top element of the row circularly following the
bottom.
• Two characters when neither on the same column
or on the same row, replaced by the character on
its row that intersects another character by col-
umn.
For every possible key there is different number of ma-
trix arrangements. So, for 25 letters, a permutation of 25
(which is approximately 1025) number of possible matrix
can be generated [7]. Also, with 26 letters there is a possi-
bility of 676 digrams, which was considerably secure for
the time when playfair invented. But, with the change of
time, different cracking method arisen, some of which
doesn’t even require technical device and can be solved
by pencil and paper [8].
3 PROPOSED MODEL
In the proposed model, a 7  7 matrix is considered for
extended character support and additional features. Pri-
marily, the matrix supports 49 characters. But, the model
uses 47 of them for general purpose and 2 for special
purpose. The character set includes 26 lower-case letters,
10 numerals, 10 most frequently used punctuation marks
and a whitespace character. The two remaining characters
serve exclusively as a filler character and a padding char-
acter. This two particular character are not eligible to par-
ticipate in plaintext or keyword. During decryption they
are omitted. They eliminate the existing ambiguity in
playfair that couldn’t resolve the following scenarios:
• Scenario 1: A substitution pair includes identical
characters and each character in the pair is filler
character. For example, if ‘X’ is a filler character,
then according to conventional playfair algorithm,
pair ‘XX’ will be replaced by ‘XXX’, which, in turn,
will create ambiguity. And according to the crypt-
analysis by Michael J. Cowan, this is a potential
source of exposure of plaintext structure [8].
• Scenario 2: Plaintext has odd number of characters.
A plaintext with odd length is processed by ap-
pending a padding character. But decryption algo-
rithm has no clue, whether that particular last pair
uses a padding character or not.
Similar algorithm exists that uses dedicated characters
to reduce these ambiguity [9].
Figure 2: Data flow diagram of matrix construction.
In the matrix construction phase, following steps are
applied:
• A character set (C.S.) is considered which is com-
posed of all 49 supported characters.
• Every character in C.S. possesses a temporary in-
dex number. And, the character groups follow an
indexing hierarchy. In the primary state, it appears
like as table 2.
TABLE 2
PRIMARY INDEXING OF CHARACTER GROUPS
Groups
Characters Index Ran
g
e
Alphabets
26 0 –
25
Numerals
10 26 –
35
Punctuations
10 36 –
45
Whites
p
aces
1 46 –
46
Filler and Paddin
g
2 47 –
48
• An array is considered where characters are tem-
porarily stored before putting in the matrix. It is
primarily empty.
• First, a keyword is chosen, which is a composition
of valid letters in C.S. (excluding padding and fill-
er character).
• Index list of keyword characters (I.K.) is calculat-

A
HNAF TAHMID SHAKIL ET AL: AN EFFICIENT MODIFICATION TO PLAYFAIR CIPHER 28
ed. Then, Keyword is placed in the empty array.
• Then, C.S. is rearranged by removing characters
that are already in the array. C.S. is also re-indexed
in a way that, index of the first character is 0; later
one is 1 and so on.
• Now, a block of characters is extracted from C.S.
by using I.K. If any character of referred index is
not available, it is simply ignored.
• The extracted characters are appended to the ar-
ray.
• This extraction and appending process iterates un-
til there is no character left in C.S. (Fig. 2 provides
an explicit view on the process).
• Finally, data from array is placed in the matrix by
following a matrix permutation pattern (3.2).
Once the matrix construction is complete, plaintext da-
ta blocks are substituted using the same principle as 5  5
playfair algorithm.
3.1 Example
Consider a keyword K = “ace”. K contains 3 characters.
Also, consider C.S. which consists of punctuations in the
list ['(', ')', '$', '&', '+', ',', '/', ':', ';', '='], C.S. is in primary
state and using ‘!’ as filler character and ‘~’ as padding
character. Table 3 shows the indexing of C.S. for primary
state.
TABLE 3
INDEXING OF C.S. IN PRIMARY STATE
Char. a b c d e ... ! ~
Index 0 1 2 3 4 … 47 48
First, index of K is calculated. So, index(K) = [0, 2, 4].
Let, A is an empty array. After appending characters from
K, A = ['a', 'c', 'e'].
Now, C.S. is rearranged by removing characters in A
and re-indexed, which is shown in table 4.
TABLE 4
INDEXING OF C.S. AFTER A REARRANGE AND RE-INDEXING
OPERATION
Char. b d f g h ... ! ~
Index 0 1 2 3 4 … 44 45
Then, a block of characters ['b', 'f', 'h'] is extracted from
C.S. by using index(K). Characters are appended to array.
Now, the array, A = [a, c, e, b, f, h]. This way, all the char-
acters are extracted. Finally, A = ['a', 'c', 'e', 'b', 'f', 'h', 'd', 'i',
'k', 'g', 'l', 'n', 'j', 'o', 'q', 'm', 'r', 't', 'p', 'u', 'w', 's', 'x', 'z', 'v', '0',
'2', 'y', '3', '5', '1', '6', '8', '4', '9', ')', '7', '$', '+', '(', ',', ':', '&', ';', '
', '/', '!', '=', '~']
Now, applying a spiral pattern (direction: clockwise,
starting point: upper-left edge) on data in A, we get the
matrix which is shown in table 5.
TABLE 5
GENERATED MATRIX FOR KEYWORD “ace” IN A SPIRAL PATTERN
CONFIGURATION
Encryption: Plaintext “aa”
Step1: Plaintext processing –
Step 2: Block substitution -
a! ew
a~ bs
Decryption: Ciphertext “ewbs”
Step 1: Block substitution -
ew a!
bs a~
Step 2: Omitting padding and filler character –
Ignoring filler and padding characters, retrieved
plaintext is “aa”
The screenshot in figure 3 gives an example of another
plaintext encryption, which is a software implementation
of the explained algorithm of modified playfair cipher.
Figure 3: A software implementation of modified
playfair cipher algorithm [10].
3.2 Matrix Permutation Patterns
Matrix permutation patterns define how data is to be ar-
ranged in matrix. For example, the traditional playfair
used a left to right and top to bottom order which is re
a c e b f h d
z v 0 2 y 3 i
x ( , : & 5 k
s + = ~ ; 1 g
w $ ! / 6 1
u 7 ) 9 4 8 n
p t r m q o j

29 ULAB JOURNAL OF SCIENCE AND ENGINEERING VOL. 5, NO. 1, NOVEMBER 2014 (I SSN: 2079-4398)
ferred in this paper as conventional pattern. Unlike a sin-
gle pattern, this model uses multiple permutation pat-
terns to choose from. Some of the permutation patterns:
Spiral Pattern
This pattern takes any of the four edges as starting point
and consumes the matrix at a spiral concentric fashion.
Or, starts from the center and expands through the matrix
at a spiral expanding fashion. A total possible variation is
16. A clockwise spiral pattern using upper-left edge as
starting point is given in table 6.
TABLE 6
A SPIRAL PATTERN CONFIGURATION USING 7  7 MATRIX
Diagonal Pattern
As the name suggests, diagonal pattern follows a diag-
onal route to consume the matrix. A total possible varia-
tion is 8. A diagonal pattern using upper-left edge as
starting point is shown in table 7.
TABLE 7
A DIAGONAL PATTERN CONFIGURATION USING 7  7 MATRIX
J-Pattern
J pattern uses a matrix consumption path that is com-
posed of multiple J shaped route. A total possible varia-
tion is 8. A J-pattern using horizontal configuration with
upper-left edge is shown in table 8.
TABLE 8
A J-PATTERN CONFIGURATION USING 7  7 MATRIX
It is also possible to generate user defined patterns.
The sole purpose of multiple patterns is to scram-
ble/permutate the matrix. Patterns can be changed with
every data exchange session, which generates a random
behavior that makes it difficult for attacker to decide what
pattern is used. At the same time, number of possible
structure rises dramatically. For example, if there are m
patterns and n possible structures for each pattern, then,
the total structures will be m  n. This makes cryptanaly-
sis more difficult.
4 ANALYSIS OF PROPOSED ALGORITHM
Playfair was considered safe at the beginning of 20th cen-
tury, because of the effort it takes to break the cipher
manually. But, after invention of computers, this became
a trivial problem [7]. The first known solution to this
digram cipher is given by J. Mauborgne in 1913 [11]. After
this, different methods are discovered to effectively crack
this substitution cipher [7], [8], [12]. There are several
common attacks on ciphers, which are – ciphertext only
attack, known plaintext attack and chosen plaintext attack
[13]. The proposed algorithm tends to increase the securi-
ty by character set extension, generation of random key
and a further permutation in the arrangement pattern of
matrix. This creates confusion for attacker that makes the
algorithm stronger. One way to exploit the security of
algorithm like this, attacker needs to know the nature of
the language. This is because the frequency of a letter in a
language is always the same. And, this may lead an at-
tacker to expose the plaintext structure. So, this possibility
must be eliminated / minimized. Hence, a pre-encryption
and post-encryption frequency analysis is required to
show the effectiveness of an algorithm. To generate fre-
quency distribution graph, number of occurrences of each
letter in character set are counted and divided by occur-
rence of e (the letter in English with highest frequency).
As a result, a relative frequency in range 0 and 1 is
gained. The points on the horizontal axis correspond to
the letters in order of decreasing frequency. More flat the
relative frequencies are, more concealed the information
is [14].
1 2 3 4 5 6 7
24 25 26 27 28 29 8
23 40 41 42 43 30 9
22 39 48 49 44 31 10
21 38 47 46 45 32 11
20 37 36 35 34 33 12
19 18 17 16 15 14 13
1 3 6 10 15 21 28
2 5 9 14 20 27 34
4 8 13 19 26 33 39
7 12 18 25 32 38 43
11 17 24 31 37 42 46
16 23 30 36 41 45 48
22 29 35 40 44 47 49
1 2 3 4 5 6 7
14 13 12 11 10 9 8
15 16 17 18 19 20 21
28 27 26 25 24 23 22
29 30 31 32 33 34 35
42 41 40 39 38 37 36
43 44 45 46 47 48 49

A
HNAF TAHMID SHAKIL ET AL: AN EFFICIENT MODIFICATION TO PLAYFAIR CIPHER 30
Figure 4: Frequency distribution in plaintext vs. convention-
al playfair ciphertext.
A frequency distribution analysis is performed on 55,900
popular words in English consists of 419,968 letters. Figure 4
shows the change in frequency distribution between a
plaintext and conventional playfair ciphertext. The
ciphertext curve is slightly flatter than plaintext, which de-
notes that some frequency information has been concealed.
On the other hand, figure 5 shows a relative comparison
between plaintext, conventional playfair and modified
playfair ciphertext. Modified playfair cipher curve shows
some significant improvement over conventional playfair.
Because, it provides a more flat curve then that of conven-
tional playfair, which is better security. But yet, like the con-
ventional playfair, it can be broken by following the identical
principles, except, the modified one requires harder effort
Figure 5: Relative frequency distribution between plaintext,
conventional playfair ciphertext and modified playfair
ciphertext.
5 CONCLUSION
This paper attempts to modify and extend the existing 5 
5 playfair cipher in different ways, by extended character
set, I and J ambiguity reduction, matrix modification and
one to one ciphertext generation. The original playfair
uses a single pattern to generate matrix in a left to right
and top to bottom order. But instead, in proposed model,
multiple matrix generation patterns are introduced. Selec-
tion of these patterns is driven by user which acts as ini-
tialization vector. This randomized behavior generates
confusion for attacker that increases the security. At the
same time, matrix extension to 7  7 produces more pos-
sible structures than original playfair. This paper can be
used as a learning resource that will help to understand
playfair, its vulnerabilities and will show an effective way
to improve it, thus, helping students in understanding
cryptography, algorithm enhancement and cryptanalysis
in an easier way, which would be otherwise difficult with
more advanced ciphers like DES or AES. It is possible to
encrypt any binary data by using modified playfair cipher
along with base 32 encoding. Wholly, the algorithm is
unique, unambiguous and simple that leaves a lot of pos-
sibilities to be a useful learning resource and possibilities
to implement it as a low-security protocol in a wide range
of devices, including low powered embedded ones.
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