Attacking Turkish Texts Encrypted by Homophonic

Attacking Turkish Texts Encrypted by Homophonic

ATTACKING TURKISH TEXTS ENCRYPTED BY HOMOPHONIC CIPHER
(HOMOFONĠK ġĠFRELENMĠġ TÜRKÇE METĠNLER ÜZERĠNE ATAKLAR)
by
Şefik İlkin SERENGİL, B.S.
Thesis
Submitted in Partial Fulfillment
of the Requirements
for the Degree of
MASTER OF SCIENCE
in
COMPUTER ENGINEERING
in the
INSTITUTE OF SCIENCE AND ENGINEERING
of
GALATASARAY UNIVERSITY
June 2011
ATTACKING TURKISH TEXTS ENCRYPTED BY HOMOPHONIC CIPHER
(HOMOFONĠK ġĠFRELENMĠġ TÜRKÇE METĠNLER ÜZERĠNE ATAKLAR)
by
Şefik İlkin SERENGİL, B.S.
Thesis
Submitted in Partial Fulfillment
of the Requirements
for the Degree of
MASTER OF SCIENCE
Date of Submission
: May 18, 2011
Date of Defense Examination: June 17, 2011
Supervisor
: Asst. Prof. Dr. Murat AKIN
Committee Members : Assoc. Prof. Dr. Tankut ACARMAN
Assoc. Prof. Dr. Y. Esra ALBAYRAK
Acknowledgements
I would like to thank with my whole heart to my supervisor, Asst. Prof. Dr. Murat
Akın, who taught me a lot of things in my academic life.
I am grateful to my beloved mother and father who do not avoid sacrificing anything
from the day I was born to ensure me to have the best conditions.
May, 2011
ġefik Ġlkin Serengil
ii
Table of Contents
Acknowledgements ........................................................................................................... ii
Table of Contents ............................................................................................................. iii
List of Figures ................................................................................................................... v
List of Tables ................................................................................................................... vi
Abstract .......................................................................................................................... viii
Résumé............................................................................................................................. ix
Özet ................................................................................................................................... x
1.
Introduction ............................................................................................................... 1
2.
Classical Cryptography ............................................................................................. 2
2.1.
Monoalphabetic Substitution ............................................................................. 2
2.1.1.
Shift Cipher ................................................................................................. 2
2.1.2.
Substitution Cipher ..................................................................................... 3
2.1.3.
Affine Cipher ............................................................................................ 15
2.2.
Block Ciphers ................................................................................................... 16
2.2.1.
Permutation Cipher ................................................................................... 16
2.2.2.
Polygraphic Substitution ........................................................................... 17
2.2.2.1.
Playfair Cipher................................................................................... 17
2.2.2.2.
Hill Cipher ......................................................................................... 18
2.2.3.
Polyalphabetic Substitution Ciphers ......................................................... 22
2.2.3.1.
Vigenere Cipher................................................................................. 22
2.2.3.2.
Kasiski Attack ................................................................................... 25
3.
Homophonic Cipher ................................................................................................ 27
4.
A New Approach On Attacking Homophonic Cipher ............................................ 32
4.1.
5.
High Frequent N-grams Consisting of Low Frequent Unigrams ..................... 33
Conclusion ............................................................................................................... 49
References ....................................................................................................................... 50
Appendix ......................................................................................................................... 52
Biographical Sketch ........................................................................................................ 54
iv
List of Figures
Figure 2.1 The Encryption Schema of the Shift Cipher ................................................... 2
Figure 2.2 An Illustration of Frequency Values of the Turkish Unigrams ....................... 5
Figure 2.3 Illustration of the Permutation Cipher ........................................................... 17
Figure 2.4 Pseudocode of Dividing Ciphertext Into Blocks to Attack ........................... 24
Figure 3.1 Domain Set and Target Set of Homophonic Cipher ...................................... 28
Figure 3.2 Illustration of Frequency Distribution of a Homophonic Encrypted Text .... 28
Figure 3.3 Substitution Table of Homophonic Cipher ................................................... 29
Figure 3.4 Algorithm for Computing the Key Space of Homophonic Cipher for Turkish
........................................................................................................................................ 30
List of Tables
Table 2.1 Substitution Cipher Encryption Table .............................................................. 3
Table 2.2 Percentage of Frequencies of Turkish Unigrams [2] ........................................ 4
Table 2.3 The Most Frequent 100 Turkish Words [1] ...................................................... 6
Table 2.4 Frequencies of 600 Most Frequent Bigrams in Turkish within 11M ............... 7
Table 2.5 Frequencies of 600 Most Frequent Trigrams in Turkish within 11M .............. 9
Table 2.6 Frequencies of 600 Most Frequent Tetragrams in Turkish within 11M ......... 11
Table 2.7 Frequencies of 600 Most Frequent Pentagrams in Turkish within 11M ........ 13
Table 2.8 Index Values of the Letter of the Turkish Alphabet ....................................... 15
Table 2.9 Encryption Process of Affine Cipher .............................................................. 15
Table 2.10 Decryption Process of Affine Cipher ........................................................... 15
Table 2.11 The Encryption Key of Playfair Cipher ........................................................ 18
Table 2.12 Mathematical Illustration of Encyrption Process of Vigenere Cipher .......... 22
Table 2.13 Mathematical Illustration of Decryption Process of Vigenere Cipher ......... 23
Table 2.14 Encryption Process of Vigenere Cipher by Using of Vigenere Table .......... 23
Table 2.15 Vigenere Table for Turkish Alphabet ........................................................... 23
Table 2.16 Distances Between Repating Characters ...................................................... 25
Table 3.1 Percentage of Turkish Letter Frequencies and Expression Count in
Homophonic Cipher [2] .................................................................................................. 29
Table 3.2 Comparison of Key Space Values of Common Algorithms ........................... 31
Table 4.1 Expression Count of Most Common 100 Words of Turkish within
Homophonic Cipher ........................................................................................................ 33
Table 4.2 Frequencies and Expression Count of High Frequent Bigrams Consisting of
Low Frequent Unigrams in 11M .................................................................................... 34
Table 4.3 Frequencies and Expression Count of High Frequent Trigrams Consisting of
Low Frequent Unigrams in 11M .................................................................................... 35
Table 4.4 Frequencies and Expression Count of High Frequent Tetragrams Consisting
of Low Frequent Unigrams in 11M ................................................................................ 36
Table 4.5 Frequencies and Expression Count of High Frequent Pentagrams Consisting
of Low Frequent Unigrams in 11M ................................................................................ 37
Table A.1 List of Novels Used in the Corpus ................................................................. 53
vii
Abstract
Emerging technologies make the vital operations performing through insecure channels.
At this point, transferring private information between parties and authentication of
transferred data can only be possible by the use of cryptography.
The security of the cryptographic methods should be examined to test for perfection.
Therefore, it is always supposed that the cryptographic method is known on
cryptographic attacks.
In this work, firstly classical encryption methods and vulnerabilities for Turkish
language are reviewed. Herein, homophonic cipher comes one step forward in the
alternative classical encryption methods because it generates ciphertexts consisting of
variable block sizes. This makes well known attacking models invalid. Therefore, a
novel attacking model is aimed to develop for Homophonic cipher in Turkish. This
model is investigated on a large data source aiming to detect the characteristic features
of Turkish language.
Key words: Turkish n-gram Frequencies, Homophonic Substitution, Cryptoanalysis of
Encrypted Turkish Texts.
Résumé
Le développement de la technologie offre la possibilité d’effectuer des opérations
vitales sur des canaux dont la sécurité n’est pas sûre. A ce point-là, le transfert de
l’information privée entre les parties et l’authentification de ces données transférées
sont possibles seulement grâce à l’utilisation de la cryptographie.
Pour pouvoir examiner la perfection d’une méthode cryptographique, il faut d’abord
questionner la sécurité qu’il offre à l’utilisateur. Par conséquence, on suppose toujours
que la méthode du chiffrement est connue quand on parle d’une attaque
cryptographique.
Dans ce travail, premièrement on révise les méthodes de chiffrement classique et on
parle des côtés vulnérables de la langue turque. Le chiffrement homophonique se diffère
des autres méthodes de chiffrement grâce à sa particularité qui rend possible de produire
des chiffres de blocs de taille variable. Cette caractéristique rend inefficaces les attaques
effectuées en utilisant des méthodes bien connues. Pour cette raison, le but de ce travail
est de proposer un nouveau modèle d’attaque propre aux textes turcs cryptés par le
chiffrement homophonique. Le modèle est examiné sur une grande base de données afin
d’évaluer les caractéristiques de la langue turque.
Mots clés: Les fréquences des n-gram turcs, la substitution homophonique,
cryptanalyse des textes turcs.
Özet
GeliĢen teknoloji ile güvenli olmayan kanallardan hayati iĢlemlerin gerçekleĢtirilmesi
günümüz dünyasında oldukça yaygın bir Ģekilde yer almaktadır. Bu noktada, gizli bir
bilginin partiler arasında aktarılması ve aktarılan bilgilerin doğruluğunun taahhüt
edilmesi ancak ancak kriptografi ile mümkün olmaktadır.
Bir
kriptografik
yöntemin
mükemmelliğinin
sınanabilmesi
için
güvenliği
sorgulanabilmelidir. Bu nedenle, kriptografik ataklarda hep kriptografik yöntemlerin
bilindikleri varsayılır.
Bu çalıĢmada öncelikle kriptografinin temelini oluĢturan klasik yöntemler ve Türkçe’ye
özgü zafiyetlere değinilmiĢtir.
Bu noktada homofonik Ģifreleme, değiĢken blok
boyutunda Ģifreler üretmesi sebebiyle alternatif Ģifreleme yöntemleri arasında kendini
belli etmektedir. Bu da bilinen yöntemler ile saldırıları etkisiz kılmaktadır. Bu nedenle,
homofonik ĢifrelenmiĢ Türkçe metinler için özgün bir saldırı modeli geliĢtirilmesi
amaçlanmıĢtır. Bunun için oldukça geniĢ bir veri kaynağı üzerinde inceleme yapılmıĢ
ve Türkçe’nin karakteristik özellikleri kestirilmeye çalıĢılmıĢtır.
Anahtar Sözcükler: Türkçe n-gram Frekansları, Homofonik Yer DeğiĢtirme, Türkçe
ġifrelenmiĢ Metinlerin Kriptoanalizi.
1
1.
Introduction
Cryptography could be implemented to provide data security, integrity and
authentication. Moreover, the cryptosystems have to be resistant against to attacks.
Therefore, detection of the vulnerebalities of a cryptographic method is a valueable
processus. Hence, it is aimed to mention the main concepts of secret key cryptography
and it is planned to focus on the attacking approaches of the secret key systems in this
work.
Statistical features of the source language are used to solve classical methods because
classical methods depend on the source language. Related work presented by Dalkılıç
[1] investigates Turkish language patterns and frequencies of Turkish. This contribution
solves some of classical methods but this study is limited by the analysis about
extraction of most frequent trigrams.
Classical cryptography is presented in the first section. The main concepts of well
known classical encryption methods are considered and attacking models are illustrated.
Most particularly, there seems to have been no previous work on the subject that
analyses homophonic cipher for Turkish. Therefore, developing an attacking model for
Turkish is notably aimed in the second section.
In this work, the corpus of size 13.4 MB is used to attain the statistical features of
Turkish to solve some of classical cryptographic methods. Also, the corpus consists of
120 articles of a columnist, Çetin Altan, from the Turkish daily newspaper Milliyet and
37 novels of 9 different authors, which are Orhan Kemal, Orhan Pamuk, Çetin Altan,
Aziz Nesin, Rıfat Ilgaz, Gülse Birsel, Ahmet Altan, Yılmaz Erdoğan and Soner Yalçın.
2. Classical Cryptography
Classical cipher is an encryption method that performs on letters of alphabet. Classical
ciphers depend on the source language. Therefore, source language specifies the key
space of the method. More generally, they are implemented by hand or they are
implemented with basic machines. Substitution or transposition techniques are often
included in classical ciphers.
In this section, most popular methods of classical
cryptography and main concepts are presented.
2.1.
Monoalphabetic Substitution
Monoalphabetic substitution is a historical encryption method that depends on replacing
each plaintext letter with another letter. The cipher alphabet remains unchanged
throughout the encryption process. Therefore, it is named as Monoalphabetic
Substitution Cipher.
2.1.1. Shift Cipher
Shift cipher depends on the principle that each character of the message is replaced by a
substitute with a shift of specified positions down or up in the alphabet. Figure 2.1
shows an example of the shift cipher. The method is also known as Caesar Cipher.
Figure 2.1 The Encryption Schema of the Shift Cipher
3
If each character of the alphabet is presented by an integer that corresponds to its
position in the alphabet, the formula of the method for replacing each character p of the
plaintext with a character C of the ciphertext with a shift of k in an alphabet consisting
of n characters could be expressed as
Ci = (pi + k) mod n
(2.1)
pi = (Ci - k) mod n
(2.2)
As an illustrative example, the following text is chosen:
Plaintext:
GELECEĞĠKESTĠREBĠLMENĠNENGÜZELYOLUONUĠCATETMEKTĠR
And by using the plaintext, it is encrypted as:
Ciphertext:
IĞOĞEĞĠLNĞUVLTĞDLOÖĞPLPĞPIZCĞOBROYRPYLEÇVĞVÖĞNVLT
The method is weak against to brute force attack. In worst case, an attacker could
detect the plaintext in (n-1) steps.
2.1.2. Substitution Cipher
Substitution cipher depends on the principle that replacing each letter by another letter.
Substitution characters are composed by a random permutation of the letters of the
source language. Caesar cipher is a special form of a substitution cipher.
Table 2.1 Substitution Cipher Encryption Table
a b c ç d e f g ğ h ı i j k l m n o ö p r s Ģ t u ü v y z
E R T Y U I O P Ğ Ü A S D F G H J K L ġ Ġ Z C V B N M Ö Ç
Table 2.1 demonstrates an instance of substitution cipher.
Each plaintext letter is
looked up in the encryption table and written the corresponding ciphertext below. The
decryption process depends on finding each ciphertext letter in the second row and
writing down the corresponding letter from the top row.
4
As an illustrative example, the following text is chosen:
: TEKNOLOJĠSENDOĞDUKTANSONRAĠCATEDĠLENHERġEYDĠR
Plaintext
And by using the plaintext, it is encrypted as:
Ciphertext
: VIJKGKDSZIJUKĞUBFVEJZKJĠESTEVIUSGIJÜIĠCIÖUSĠ
The key space of substitution cipher is equal to n! on an alphabet consisting of n letters.
For Turkish, the key space is equal to 29!, that is a number larger than 1030. This is
larger than many times of key space of DES which is equal to 1016.
Suppose that the attacker is able to check a possibility per microsecond, it would take
time more than 1016 years to solve ciphertext in the worst case1.
Obviously, the
encipherment rules out a brute force attack.
However, the attacker does not need to check all possibilities to solve ciphertext. It is a
fact that the characteristic distribution of the texts is similar. Table 2.2 and Figure 2.2
illustrate the unigram frequencies of Turkish language. Therefore attacking by using an
analysis of frequencies can lead to reveal encryption table.
Table 2.2 Percentage of Frequencies of Turkish Unigrams [2]
Letter
A
B
C
Ç
D
E
F
G
Ğ
H
1
10 30 10 −6
60.60.24.265
> 1016
Freq.
11,92
2,844
0,963
1,156
4,706
8,912
0,461
1,253
1,125
1,212
Letter
I
Ġ
J
K
L
M
N
O
Ö
P
Freq.
5,114
8,6
0,034
4,683
5,922
3,752
7,484
2,476
0,777
0,886
Letter
R
S
ġ
T
U
Ü
V
Y
Z
Freq.
6,722
3,014
1,78
3,314
3,235
1,854
0,959
3,336
1,5
5
Figure 2.2 An Illustration of Frequency Values of the Turkish Unigrams
However, the letter frequencies of the ciphertext could not exactly match the letter
frequencies of the source language in a short message. Looking at the most common
words as listed in Table 2.3 and the most common n-grams is a valuable tool to encrypt
the data. The rest of the operation depends on the heuristic approach. The structure of
the words and stream of the sentence would help to detect the plaintext.
6
Table 2.3 The Most Frequent 100 Turkish Words [1]
Word
Bir
Ve
Bu
De
Da
Ne
O
Gibi
Ġçin
Çok
Sonra
Daha
Ki
Kadar
Ben
Her
Diye
Dedi
Ama
Hiç
Ya
Ġle
En
Var
Türkiye
Word
Mi
Ġki
Değil
Gün
Büyük
Böyle
Nin
Mı
In
Zaman
Ġn
Ġçinde
Olan
Bile
Olarak
ġimdi
Kendi
Bütün
Yok
Nasıl
ġey
Sen
BaĢka
Onun
Bana
Word
Önce
Nın
Ġyi
Onu
Doğru
Benim
Öyle
Beni
Hem
Hemen
Yeni
Fakat
Bizim
Küçük
Artık
Ġlk
Olduğunu
ġu
Kadın
KarĢı
Türk
Olduğu
ĠĢte
Çocuk
Son
Word
Biz
Vardı
Oldu
Aynı
Adam
Ancak
Olur
Ona
Biraz
Tek
Bey
Eski
Yıl
Bunu
Tam
Ġnsan
Göre
Uzun
Ġse
Güzel
Yine
Kız
Biri
Çünkü
Gece
Table 2.4, Table 2.5, Table 2.6 and Table 2.7 illustrate the most common n-grams in
Turkish. The n-gram data presented below is collected from the data set of size 13.4
MB.
7
Table 2.4 Frequencies of 600 Most Frequent Bigrams in Turkish within 11M
Ngr
AR
LA
AN
ER
ĠN
LE
EN
DE
IN
DA
BĠ
ĠR
KA
YA
DĠ
MA
ND
RA
AL
AK
RĠ
ĠL
NĠ
BA
RD
AY
OR
NI
LĠ
ME
RI
TA
NE
EL
AM
EK
DI
YO
KĠ
UN
ĠM
AD
ĠY
HA
SĠ
YE
NA
OL
TE
LI
Fre
210907
193023
190681
167490
166362
147573
145677
138507
132807
127637
125824
120936
113213
107833
101972
100389
98136
94205
92166
87361
84497
76889
73277
71504
71256
70636
70300
69437
69339
68578
66743
65232
64209
64209
63808
62698
62359
61044
59905
59182
59020
58667
57222
56075
55239
55184
54770
54389
53881
53814
Ngr
SA
RE
MĠ
DU
TI
TĠ
AT
SI
ET
VE
ED
NL
AS
Aġ
ON
BE
KE
SE
BU
EY
IR
KL
ÜN
EM
IK
GE
IL
ES
ĠK
Ġġ
UR
ĞI
LD
ĠS
IM
CE
RL
MI
NU
ĞĠ
GĠ
ĠZ
CA
AH
AZ
Iġ
YL
LM
ST
KI
Fre
53696
53009
52476
52283
51386
50968
50661
50362
49927
49863
49401
47564
47413
46294
45874
45640
45296
44712
44624
44573
43789
43444
43059
42649
40865
40841
39898
39387
38939
38227
38171
37718
37375
37263
37245
37156
36959
36784
36391
36283
35787
35238
33993
33171
32755
32622
32373
32197
31918
31841
Ngr
ĠÇ
RK
UL
KT
RU
SO
AB
IY
OK
ÇĠ
LU
AP
ÜR
ġT
AĞ
UM
KO
EV
DÜ
GÖ
YI
IĞ
RM
ZA
TÜ
KU
VA
MU
IZ
ġI
ZE
TU
ġA
LL
SU
ĠĞ
NC
PA
HE
ĠT
UY
RT
GÜ
YĠ
ġE
TL
EC
EĞ
TT
AC
Fre
31429
29528
29371
28964
28453
27989
27564
27516
27389
27377
27338
27085
27057
26972
26617
26139
25764
25568
25363
25203
24913
24106
24077
23774
23620
23617
23616
23551
23091
22692
22563
22533
22239
22196
22168
21975
21614
21525
21182
20510
20367
20288
20124
19854
19742
19492
19480
19472
19323
18985
Ngr
HĠ
ĞU
ġL
ÇI
ÖR
ÇE
ÜZ
ġĠ
ÇA
UĞ
ZL
ĠB
RS
ÖN
UZ
UK
ÇO
ÖY
Uġ
ZI
YÜ
ZĠ
RÜ
TM
Eġ
AV
ÜK
LÜ
YD
UT
ÜL
NM
Üġ
AÇ
ÖZ
DO
ML
ĠD
FA
ġK
MÜ
ÜM
CĠ
BÜ
MD
KÜ
ÜY
YU
AF
NÜ
Fre
18821
18753
18154
18112
17778
17736
17636
17282
17193
16907
16237
15851
15816
15278
15172
15139
14880
14744
14641
14561
14156
13862
13654
13595
13465
13357
13284
13272
13222
13198
13181
13100
13030
12668
12477
12350
12350
11953
11877
11863
11630
11563
11387
11348
11337
11279
11253
11219
11150
10971
Ngr
NR
ĠP
OĞ
IS
GA
VĠ
CI
SÖ
PE
ÜS
US
IP
NS
EZ
LK
CU
ġM
TO
BO
NT
EÇ
PI
OY
FE
ZD
EF
ÜT
NK
SL
LT
SÜ
KS
OT
ĞR
OC
EH
KM
PL
ĞL
ZÜ
DÖ
ÖL
ĠH
ĞA
SK
ġÜ
FĠ
LG
RG
ġU
Fre
10949
10803
10648
10610
10575
10524
10287
10196
10171
10146
10074
10041
9885
9758
9755
9701
9568
9312
9184
8977
8691
8685
8640
8636
8012
7925
7852
7820
7774
7738
7729
7683
7353
7347
7324
7137
7097
7068
7029
7025
6918
6801
6744
6727
6723
6549
6520
6372
6210
6102
Ngr
EP
KÖ
KK
BI
NG
EB
YR
ĠF
ÜÇ
OM
YN
ÇL
ZU
AA
Rġ
ÇÜ
RB
Oġ
OP
PT
RO
MS
OS
PO
VL
UP
BÖ
AĠ
OD
ĞÜ
NB
ÜĞ
NN
GU
TR
SS
LS
LO
RÇ
ID
FI
SM
UD
ĠC
VR
NÇ
VU
PĠ
HI
KR
Fre
6092
5975
5957
5760
5692
5667
5622
5528
5469
5460
5457
5262
5205
5193
5193
5186
5141
5093
5075
5061
4899
4790
4774
4765
4745
4701
4683
4625
4565
4516
4482
4463
4404
4374
4288
4284
4266
4242
4136
4104
4036
4030
3968
3936
3925
3916
3907
3837
3786
3777
8
NY
HU
ĞE
HT
ÖĞ
KÇ
RC
HO
ÖT
ZM
UH
CÜ
YM
UC
HM
ÇT
ÇM
UÇ
IC
ÜC
PR
ĠV
IT
YG
DD
FO
HL
PM
VD
FT
MO
GI
LN
ÜD
MB
ÜP
ÇB
FL
ZO
NO
ÖP
ÖS
RH
SY
RN
UV
HÜ
ĠĠ
YS
FÜ
3776
3772
3688
3651
3603
3575
3536
3481
3447
3369
3327
3312
3282
3174
3131
3122
3122
3043
2972
2954
2926
2888
2823
2798
2723
2692
2646
2626
2621
2587
2566
2534
2528
2508
2470
2425
2412
2401
2386
2385
2371
2368
2368
2367
2353
2325
2320
2309
2280
2208
ZG
TS
OZ
HR
LY
Kġ
UB
ĞM
PS
NZ
HÇ
ZC
FR
ÖK
RP
LB
PK
MC
OB
DR
TÇ
ÖM
LC
YK
VG
BR
HB
TK
OF
ÜV
ÇU
YB
ÖV
PU
Öġ
UA
ĠG
LÇ
ZY
AJ
YÖ
BD
HV
FU
FK
SR
ġÖ
ĠA
MN
IF
2195
2172
2171
2058
2043
2033
2008
1998
1994
1976
1975
1923
1908
1877
1853
1820
1805
1777
1620
1594
1573
1570
1541
1531
1525
1522
1515
1512
1492
1476
1434
1426
1414
1407
1381
1381
1369
1352
1351
1341
1319
1292
1289
1275
1263
1257
1235
1235
1199
1137
IV
GR
MM
HS
MR
ZS
SP
ÜF
ġS
JA
IÇ
HK
ġB
VK
RY
RV
RF
ÇÖ
UG
YF
ÖF
ÖB
MP
DL
OV
YV
JĠ
ġY
ĞD
YT
MH
RR
MK
RZ
VV
TÖ
ĞZ
VÜ
PÜ
AG
GO
TF
ZB
PH
OO
BL
TH
HN
ġÇ
DY
1134
1123
1121
1106
1098
1088
1075
1070
1066
1054
1042
1029
1028
1021
1008
1005
991
990
963
960
954
938
931
916
906
896
883
876
864
859
851
842
815
814
808
804
799
791
784
745
739
730
726
713
713
710
709
709
703
683
CO
EE
ġO
YH
VI
UF
VM
TB
ġV
OG
OH
VC
ÇK
FF
Mġ
MZ
LV
Hġ
LP
IA
CH
ÖD
AE
EG
KN
EĠ
CR
AU
SN
FÖ
SH
ÜB
IH
IB
KY
ZZ
EO
FÇ
EA
HP
ĠE
OJ
RÖ
MY
KD
ġH
SV
MT
CL
JE
672
655
644
640
639
629
602
596
596
593
571
568
558
536
534
533
533
529
523
522
519
516
516
514
514
513
502
495
491
483
481
481
478
478
473
468
467
456
448
447
446
438
435
434
432
425
425
423
416
415
Nġ
VS
UĠ
OÇ
YC
ZK
ÇS
ĞC
ÇR
TV
PÇ
EJ
HZ
FS
ġR
OĠ
VO
KB
YY
MG
FY
ĞN
ġG
Vġ
HD
LH
CD
TY
UE
BB
ZR
ÜH
SB
ÖC
KH
VN
ĠO
YZ
ġF
VY
NP
ZN
ĞS
ÜE
NF
RJ
II
NÖ
UU
JI
413
401
393
393
391
382
381
381
372
365
362
361
357
352
349
344
332
330
327
327
326
324
321
319
318
317
315
315
301
300
298
297
292
291
290
287
284
279
277
274
274
273
270
270
262
250
250
249
235
235
AO
GL
BN
TN
KG
TD
PY
SF
CC
JD
IO
VH
ġN
LF
VZ
NH
HY
LZ
ÇG
BZ
IG
KF
JL
OU
CK
JU
ZT
DN
NV
ĠJ
SC
CB
ÖH
UO
ÖÇ
TG
ġġ
ÇH
HH
TP
OE
ĠU
PP
JO
ĞB
KV
TC
MF
Yġ
ZH
234
231
227
223
222
220
218
208
203
201
200
200
197
195
183
183
178
177
176
170
166
165
163
163
161
156
155
154
152
151
143
142
137
134
132
131
129
126
126
125
118
118
118
117
114
114
109
108
102
97
9
Table 2.5 Frequencies of 600 Most Frequent Trigrams in Turkish within 11M
Ngr
LAR
BĠR
LER
ERĠ
ARI
YOR
ARA
NDA
ĠNĠ
INI
RĠN
DEN
AMA
NDE
EDĠ
ANI
ASI
DAN
NLA
AYA
RIN
IND
ENĠ
ADA
ĠLE
ĠND
ALA
NIN
ANL
KAR
LAN
IĞI
ADI
SIN
SĠN
ESĠ
YLE
KEN
RDU
ELE
ĠYO
ĠĞĠ
ĠNE
ARD
KLA
ĠÇĠ
TAN
NĠN
BĠL
ERE
Fre
89715
77192
68463
58199
56640
46374
39442
38533
36926
34233
32092
31700
31046
30920
29711
29369
28332
28109
28015
27995
27197
26780
26210
25992
25278
24708
24559
23573
23470
23010
22870
22842
22334
22148
21714
21362
21319
21223
21110
20913
20215
20109
19994
19356
19224
19160
18914
18606
18502
18440
Ngr
ORD
ĠYE
BAġ
EDE
ALI
UNU
END
BEN
NDĠ
ÇĠN
ELĠ
MIġ
EĞĠ
RLA
MAN
YAN
ĠLĠ
SON
IYO
ONU
ECE
KAD
UĞU
EME
ĠST
AĞI
OLA
INA
ERD
ANA
AYI
MĠġ
KAL
LMA
DĠY
EYE
ÖYL
ĠRĠ
RDI
RAK
KLE
ĠBĠ
ABA
ATI
LDU
ILA
EKĠ
ACA
ĞIN
GEL
Fre
18348
18295
18165
18132
17950
17894
17848
17793
17595
17466
17380
16453
16136
16134
16042
15605
15586
15500
15455
15454
15382
15378
15363
14961
14871
14823
14792
14787
14758
14707
14639
14564
14496
14485
14100
13914
13810
13799
13746
13357
13276
13215
13100
12815
12749
12665
12626
12607
12555
12534
Ngr
SAN
YAP
ORU
AġI
AHA
GÖR
EMĠ
DĠĞ
VER
RDĠ
RKE
OLD
GĠB
AKL
LEN
KAN
ĠMĠ
MAK
ÇIK
STE
DER
DED
DIĞ
MEK
ĞĠN
NUN
ġLA
RLE
AND
ĠSĠ
DUĞ
MAY
RDE
NRA
ONR
LAM
NCE
LĠK
LLA
AMI
VAR
EYĠ
ġTI
BUL
AKĠ
LIK
BAK
ETĠ
SUN
TTĠ
Fre
12433
12361
12334
12303
12211
12199
12047
11989
11988
11935
11897
11673
11642
11636
11505
11473
11433
11343
11312
11290
11222
11197
11092
11090
11013
10991
10966
10783
10735
10718
10666
10661
10552
10535
10532
10391
10390
10323
10321
10253
10250
10232
10166
10087
10042
10011
10007
9978
9885
9836
Ngr
ÇOK
CAK
RDA
DĠM
EKL
AKI
MAS
ARK
OLM
HER
LDI
GÜN
AġL
RUM
URU
YLA
YER
MAD
DEĞ
ĠġT
DAR
PAR
ġEY
YAZ
TÜR
AZI
REK
NLE
AKA
ULA
IMI
DAH
LAY
TIR
HAY
ARL
STA
ULU
AKT
ERL
YAR
IġT
RAN
TĠR
TER
ĠZĠ
ÜZE
REN
IKL
ILI
Fre
9685
9670
9602
9595
9211
9195
9191
9173
9072
9055
9052
8955
8928
8917
8887
8818
8793
8788
8728
8673
8657
8558
8555
8511
8501
8491
8457
8440
8404
8404
8366
8348
8336
8325
8312
8309
8261
8249
8218
8198
8153
8101
8039
7980
7975
7951
7943
7922
7896
7881
Ngr
AġK
ĞUN
DIN
ĠKĠ
YEN
LDĠ
ġTĠ
TEN
KTA
RMA
OLU
ENE
DIR
SEN
IRA
ĠLM
DAK
ETT
YIL
MEY
AġA
GEÇ
HAL
API
ISI
YAT
NLI
ERK
HĠÇ
TAR
KON
SĠZ
RME
YAL
LĠY
BAN
LĠN
UND
ART
EVĠ
DÜġ
ĠġĠ
DIM
TLE
TÜN
ATL
DUR
ZAM
MUġ
SÖY
Fre
7880
7798
7781
7729
7718
7710
7687
7679
7655
7648
7646
7566
7561
7524
7521
7493
7486
7422
7367
7323
7319
7184
7150
7113
7107
7107
7106
7084
7076
7068
7066
7050
7010
6996
6993
6993
6979
6965
6934
6931
6913
6894
6881
6795
6788
6759
6718
6688
6665
6645
Ngr
KTI
ĞIM
ĠRD
YET
ÜRÜ
LAD
RAD
BĠZ
ġKA
ÜND
DĠN
OKU
ĠRL
RAS
TĠN
LĠR
ĞĠL
KTE
EKT
RKA
ALD
IRI
CEK
DĠK
ALĠ
KUR
ÜNÜ
LIĞ
MED
TUR
NDI
GER
BUN
ĞĠM
DĠL
ALL
APA
LEM
DĠR
KAY
HAN
LAT
ĠYĠ
IġI
MĠN
KĠM
KAP
URA
YAK
NĠZ
Fre
6634
6633
6624
6601
6600
6597
6581
6558
6553
6552
6550
6541
6541
6510
6489
6475
6469
6450
6425
6408
6403
6402
6396
6394
6378
6374
6358
6354
6340
6339
6336
6326
6301
6279
6269
6264
6244
6223
6200
6196
6158
6084
6065
6043
6041
6030
6015
5976
5970
5970
10
RAL
MĠZ
SEV
TIN
ĠKA
ATA
UYO
ĠRA
ÜRK
ASA
ĠDE
YOK
TME
ETM
BEL
TEK
NAN
LME
MES
TLA
GEN
ÜġÜ
ZLE
ġIN
RĠM
MAL
LAġ
GÖZ
ÇEK
KIN
UNA
ATT
MEN
ġMA
ÜTÜ
ĠKL
TIK
TEL
MLE
NIZ
NCA
YÜZ
USU
DEM
ĠMD
LLE
YAġ
HAT
DEK
RIM
5950
5940
5934
5920
5915
5895
5892
5890
5850
5849
5841
5827
5817
5816
5815
5813
5808
5807
5803
5792
5791
5781
5781
5779
5772
5770
5765
5755
5729
5699
5677
5657
5641
5637
5629
5622
5614
5589
5585
5575
5570
5561
5550
5541
5524
5489
5446
5435
5412
5358
ĠRE
ĠLD
MIZ
ABĠ
IKA
MET
ORL
AVA
RES
KAT
ETE
RĠY
ANM
MER
AZA
LIN
ÜST
SOR
MAM
ĠYA
LEY
UKL
LED
KLI
RAR
LIY
KIZ
MEM
RTI
RLĠ
DUM
ĠNC
CAN
BEY
ILM
PLA
TIĞ
BÜT
ÇAL
ARĠ
BAS
DAM
ZEL
ONL
NĠM
LIġ
ERS
AÇI
LUN
ETL
5347
5343
5288
5264
5253
5247
5241
5235
5233
5228
5182
5156
5153
5148
5111
5066
5059
5046
5039
4988
4987
4931
4930
4929
4927
4922
4908
4893
4887
4887
4886
4866
4864
4863
4860
4859
4856
4849
4831
4831
4829
4827
4823
4821
4793
4790
4786
4762
4753
4733
LĠM
IZI
NER
ILD
KĠL
CAĞ
TAK
IRL
ACI
MAZ
ÖRÜ
ALM
IYL
ALT
ĠNS
DÖN
MĠY
ZER
ġAR
RET
ELL
ĠYL
UMU
NSA
ġÜN
ĠZL
TĠM
KOR
ġLE
DOĞ
LAH
NEM
ZLA
ĠRM
KES
CEĞ
SES
ĠNL
GĠT
KUL
ĠKT
YÜK
UYU
NMA
ÜNE
ANT
TĠĞ
ARġ
AYD
RTA
4722
4709
4696
4693
4674
4672
4655
4650
4645
4629
4600
4600
4589
4586
4586
4583
4573
4571
4566
4558
4554
4550
4525
4519
4498
4488
4477
4476
4460
4452
4450
4436
4434
4431
4418
4410
4392
4392
4392
4389
4375
4374
4351
4344
4338
4327
4325
4323
4317
4302
GĠR
ÜYO
RAM
RIL
EVE
LAC
SAL
YDI
LĠĞ
SIL
MIN
DUY
HEM
YĠN
IKT
ÜĞÜ
MUT
LMĠ
TIL
EVL
ARE
GĠD
ġĠM
STĠ
ÜYÜ
KLĠ
APT
TIM
ENL
KĠN
UNL
KER
BAB
ÖNC
AĞA
RDÜ
BĠN
BAL
MLA
SAR
SÜR
IRD
KAÇ
MDA
ERM
ANE
DIK
ÖNE
EYL
BUR
4301
4299
4292
4243
4233
4210
4207
4205
4201
4194
4180
4180
4177
4163
4160
4160
4153
4144
4134
4123
4118
4114
4112
4110
4106
4104
4089
4085
4084
4080
4059
4042
4017
4016
4008
3998
3983
3973
3966
3960
3954
3932
3930
3927
3920
3918
3917
3917
3914
3912
OCU
EKE
ÜRE
TĠK
URD
TĠY
ÖRE
RġI
IKI
TMA
BER
RĠL
KIR
ÜZÜ
ÇOC
RAY
YDĠ
NME
NĠY
ADE
LEC
ANK
ġTU
SIZ
HAR
UZU
KTĠ
ERA
YOL
ĠġL
IRM
ARM
NED
LMI
KAS
ANN
EġĠ
ELD
SĠY
IZL
PEK
SER
ĠNA
NAS
ZĠN
YON
SIR
UġT
LET
ALE
3910
3906
3906
3904
3904
3902
3901
3901
3897
3892
3883
3878
3874
3851
3833
3833
3832
3829
3819
3813
3809
3808
3803
3789
3783
3780
3770
3754
3749
3743
3742
3735
3722
3721
3718
3715
3699
3697
3688
3682
3670
3661
3654
3646
3644
3623
3620
3615
3615
3608
ĠTA
LTI
SAY
KKA
TEM
NNE
LLĠ
BÜY
NIM
SEL
EBĠ
TTI
TAL
MEL
ÖNÜ
ORA
ONA
BAH
DÜR
OYU
MDE
INL
AYR
AYN
RMĠ
ĠLG
MEZ
BEK
RIY
LĠS
DOL
ZAR
ANB
DAY
ĠML
NEL
ĠZE
OTU
TAB
AST
ĠDĠ
LUK
SEY
OCA
RAF
ORT
KET
PTI
EFE
RSU
3599
3599
3588
3587
3583
3583
3581
3577
3571
3567
3563
3547
3546
3545
3537
3529
3524
3523
3520
3519
3517
3494
3493
3478
3475
3468
3467
3453
3439
3437
3435
3426
3423
3420
3408
3406
3395
3383
3381
3370
3353
3349
3345
3344
3343
3330
3327
3326
3324
3316
11
Table 2.6 Frequencies of 600 Most Frequent Tetragrams in Turkish within 11M
Ngr
LARI
LERĠ
ERĠN
ARIN
INDA
ĠNDE
ĠYOR
ORDU
ANLA
ĠÇĠN
NLAR
YORD
ENDĠ
IYOR
ASIN
ÖYLE
KLAR
ALAR
NDAN
ANIN
GĠBĠ
DĠĞĠ
OLDU
DIĞI
ININ
DUĞU
ĠLER
ESĠN
ELER
DEDĠ
ONRA
SONR
ARDI
ĠNĠN
KEND
NDEN
RĠNĠ
LARD
KADA
RINI
RLAR
KLER
DĠYE
SĠNĠ
IĞIN
LDUĞ
DAHA
AKLA
IġTI
DEĞĠ
Fre
43055
36077
26911
26117
25969
22658
19578
17770
17328
16930
16745
16018
15616
15398
14773
12783
12718
12303
12068
12011
11641
11316
11130
11066
10737
10666
10665
10658
10580
10528
10527
10525
10515
10499
10462
10226
10148
10110
9380
9329
8666
8628
8587
8576
8441
8212
8071
7957
7948
7914
Ngr
LARA
BENĠ
YORU
ILAR
AMAN
MAYA
EDEN
ĠĞĠN
AġLA
ARDA
SINI
ARAK
ERDE
KARA
SIND
OLMA
UĞUN
ACAK
ERDĠ
RĠND
ENĠN
ERLE
ĠSTE
ĞINI
SÖYL
ORUM
RKEN
DAKĠ
BĠRĠ
ERKE
MASI
EĞĠL
ĠġTĠ
LERD
RLER
IKLA
ĞĠNĠ
LADI
ARLA
ZAMA
EKLE
BAġK
ETTĠ
ADAR
AġKA
ANLI
ADIN
BĠLĠ
UYOR
UNDA
Fre
7760
7737
7724
7684
7633
7631
7603
7583
7523
7507
7449
7434
7387
7375
7361
7267
7229
7067
6895
6817
6815
6737
6723
6721
6638
6634
6627
6596
6585
6575
6487
6466
6459
6405
6398
6377
6342
6309
6278
6262
6261
6236
6220
6171
6152
6125
6108
6067
5887
5828
Ngr
BĠLE
RĠNE
EREK
LIĞI
ġLAR
MIġT
ONUN
ECEK
NLER
ANDI
MADI
ĞUNU
ĠSĠN
LAMA
ADAN
ALDI
TÜRK
RIND
MEYE
HAYA
RADA
KONU
BAġL
ADIĞ
RASI
ÜTÜN
DEKĠ
MĠġT
ARKA
ORLA
EDĠĞ
ĠMĠZ
TIĞI
ĠKLE
BÜTÜ
ÜNDE
ĠRDĠ
DÜġÜ
LĠYO
DĠYO
ONLA
ÇIKA
YANI
KADI
CAĞI
STAN
ĠLDĠ
TLER
IYLA
ANDA
Fre
5796
5782
5771
5697
5661
5623
5615
5589
5532
5526
5480
5384
5370
5364
5327
5282
5234
5201
5166
5148
5137
5135
5124
5096
5053
5028
5003
4976
4914
4901
4845
4816
4806
4799
4768
4766
4765
4740
4698
4691
4676
4635
4629
4625
4623
4608
4583
4583
4575
4574
Ngr
ĠYLE
IĞIM
ÜġÜN
ĠĞĠM
ENĠM
LEDĠ
SĠNE
CEĞĠ
ECEĞ
KALA
KARI
UNUN
TĠĞĠ
ÜYOR
RDEN
MESĠ
ACAĞ
YENĠ
ERĠM
ARIM
ÇĠND
AġIN
MEDĠ
SĠND
ETME
LLAR
ZLER
ALAN
AĞIN
YORL
KTAN
GÖRÜ
AYAN
ALIġ
ĠNSA
AMIġ
NSAN
BANA
BAġI
ĠSTA
AKTI
OLAN
ÖNCE
BABA
ARġI
BĠRL
ÇOCU
BULU
GELĠ
UKLA
Fre
4546
4538
4495
4494
4474
4378
4361
4351
4324
4312
4301
4298
4288
4287
4284
4237
4232
4232
4226
4211
4209
4204
4189
4154
4153
4143
4135
4092
4088
4081
4080
4073
4065
4025
4014
4013
4000
3998
3993
3990
3981
3964
3964
3933
3901
3843
3833
3821
3817
3813
Ngr
LĠĞĠ
IRLA
EDĠM
ILDI
ASIL
ĠRĠN
ABĠL
LECE
SINA
AYAT
ETLE
IMIZ
NLAT
LERE
STER
LAYA
ARTI
ISIN
ARAS
ULAR
TANI
VARD
KARġ
ADAM
IKAR
RDAN
ÇALI
LIYO
BÜYÜ
ĠLME
ALLA
AKTA
ĠKTE
ELĠN
EMĠġ
UNLA
LMIġ
DĠLE
BAKA
LACA
YAPI
EDER
EMEK
ĠLĠR
UġTU
NDAK
ĠRLĠ
EĞĠN
ÜZER
ĠġLE
Fre
3804
3775
3763
3759
3731
3728
3726
3715
3715
3715
3715
3694
3693
3686
3685
3680
3678
3676
3674
3658
3654
3642
3635
3615
3612
3608
3591
3585
3575
3568
3567
3559
3553
3547
3540
3513
3509
3507
3505
3488
3483
3476
3465
3464
3451
3434
3421
3420
3420
3412
Ngr
GÖRE
KAPI
ĠNĠZ
ġLER
YAZI
ANIM
OLAR
ĠNLE
RDUM
LANI
ALTI
URDU
NASI
SENĠ
MĠYO
TANB
ANBU
NBUL
IRDI
ĠSTĠ
LEME
GELE
AKLI
ETĠN
APTI
EYLE
ATIR
ĠMDĠ
TELE
ENLE
KORK
ĠRLE
YAPA
ANNE
BĠLM
GENE
ELDĠ
OCUK
ATTI
SUNU
KANI
AĞIR
ĠLMĠ
EVLE
ĠLGĠ
ÜZEL
RESĠ
RINA
DENĠ
ALMA
Fre
3399
3395
3380
3377
3376
3367
3366
3361
3356
3327
3319
3315
3286
3286
3281
3251
3240
3236
3222
3212
3205
3203
3202
3186
3185
3174
3167
3141
3134
3130
3116
3107
3098
3096
3092
3092
3088
3087
3086
3086
3081
3075
3066
3053
3052
3045
3045
3042
3038
3029
12
ANMA
BÖYL
GECE
EDĠY
YORS
YAġA
VERĠ
ĠTTĠ
NDĠM
TLAR
DĠSĠ
YAPT
OTUR
ġĠMD
LLER
BĠZĠ
NEDE
NDEK
ONUġ
LAMI
ÜYÜK
ADIM
NDĠS
ORTA
ZERĠ
YATI
YACA
TTĠĞ
MANI
ATLA
ĠYET
LLAH
ÖZLE
KTEN
RALA
PARA
RSUN
MLER
ĠLĠY
BAKI
GÜZE
BUNU
RKAD
RLĠK
ESKĠ
MEKT
ġTIR
ġTĠR
EDĠL
MANL
3024
3012
3002
2997
2984
2983
2978
2978
2978
2974
2971
2956
2945
2940
2925
2919
2908
2906
2903
2902
2902
2887
2884
2881
2875
2873
2867
2865
2857
2853
2824
2822
2819
2817
2805
2802
2800
2784
2783
2781
2774
2773
2769
2762
2751
2750
2749
2743
2737
2735
AYIN
KĠTA
GELD
DÜĞÜ
ULUN
DURU
LĠKT
IRAK
ILMA
LIKL
EKLĠ
AKIN
MADA
LMAS
ERĠY
RTIK
EVĠN
ELĠM
LANM
NLIK
ATIN
ELLĠ
EKTĠ
LMĠġ
ARAR
YÜZÜ
LEYE
AYDI
ĠMLE
ÖRDÜ
ĠNCE
DOĞR
APIL
YARA
GEÇĠ
ATLI
DEMĠ
OĞRU
ELEN
EYEN
INIZ
LAND
UĞUM
ARIY
ADAġ
LAYI
VERD
BASI
INLA
ĞĠMĠ
2732
2727
2722
2719
2708
2702
2695
2688
2682
2680
2672
2666
2663
2652
2652
2648
2646
2641
2641
2638
2636
2624
2619
2611
2607
2595
2591
2585
2579
2573
2562
2562
2560
2553
2546
2543
2541
2540
2531
2512
2507
2504
2499
2497
2497
2493
2488
2484
2484
2480
OYUN
USUN
ULLA
ĠZLĠ
EYĠN
NĠYE
EMĠN
ALNI
ORSU
ĠDEN
SANI
ÜZÜN
MALA
ÖĞRE
EYEC
DERĠ
AYAC
AYLA
RMĠġ
GÖRD
MLAR
BEKL
UZUN
HMET
ĠLEN
KASI
LARL
ĠRME
EBĠL
EMEN
ARAN
BIRA
AMIN
HĠÇB
ĞIMI
ĠÇBĠ
GERE
YILL
ĠMDE
ILAN
IRMA
RDĠĞ
LMUġ
GĠTT
KÜÇÜ
ABAS
ÜNYA
AĞLA
DÜNY
AYNI
2477
2473
2471
2470
2461
2461
2459
2459
2453
2452
2448
2446
2446
2436
2427
2422
2421
2415
2413
2411
2410
2408
2406
2403
2402
2402
2394
2391
2388
2374
2373
2373
2372
2367
2366
2365
2358
2356
2347
2345
2341
2332
2331
2324
2320
2316
2315
2315
2311
2307
MIYO
YECE
ÜSTÜ
LMAD
EKTE
LMAK
LDĠĞ
ÖSTE
LNIZ
YALN
KĠġĠ
SONU
RĠMĠ
ÇBĠR
RECE
ġIND
GÖZL
ANIY
AMAY
SORU
LDIR
MAYI
YAPM
AMAD
BURA
ENCE
ERME
ILLA
GĠDE
GÖST
ELĠR
REDE
DEME
ALIN
IġLA
LDIĞ
ARMA
DĠNĠ
ĠZĠN
KANL
YERĠ
ALIK
OLAY
ETĠR
LERL
ENĠZ
VERM
AġTI
TEDĠ
BĠRA
2304
2300
2298
2295
2290
2289
2287
2286
2286
2286
2283
2283
2281
2276
2276
2275
2267
2266
2263
2260
2260
2258
2258
2257
2257
2256
2255
2250
2248
2246
2246
2244
2239
2239
2237
2232
2231
2224
2222
2222
2222
2219
2217
2208
2202
2202
2199
2198
2195
2193
TARA
LTIN
ĞIND
NDĠN
HATI
YLER
IKTI
NESĠ
ILMI
KALI
ĠNAN
AKAL
MAMI
RDIM
ĠNCĠ
YERE
ZETE
RAYA
AKAN
SIRA
ĠMSE
ĠġTE
ġKAN
GETĠ
AZET
ARKE
URMA
HEME
KALD
ġLAD
GAZE
IZLA
ĠRAZ
MUTL
ĠYDĠ
LĠKL
KESĠ
ARAL
AMLA
DINI
ATIL
AĞIM
ĠZĠM
RMUġ
IMDA
ĠLEC
ĞREN
ENDE
ERSE
CUKL
2190
2185
2182
2181
2176
2176
2175
2173
2171
2170
2164
2164
2164
2155
2155
2153
2147
2146
2140
2138
2135
2131
2126
2126
2124
2124
2120
2119
2118
2116
2115
2113
2113
2104
2100
2099
2098
2095
2088
2087
2087
2087
2082
2077
2074
2068
2068
2067
2066
2064
ERÇE
HĠSS
MAKT
YLED
LUĞU
ANCA
LMAY
ĠSSE
NIYO
FEND
MELE
RABA
TMĠġ
GELM
EFEN
SÜRE
EDĠK
OLUR
YÜRÜ
TILA
YAKI
SEVĠ
ORKU
SOKA
LANA
MASA
ARAY
ĠZLE
SAAT
ZLAR
RMIġ
ARAB
KARD
YARI
GÖRM
ATTA
ERĠL
IKTA
KĠYE
NERE
BĠRB
AYRI
ÜNKÜ
AZIL
HANE
ĠRMĠ
MIZI
RBĠR
RIMI
AZAN
2063
2062
2062
2054
2046
2044
2043
2041
2037
2033
2026
2026
2025
2025
2025
2024
2024
2023
2023
2022
2022
2021
2019
2016
2015
2014
2009
2006
2005
2004
2000
1994
1993
1986
1985
1983
1979
1979
1977
1972
1969
1968
1963
1963
1962
1961
1961
1956
1956
1953
13
Table 2.7 Frequencies of 600 Most Frequent Pentagrams in Turkish within 11M
Ngr
LARIN
LERĠN
YORDU
SONRA
KENDĠ
ARINI
KLARI
ERĠNĠ
LDUĞU
INDAN
ANLAR
OLDUĞ
NLARI
SINDA
ALARI
ĠNDEN
ĠYORD
RĠNDE
DEĞĠL
LARDA
ZAMAN
ERĠND
KADAR
BAġKA
YORUM
ASIND
SÖYLE
KLERĠ
ELERĠ
MIġTI
IYORD
DUĞUN
UĞUNU
RINDA
ARIND
ADIĞI
ERĠNE
LERDE
MĠġTĠ
EDĠĞĠ
AKLAR
BÜTÜN
LĠYOR
ĠLERĠ
DĠYOR
BAġLA
IĞINI
ASINI
ĠĞĠNĠ
IKLAR
Fre
23638
19659
16000
10524
10266
9092
8788
8428
8212
7993
7940
7706
7546
7329
7133
7047
6793
6778
6254
6239
6158
6144
6113
6106
6049
5970
5963
5814
5801
5606
5448
5346
5192
5148
5101
5089
4906
4894
4892
4844
4806
4767
4693
4689
4671
4638
4627
4582
4535
4519
Ngr
ONLAR
ORLAR
KADIN
ECEĞĠ
DÜġÜN
BENĠM
ACAĞI
ĠÇĠND
ÇĠNDE
YORLA
SĠNDE
ĠNSAN
ESĠNĠ
LARDI
DĠĞĠN
RASIN
ĠSTAN
HAYAT
KARġI
ĠYORU
ARASI
LIYOR
DIĞIN
ANLAT
VARDI
ĠKLER
EKLER
ÇIKAR
NDAKĠ
RĠNĠN
RININ
MASIN
ERLER
MĠYOR
ANBUL
STANB
TANBU
ÇALIġ
ILARI
LARAK
LARIM
ARDAN
ÇOCUK
RLERĠ
ESĠND
BÖYLE
UKLAR
ARINA
YAPTI
AġLAR
Fre
4418
4406
4359
4269
4234
4232
4212
4181
4147
4081
4041
3937
3920
3858
3785
3785
3711
3673
3633
3615
3592
3574
3560
3543
3535
3516
3504
3490
3401
3366
3337
3326
3323
3267
3235
3234
3234
3219
3176
3175
3174
3095
3085
3077
3039
3012
2999
2989
2948
2947
Ngr
BĠLĠR
ASINA
BÜYÜK
KONUġ
ORDUM
NDEKĠ
DĠĞĠM
TTĠĞĠ
LIĞIN
ġĠMDĠ
ENDĠS
ERDEN
ZLERĠ
NASIL
RKADA
BĠRĠN
ARKAD
NDĠSĠ
YANIN
GÜZEL
DIĞIM
ENDĠM
GELDĠ
ÜZERĠ
UNLAR
OLARA
BĠRLĠ
ETLER
TLERĠ
ġLARI
ĠSĠNĠ
ĠLĠYO
LĠKTE
MADIĞ
ĠġLER
SĠNĠN
ERKEN
INDAK
DĠLER
ARTIK
DOĞRU
ZERĠN
KADAġ
VERDĠ
ENLER
ORSUN
YORSU
NEDEN
AYACA
GÖRDÜ
Fre
2942
2931
2902
2897
2889
2884
2866
2862
2857
2839
2830
2823
2781
2776
2768
2768
2766
2762
2756
2753
2742
2727
2720
2716
2710
2693
2687
2670
2669
2653
2645
2633
2632
2607
2599
2587
2586
2579
2556
2551
2536
2529
2485
2475
2450
2448
2438
2417
2417
2408
Ngr
RLARD
ĠRLĠK
LMASI
BIRAK
LARLA
HĠÇBĠ
ĠNDEK
LERĠM
ĠRLER
RALAR
RDĠĞĠ
GĠTTĠ
ÖZLER
LANDI
DÜNYA
IYORU
SININ
LIKLA
MIYOR
BULUN
LDĠĞĠ
YALNI
ALNIZ
EDĠYO
MESĠN
ĠÇBĠR
LACAK
BAġIN
GÖSTE
ÖSTER
MADAN
LDIĞI
GEREK
ARLAR
ESĠNE
ġINDA
RLĠKT
NLERĠ
ALTIN
ILLAR
MALAR
LERLE
ĞINDA
AYATI
ENDĠN
HATIR
MANLA
GETĠR
HEMEN
AZETE
Fre
2396
2386
2377
2372
2371
2364
2363
2357
2352
2337
2331
2323
2323
2317
2305
2301
2300
2299
2299
2295
2287
2286
2286
2285
2277
2272
2270
2252
2246
2246
2232
2229
2213
2199
2199
2188
2188
2187
2182
2180
2180
2172
2161
2149
2145
2145
2129
2126
2119
2106
Ngr
YILLA
GAZET
BĠLME
ġLADI
KALDI
AĞINI
UYORD
ILMIġ
BĠLĠY
AġLAD
ĠLECE
ETTĠĞ
YLEDĠ
LĠKLE
DĠSĠN
HĠSSE
ÖYLED
LĠĞĠN
BĠZĠM
OCUKL
FENDĠ
NIYOR
KORKU
DEDĠM
ALLAH
ANLIK
EFEND
BĠRAZ
NINDA
BĠRBĠ
ĠRBĠR
TĠYOR
ÖĞREN
LLERĠ
BUNLA
GÖZLE
BEKLE
IġLAR
UNDAN
LMADI
MANIN
LAMIġ
KÜÇÜK
TLARI
ATIRL
SENĠN
CAĞIN
RĠYOR
GERÇE
ANIYO
Fre
2106
2105
2103
2101
2081
2080
2076
2069
2066
2063
2062
2053
2053
2052
2039
2034
2025
2025
2024
2023
2023
2013
2012
2002
2002
2002
1993
1942
1933
1927
1926
1920
1915
1912
1912
1904
1902
1901
1891
1881
1879
1877
1876
1865
1863
1854
1853
1846
1846
1846
Ngr
ALDIR
ARIMI
KĠMSE
YÜZÜN
AMAYA
YAPIL
MAKTA
ADINI
ĠĞĠMĠ
STEDĠ
ANIND
ĠSTED
EĞĠNĠ
FÜSUN
ĠġTĠR
NDIĞI
LENDĠ
AMIġT
RLARI
ÇÜNKÜ
KARAR
ANLAM
ÜNDEN
AMADI
IĞIMI
IġTIR
OLACA
BAKAN
ĠSTĠY
MUTLU
ĠLMĠġ
AġKAN
ÇIKTI
ERKES
HERKE
ĠKAYE
TÜRKĠ
MUġTU
RKĠYE
YERĠN
ÜRKĠY
ABASI
MEDEN
LMAYA
BELKĠ
ERĠMĠ
TARĠH
ĠMLER
LĠNDE
CEĞĠN
Fre
1841
1834
1833
1827
1823
1818
1817
1811
1806
1806
1803
1801
1801
1797
1796
1795
1795
1793
1790
1786
1785
1780
1768
1768
1763
1761
1750
1743
1741
1740
1736
1734
1733
1733
1726
1722
1719
1715
1708
1707
1706
1706
1704
1701
1701
1699
1696
1695
1693
1686
14
ĞĠNDE
INLAR
ARKEN
DUĞUM
RANLI
EHMET
STĠYO
MEHME
EYECE
LLARI
MEDĠĞ
NLIĞI
TINDA
YAPMA
BĠLDĠ
BĠLEC
ARABA
ERÇEK
ANDIĞ
ĠYORL
DĠKLE
ANMIġ
ÜYORD
AġIND
OLMUġ
DENĠZ
ULARI
NSANL
AKTAN
ANDIR
GELEN
GÖRÜN
ġEYLE
TIRLA
ÜSTÜN
AKġAM
MLERĠ
IĞIND
KARAN
KANLI
MAMIġ
SABAH
YACAK
EYLER
ABĠLĠ
LADIĞ
RIYLA
ARDIM
SANLA
TILAR
1679
1676
1675
1672
1662
1658
1658
1655
1654
1654
1647
1644
1644
1643
1642
1639
1636
1631
1631
1631
1630
1626
1622
1620
1619
1617
1616
1613
1611
1595
1595
1592
1590
1590
1587
1579
1572
1572
1567
1565
1564
1557
1550
1549
1548
1547
1546
1545
1542
1541
LANMA
LECEĞ
NLARD
MEKTE
ĠSTEM
KĠTAP
GÖRME
OLMAD
LINDA
ĠNLER
MELER
ARIYL
DEĞĠġ
ANLIĞ
EMĠġT
CAĞIM
ĠLGĠL
RĠYLE
LUYOR
TĠĞĠN
LECEK
ġIYOR
LERDĠ
RUYOR
ÖLDÜR
ġLERĠ
KASIN
LAġTI
ĠYORS
LABĠL
SOKAK
BAKTI
KIYOR
ĠMĠZĠ
CEĞĠM
HABER
YORUZ
NLARA
DINLA
LARIY
YAKIN
ĠLDĠĞ
NELER
IYORL
ÜNLER
ATLAR
ASKER
POLĠS
HĠKAY
HAYAL
1540
1540
1539
1539
1538
1535
1535
1533
1528
1527
1527
1522
1518
1516
1515
1511
1511
1511
1511
1508
1507
1506
1505
1491
1491
1489
1484
1481
1480
1480
1479
1478
1475
1474
1469
1469
1468
1467
1464
1461
1455
1453
1452
1450
1449
1448
1443
1443
1442
1438
ALMIġ
DIKLA
IKTAN
PTIĞI
GEÇĠR
ÖYLEM
SANKĠ
EMEDĠ
SONUN
APTIĞ
BASIN
EMEYE
YERLE
MAYAC
ANCAK
ARALA
ARANL
ĠĞĠND
RĠMĠZ
ETMĠġ
ISINI
BABAM
TARAF
ÖYLEY
DUYGU
RIYOR
OLMAS
VERME
ERKEK
AMLAR
ĠRDEN
ISIND
MLARI
TĠRDĠ
NUNDA
DILAR
KULLA
GÜNLE
ĠRĠNĠ
ORMUġ
TIĞIN
LATTI
ARDIR
EREDE
ENDEN
AMANL
DĠNLE
LERĠY
ĞĠMĠZ
RADAN
1433
1423
1422
1418
1411
1410
1410
1408
1406
1405
1404
1399
1398
1397
1395
1388
1384
1378
1372
1370
1369
1368
1364
1363
1360
1356
1355
1353
1352
1348
1346
1340
1339
1339
1333
1332
1329
1329
1327
1326
1326
1325
1324
1324
1320
1319
1316
1312
1312
1312
CUKLA
ÇLARI
SEYRE
SEVER
TELEF
ELEFO
LEFON
TOPLA
EKTEN
ARġIL
YECEK
ARMIġ
NDĠNĠ
ERĠYL
YACAĞ
ORADA
YATIN
ALARD
CAKLA
ĞIMIZ
ÜġÜNÜ
UġTUR
RDÜĞÜ
TIĞIM
ĠSTER
AZILA
URADA
ELLER
RESĠM
YOKTU
SĠNĠZ
EMĠYO
SUNUZ
LAYAN
MIġLA
ULLAN
TIYOR
KINDA
EĞĠLD
ĞĠLDĠ
ĠSĠNE
ARISI
LENME
YAKLA
SĠZLĠ
ANNEM
ĠRMĠġ
HANGĠ
MAYAN
CAKTI
1311
1310
1309
1309
1309
1303
1303
1301
1299
1295
1291
1285
1281
1280
1280
1280
1277
1276
1275
1273
1264
1263
1261
1259
1258
1257
1257
1247
1246
1241
1239
1238
1236
1236
1232
1231
1230
1230
1225
1223
1220
1219
1217
1215
1214
1214
1211
1209
1206
1205
ENDĠL
ÜġÜND
ZÜNDE
ERMĠġ
LMIġT
ĠRDĠĞ
KARIġ
LEDĠĞ
DERDĠ
SĠYLE
TĠĞĠM
LADIM
BĠRDE
AÇLAR
ARADA
LAMAY
LEġTĠ
BAĞIR
AMIYO
BELĠR
SORDU
ADINL
IRLAR
KĠLER
BURAD
ONUġM
SESSĠ
ACAKT
ALDIĞ
EDĠLE
ESSĠZ
URUYO
ĠKTEN
IMIZI
UĞUMU
KĠTAB
ÇATLI
MEMĠġ
ĠÇERĠ
YAZAR
ONUND
KANIN
GĠRDĠ
HAZIR
IZLAR
DAġLA
ELERD
BĠRLE
HANIM
SĠLAH
1205
1202
1200
1200
1200
1199
1199
1199
1198
1198
1193
1192
1190
1190
1190
1189
1189
1188
1183
1182
1182
1182
1182
1181
1179
1179
1178
1177
1175
1174
1174
1169
1169
1168
1167
1166
1165
1164
1162
1162
1160
1160
1158
1158
1157
1157
1156
1155
1155
1152
HAREK
NLATI
OLMAK
MĠġLE
RESĠN
LACAĞ
YARDI
YORMU
NDĠMĠ
ADAġL
ENCER
ġÜNDÜ
NCERE
NĠDEN
AKLAġ
ELĠYO
ERDĠĞ
LANLA
LÜYOR
LMESĠ
YÜKSE
FAZLA
BENZE
RÜYOR
YERDE
ALIġI
GÖTÜR
DEVLE
GEÇTĠ
OLSUN
NĠYET
ANDAN
GENEL
CĠLER
ELĠND
LĠġKĠ
HATTA
HEPSĠ
DEMĠġ
ERDĠM
MERAK
EVLET
BENDE
ACAKL
PARÇA
GÖREV
ALABA
BALAR
APLAR
ĠSSET
1151
1151
1151
1147
1145
1144
1143
1142
1141
1138
1137
1137
1134
1134
1133
1133
1132
1131
1131
1130
1129
1129
1128
1128
1126
1126
1125
1125
1125
1122
1121
1120
1119
1119
1118
1117
1116
1114
1109
1106
1106
1104
1102
1102
1102
1101
1098
1097
1096
1092
15
2.1.3. Affine Cipher
The encryption method aims to perform the encryption process on the linear equation of
yi = axi+b (mod n) where xi refers to plaintext, yi refers to ciphertext, n refers to size of
the alphabet and pair of (a, b) refer to key. In the equation, (a, n) must be coprime.
Substitution cipher is a special form of Affine cipher where a is equal to 1. And vice
versa, affine cipher is a special form of substitution cipher where composing
substitution table is formulised.
Table 2.8 Index Values of the Letter of the Turkish Alphabet
A B C Ç D E F G Ğ H I Ġ J K L M N O Ö P R S ġ T U Ü V Y Z
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 27 28
Suppose that the plaintext is ALANKAY and the key is (2, -4)2. The plaintext would have
the corresponding values found in Table 2.8. By using the plaintext, it is encrypted as
illustrated in Table 2.9 and the ciphertext is decrypted as demonstrated in Table 2.10.
Table 2.9 Encryption Process of Affine Cipher
Plaintext
Index values
y= 2x - 4
y= 2x - 4
Mod 29
Ciphertext
A
0
0.2-4
-4
25
Ü
L
14
14.2-4
24
24
U
A
0
0.2-4
-4
25
Ü
N
16
16.2-4
28
28
Z
K
13
13.2-4
22
22
Ş
A
0
0.2-4
-4
25
Ü
Y
27
27.2-4
50
21
S
Table 2.10 Decryption Process of Affine Cipher
Ciphertext
Index values
x=(y+4)/2
x=(y+4)/2
Mod 29
Mod 29
Plaintext
2
Ü
U
Ü
Z
Ş
25
24
25
28
22
(25+4)/2 (24+4)/2 (25+4)/2 (28+4)/2 (22+4)/2
14,5
14
14,5
16
13
145+5.29
145+5.29
14
16
13
10
0
A
10
14
L
0
A
16
N
13
K
Ü
25
(25+4)/2
14,5
S
21
(21+4)/2
12,5
0
A
27
Y
145+5.29
10
125+5.29
10
The key (2, -4) is equal to (2, 25) because of the principle y mod n = ax+b mod n = ax mod n + b mod n
16
The key space of the affine cipher is 812 for Turkish3. Therefore, the method is weak
against to brute force attack.
Moreover, the method is also insecure against to
frequency analysis attack because the method is a special form of substitution cipher.
Furthermore, if two ciphertext symbols of the plaintext are detected, the key could be
calculated from the equation easily.
2.2.
Block Ciphers
Most generally, plaintext is divided into blocks, and each block is encrypted
respectively in block ciphers. Block ciphers manipulates the frequency distribution of
the ciphertext and makes the frequency analysis attacks difficult.
2.2.1.
Permutation Cipher
Permutation cipher depends on the principle that transposing the plaintext letters each
other. In order to implement the method, a permutation rule is specified and the
plaintext divided into blocks. Finally, each block is permuted within the permutation
rule.
Figure 2.3 illustrates an example of permutation cipher.
The method is weak against to frequency analysis attack because letters of the plaintext
would not be changed in the ciphertext. Moreover, the key space of the permutation
cipher is equal to m! and m could be equal to the length of the plaintext in worst case.
Therefore, the method could be revealed by brute force attack easily.
3
The number of letters of the Turkish alphabet is equal to 29 which is a prime number. In the equation
y= ax+b mod n, a has to be coprime with 29 to equation be reversible. That’s why, key space of the a is
equal to 28 according to restriction. Moreover, key space of the b is always equal to n. Thus, key space
of the affine cipher 28x29=812 for Turkish.
17
Figure 2.3 Illustration of the Permutation Cipher
2.2.2.
Polygraphic Substitution
Polygraphic substitution performs substitutions on blocks instead of substituting a letter.
Substituting multiple characters at a time destroys the structure of the plaintext. That
makes the frequency analysis attacks impossible.
2.2.2.1.
Playfair Cipher
Playfair cipher is one of the best known encryption techniques of multi-character
substitution. Firstly, the encryption key is picked up. Secondly, the key would be filled
into the 5x5 matrix.
However, duplicated letters has to be dropped in the key.
Remaining letters in the alphabet would be filled into the rest of the cells of matrix
alphabeticlly. The letters of the alphabet has to be filled into 25 cells. Therefore, some
letters can be filled into same cells.
Encryption rule is based on a simple technique. The ciphertext is grouped into blocks
of length 2. The encryption rule performs on each block. Specific letters should be
inserted between repeating letters in the plaintext. If the letters of the current block are
located in the same row of the matrix, the current block is replaced by letters to the right
of each letter in the row. If the letters of the current block are located in the same
column, the current block is replaced by letters below them. Otherwise, letters of the
current block are located in neither same row nor same column, a virtual rectangle is
composed. The rectangle has to contain the letters of the current block in the corner.
The block is replaced by the the other corner elements.
18
Suppose that the key is İstanbul and the plaintext is Florya. The key is filled into the
matrix as illustrated in Table 2.11. The plaintext is grouped into blocks of length 2.
FL
OR
YA
Table 2.11 The Encryption Key of Playfair Cipher
Ġ
B
E
K
ġ
S
U
F
M/N
Ü
T
L
G/Ğ
O/Ö
V
A
C/Ç
H
P
Y
PK
AC
N
D
I/J
R
Z
Finally, the ciphertext is represented as:
GU
Thus, the plaintext FLORYA is encrypted as GUPKAC in Playfair Cipher.
Frequency analysis attacks fail against to playfair cipher [4]. It is a fact that the playfair
cipher is based on bigram substitution. Therefore, the cipher would not balance out the
bigram frequencies of ciphertext. Bigram frequencies of the source language could be
used to attack playfair ciphers.
2.2.2.2.
Hill Cipher
Hill Cipher is a block cipher model based on matrix manipulations. The plaintext is
divided into blocks and each block would be encrypted respectively. Suppose that
block size is decided as n. A (nxn) matrix is specified as key and the each block of the
plaintext is multiply to the matrix to encrypt the plaintext.
C=[K] P mod m
(2.3)
19
C and P are column vectors of length n, representing the plaintext and ciphertext
respectively, and K is a nxn matrix, which is the encryption key. Decryption requires
using the inverse matrix of the matrix K.
P=[K]-1 C mod m
(2.4)
The inverse matrix K-1 is defined by the equation K K-1 = I, where I is the Identity
matrix. It is a fact that the inverse matrix does not always exist.
Suppose that the size of the key matrix is 2x2, and the key matrix is
𝐾=
1 2
3 4
Assume the plaintext would be alankay. First, the plaintext is grouped into blocks of
length 2. The first letter of the plaintext is appended at the end of the plaintext because
the plaintext consists of odd number.
al
an
ka
ya
Secondly, letters of the plaintext are replaced by the corresponding numbers
0 14
0 16
13 0
27 0
Thirdly, each block is multiplied by K
0 1
14 3
0.1 + 14.2
2
28
28
=
=
𝑚𝑜𝑑 29 =
0.3 + 14.4
4
56
27
0.1 + 16.2
0 1 2
32
3
=
=
𝑚𝑜𝑑 29 =
0.3 + 16.4
16 3 4
64
6
13 1
0 3
13.1 + 0.2
2
13
13
=
=
𝑚𝑜𝑑 29 =
13.3 + 0.4
4
39
10
20
27 1
0 3
27.1 + 0.2
2
27
27
=
=
𝑚𝑜𝑑 29 =
27.3 + 0.4
4
81
23
Fourth, the numbers
28 27 3 6
13 10 27 23
represented as:
ZYÇFKIYT
Thus, the ciphertext ALANKAYA would be encrypted as ZYÇFKIYT in Hill Cipher.
The inverse matrix is used to implement the decryption process. A matrix has an inverse
matrix if and only if its determinant is not equal to 0.
K=
a b
, K =ad-bc
c d
1
K-1 = |K|
d
-c
-b
, |K|≠0
a
𝐾𝐾 −1 =
1 0
0 1
Firstly, the inverse matrix is calculated to decrypt the ciphertext.
K = 1.4 − 2.3 = −2 ≠ 0
𝐾 −1 =
1 4
−2 −3
−2
−2
=
1,5
1
27
𝐾 −1 = 15 + 5.29
10
𝐾 −1 =
1
𝑚𝑜𝑑 29
−0,5
1
5.29 − 5 𝑚𝑜𝑑29
10
27
16
1
14
(2.5)
(2.6)
21
Secondly, the letters is grouped into blocks
ZY
ÇF
KI
YT
Thirdly, the letters is replaced by the corresponding numbers
28 27 3 6
13 10 27 23
Fourthly, each block is multiplied by K-1
28 27
27 16
3 27
6 16
28.27 + 27.1
1
783
0
=
=
𝑚𝑜𝑑 29 =
28.16 + 27.14
14
826
14
3.27 + 1.6
1
87
0
=
=
𝑚𝑜𝑑 29 =
3.16 + 6.14
14
132
16
13 27
10 16
13.27 + 10.1
1
361
13
=
=
𝑚𝑜𝑑 29 =
13.16 + 10.14
14
348
0
27 27
23 16
27.27 + 23.1
1
27
752
=
=
𝑚𝑜𝑑 29 =
27.16 + 23.14
14
0
754
Finally, the numbers
0 14
0 16
13 0
27 0
represented as:
alankay
Hill cipher is secure against to frequency analysis attack. Moreover, the Hill cipher is
strong against to brute force attack. The key space of the hill cipher is equal to 29nxn
which is an efficiently large value. However, Hill cipher succumbs to a known plaintext
attack [3]. The key matrix can be calculated easily from a set of known 𝑃 , 𝐶 .
22
2.2.3.
Polyalphabetic Substitution Ciphers
Remaining the substitution rules same for every substitution makes the frequency
analysis attacks applicable on monoalphabetic ciphers. In a polyalphabetic substitution
cipher, multiple substitution alphabets are used throughout the encryption process.
Therefore, same plaintext character could be encrypted to different ciphertext symbols.
That makes the frequency analysis difficult.
2.2.3.1.
Vigenere Cipher
Suppose that an n character alphabet and an m character key, K = (k1, k2, …, km) is
given.
The Vigenere cipher consists of m shift ciphers and ki specifies the
monoalphabetic substitution [10].
Encryption process could be implemented by adding plaintext and key values.
Accordingly, decryption process could be performed by substruction of ciphertext and
key values.
Ci = ( Pi + ki ) mod n
(2.7)
Pi = ( Ci - ki ) mod n
(2.8)
Suppose that the plaintext is MUSTAFAKEMALATATÜRK and the key is İSTANBUL.
The plaintext is encrypted as illustrated in Table 2.12 and the ciphertext is decrypted as
demonstrated in Table 2.13.
Table 2.12 Mathematical Illustration of Encyrption Process of Vigenere Cipher
Plaintext
Key
Plaintext
Key
Plaintext+Key
mod 29
Ciphertext
M
Ġ
15
11
26
26
V
U
S
24
21
45
16
N
S
T
21
23
44
15
M
T
A
23
0
23
23
T
A
N
0
16
16
16
N
F
B
6
1
7
7
G
A
U
0
24
24
24
U
K
L
13
14
27
27
Y
E
Ġ
5
11
16
16
N
M
S
15
21
36
7
G
A
T
0
23
23
23
T
L
A
14
0
14
14
L
A
N
0
16
16
16
N
T
B
23
1
24
24
U
A
U
0
24
24
24
U
T
L
23
14
37
8
Ğ
Ü
Ġ
25
11
36
7
G
R
S
20
21
41
12
J
K
T
13
23
36
7
G
23
Table 2.13 Mathematical Illustration of Decryption Process of Vigenere Cipher
Ciphertext
Key
Ciphertext
Key
Ciphertext-Key
mod 29
Plaintext
V
Ġ
26
11
15
15
M
N
S
16
21
-5
24
U
M
T
15
23
-8
21
S
T
A
23
0
23
23
T
N
N
16
16
0
0
A
G
B
7
1
6
6
F
U
U
24
24
0
0
A
Y
L
27
14
13
13
K
N
Ġ
16
11
5
5
E
G
S
7
21
-14
15
M
T
T
23
23
0
0
A
L
A
14
0
14
14
L
N
N
16
16
0
0
A
U
B
24
1
23
23
T
U
U
24
24
0
0
A
Ğ
L
8
14
-6
23
T
G
Ġ
7
11
-4
25
Ü
J
S
12
21
-9
20
R
G
T
7
23
-16
13
K
Table 2.14 Encryption Process of Vigenere Cipher by Using of Vigenere Table
M U S T A F A K E M A L A T A T Ü R K
Ġ S T A N B U L Ġ S T A N B U L Ġ S T
V N M T N G U Y N G T L N U U Ğ G J G
Plaintext
Key
:
Ciphertext
:
:
Table 2.15 Vigenere Table for Turkish Alphabet
A
B
C
Ç
D
E
F
G
Ğ
H
I
Ġ
J
K
L
M
N
O
Ö
P
R
S
ġ
T
U
Ü
V
Y
Z
A B
A B
B C
C Ç
Ç D
D E
E F
F G
G Ğ
Ğ H
H I
I Ġ
Ġ J
J K
K L
L M
MN
N O
O Ö
Ö P
P R
R S
S ġ
ġ T
T U
U Ü
Ü V
V Y
Y Z
Z A
C
C
Ç
D
E
F
G
Ğ
H
I
Ġ
J
K
L
M
N
O
Ö
P
R
S
ġ
T
U
Ü
V
Y
Z
A
B
Ç
Ç
D
E
F
G
Ğ
H
I
Ġ
J
K
L
M
N
O
Ö
P
R
S
ġ
T
U
Ü
V
Y
Z
A
B
C
D
D
E
F
G
Ğ
H
I
Ġ
J
K
L
M
N
O
Ö
P
R
S
ġ
T
U
Ü
V
Y
Z
A
B
C
Ç
E
E
F
G
Ğ
H
I
Ġ
J
K
L
M
N
O
Ö
P
R
S
ġ
T
U
Ü
V
Y
Z
A
B
C
Ç
D
F
F
G
Ğ
H
I
Ġ
J
K
L
M
N
O
Ö
P
R
S
ġ
T
U
Ü
V
Y
Z
A
B
C
Ç
D
E
G
G
Ğ
H
I
Ġ
J
K
L
M
N
O
Ö
P
R
S
ġ
T
U
Ü
V
Y
Z
A
B
C
Ç
D
E
F
Ğ
Ğ
H
I
Ġ
J
K
L
M
N
O
Ö
P
R
S
ġ
T
U
Ü
V
Y
Z
A
B
C
Ç
D
E
F
G
H
H
I
Ġ
J
K
L
M
N
O
Ö
P
R
S
ġ
T
U
Ü
V
Y
Z
A
B
C
Ç
D
E
F
G
Ğ
I
I
Ġ
J
K
L
M
N
O
Ö
P
R
S
ġ
T
U
Ü
V
Y
Z
A
B
C
Ç
D
E
F
G
Ğ
H
Ġ
Ġ
J
K
L
M
N
O
Ö
P
R
S
ġ
T
U
Ü
V
Y
Z
A
B
C
Ç
D
E
F
G
Ğ
H
I
J
J
K
L
M
N
O
Ö
P
R
S
ġ
T
U
Ü
V
Y
Z
A
B
C
Ç
D
E
F
G
Ğ
H
I
Ġ
K
K
L
M
N
O
Ö
P
R
S
ġ
T
U
Ü
V
Y
Z
A
B
C
Ç
D
E
F
G
Ğ
H
I
Ġ
J
L
L
M
N
O
Ö
P
R
S
ġ
T
U
Ü
V
Y
Z
A
B
C
Ç
D
E
F
G
Ğ
H
I
Ġ
J
K
M
M
N
O
Ö
P
R
S
ġ
T
U
Ü
V
Y
Z
A
B
C
Ç
D
E
F
G
Ğ
H
I
Ġ
J
K
L
N
N
O
Ö
P
R
S
ġ
T
U
Ü
V
Y
Z
A
B
C
Ç
D
E
F
G
Ğ
H
I
Ġ
J
K
L
M
O
O
Ö
P
R
S
ġ
T
U
Ü
V
Y
Z
A
B
C
Ç
D
E
F
G
Ğ
H
I
Ġ
J
K
L
M
N
Ö
Ö
P
R
S
ġ
T
U
Ü
V
Y
Z
A
B
C
Ç
D
E
F
G
Ğ
H
I
Ġ
J
K
L
M
N
O
P
P
R
S
ġ
T
U
Ü
V
Y
Z
A
B
C
Ç
D
E
F
G
Ğ
H
I
Ġ
J
K
L
M
N
O
Ö
R
R
S
ġ
T
U
Ü
V
Y
Z
A
B
C
Ç
D
E
F
G
Ğ
H
I
Ġ
J
K
L
M
N
O
Ö
P
S
S
ġ
T
U
Ü
V
Y
Z
A
B
C
Ç
D
E
F
G
Ğ
H
I
Ġ
J
K
L
M
N
O
Ö
P
R
ġ
ġ
T
U
Ü
V
Y
Z
A
B
C
Ç
D
E
F
G
Ğ
H
I
Ġ
J
K
L
M
N
O
Ö
P
R
S
T
T
U
Ü
V
Y
Z
A
B
C
Ç
D
E
F
G
Ğ
H
I
Ġ
J
K
L
M
N
O
Ö
P
R
S
ġ
U
U
Ü
V
Y
Z
A
B
C
Ç
D
E
F
G
Ğ
H
I
Ġ
J
K
L
M
N
O
Ö
P
R
S
ġ
T
Ü
Ü
V
Y
Z
A
B
C
Ç
D
E
F
G
Ğ
H
I
Ġ
J
K
L
M
N
O
Ö
P
R
S
ġ
T
U
V
V
Y
Z
A
B
C
Ç
D
E
F
G
Ğ
H
I
Ġ
J
K
L
M
N
O
Ö
P
R
S
ġ
T
U
Ü
Y
Y
Z
A
B
C
Ç
D
E
F
G
Ğ
H
I
Ġ
J
K
L
M
N
O
Ö
P
R
S
ġ
T
U
Ü
V
Z
Z
A
B
C
Ç
D
E
F
G
Ğ
H
I
Ġ
J
K
L
M
N
O
Ö
P
R
S
ġ
T
U
Ü
V
Y
24
Intersection of the plaintext and the key on Vigenere table states the ciphertext.
Similarly, the plaintext could be obtained by performing inverse process. A sample
scenario is illustrated in Table 2.14 while Table 2.15 is used as Vigenere table.
Note that A would be replaced by N, U, T, N, and U respectively.
The action
manipulates the frequency distribution of the ciphertext. Therefore, frequency analysis
attacks cannot be performed as easily on Vigenere cipher.
// C is an array consisting of elements of ciphertext respectively
// K is an array consisting of elements of key respectively
for from i=0 to K.length by 1
print ‘Block ’+i+’:’
for from j=i to C.length by K.size
print C[j]
end for
end for
Figure 2.4 Pseudocode of Dividing Ciphertext Into Blocks to Attack
Suppose that the length of the key is n. In other words, the ciphertext consists of n
monoalphabetic substitution ciphers. Note that, the letters of the plaintext at positions
1, n+1, 2n+1, 3n+1 would be encrypted by the same monoalphabetic substitution cipher.
Thereby, the ciphertext could be divided into blocks of key length. Implementing
frequency analysis to each block respectively makes frequency analysis attacks
possible. Figure 2.4 illustrates the algorithm of dividing ciphertext into blocks.
An attacker needs to check all possibilities of key between length of 2 and 28 if the key
size is not known. Thus, the key space of the Vigenere cipher would be larger than
affine cipher and substitution cipher.
25
2.2.3.2.
Kasiski Attack
Kasiski attack is a method that tries to determine the key size of the polyalpahabatic
substitution cipher. The ciphertext could contain a recurrent pattern if the letters of the
plaintext are encrypted by the same sequence of key. It is assumed that the distance
between the repeating groups of characters could be related with the key length.
Greatest common divisor of the distances of the repetations could give a clue about the
key size [11].
Suppose that the following ciphertext is given:
AUYAJAMĞÖSCMĠRĞYRRMVEIGIZCTSĠALNDIFDARBKMNAOULCRMYEĠGĠ
ZTCZÖAġBKRBMASYLÜRĠÇUZEEBYYMÜZDYZġRRKVYAĠINOĞKRDAGRÜP
ELAÖLCMEBÖRCNSSVĠVAYSGSCZOBOUZUNĠLUUERRÖDNġMSOEGÖNÖÖB
CRYSDVRRBYYĠÖORĠZHÜRġSĠĠJÖYBÖMÜKMJZKNNEFÖYġEYNVLRġMVFIF
DULĞYĞRUCKNEATNZIÖORĠZ
Table 2.16 Distances Between Repating Characters
Character
CM
IFD
BYY
ÖORĠZ
Times
2
2
2
2
Distance
102
180
90
60
In the example, repeating characters CM, IFD, BYY and ÖORİZ appear two times in the
ciphertext. Distances between the characters are illustrated in the Table 2.16.
The greatest common divisor of the 60, 90, 102 and 180 is 6. Therefore, 6 and its
dividers (2, 3) are candidates of the key length. Indeed, the key is specified as ANKARA
and the plaintext is selected from the following text.
26
AĞLASAMSESĠMĠDUYARMISINIZMISRALARIMDADOKUNABĠLĠRMĠSĠNĠZG
ÖZYAġLARIMAELLERĠNĠZLEBĠLMEZDĠMġARKILARINBUKADARGÜZELKE
LĠMELERĠNSEKĠFAYETSĠZOLDUĞUNUBUDERDEDÜġMEDENÖNCEBĠRYERV
ARBĠLĠYORUMHERġEYĠSÖYLEMEKMÜMKÜNEPEYCEYAKLAġMIġIMDUYU
YORUMANLATAMIYORUM
3.
Homophonic Cipher
Homophonic cipher is developed as an alternative to substitution cipher to compose
more resistant ciphertexts against to the frequency analysis attacks. Homophonic cipher
could be thought as the extended version of substitution cipher [2].
In the classical substitution, each plaintext character is replaced with a corresponding
symbol by means of one to one mapping. Homophonic substitution is similar to the
classical substitution, except that the mapping is one to many. Each source character is
mapped into a set of symbols referred to as homophones [12].
The number of
substitutes is proportional to the frequency of the letter in the source language. It can be
used to provide randomization. That makes the frequency occurrence of the ciphertext
symbols more uniform [3]. The term of homophonic means to sound the same that is an
indication of the fact that different symbols refer to same source character.
An
important attribute of the homophonic coding is that a symbol is picked at random from
the set of homophones to represent the given source character in the one to many
mapping. Thus, homophonic cipher is transforming a given non-uniformly distributed
plaintext into a random uniformly distributed ciphertext [13].
Homophonic substitution is also a cryptographic technique that reduces the redundancy
of a message [14]. Homophonic cipher replaces each plaintext letter with different
symbols proportional to its frequency rate. Its main goal is to convert the plaintext into
a sequence of completely random code symbols. The idea behind homophonic cipher is
to balance out the symbol frequencies. The frequency distribution of the ciphertext is
manipulated and smoothed. Symbols located in the ciphertext have relatively equal
frequencies. Each symbol takes space of about one percent of ciphertext.
28
Suppose that the source language consists of the alphabet A = {a, b} with probabilities
pa=3/4, pb=1/4 and the plaintext letters would be substituted according to substitution
rule a→{00, 01, 10} and b→{11} as illustrated in Figure 3.1. The message is encrypted
at random into one of its homophones with equal probabilities [15].
So, the
homophonic cipher provides the encrypted text appearing random.
Figure 3.1 Domain Set and Target Set of Homophonic Cipher
Figure 3.2 Illustration of Frequency Distribution of a Homophonic Encrypted Text
The article of Bir Tılsımı Olmalıdır Hayatın written by Çetin Altan is encrypted by
homophonic cipher corresponding to Figure 3.3. The text consists of 3856 letters.
Finally, the Figure 3.2 is retrieved.
29
Table 3.1 Percentage of Turkish Letter Frequencies and Expression Count in
Homophonic Cipher [2]
Letter Freq.
A
B
C
Ç
D
E
F
G
Ğ
H
11,92
2,844
0,963
1,156
4,706
8,912
0,461
1,253
1,125
1,212
Exp.
Count
12
3
1
1
5
9
1
1
1
1
Letter Freq.
I
Ġ
J
K
L
M
N
O
Ö
P
5,114
8,6
0,034
4,683
5,922
3,752
7,484
2,476
0,777
0,886
Exp.
Count
5
9
1
5
6
4
7
2
1
1
Letter Freq.
R
S
ġ
T
U
Ü
V
Y
Z
6,722
3,014
1,78
3,314
3,235
1,854
0,959
3,336
1,5
Exp.
Count
7
3
2
3
3
2
1
3
2
The unigram frequencies of the source language assess how many symbols the letter
would be expressed within homophonic cipher. Each letter would be replaced by
different symbols proportional to its frequency rate. Table 3.1 illustrates the expression
count of Turkish unigrams.
A B C Ç D E F G Ğ H I İ J K L M N O Ö P R S Ş T U Ü V Y Z
009 048 013 062 001 014 010 006 025 023 032 083 015 004 026 022 018 000 072 038 029 011 076 017 008 063 034 021 002
012 081
003 016
070 088
096 037 027 058 005
035 019 086 020 061 085
052 069
033 028
045 024
073 093
056 051 039 059
040 036
030 097
075
047
079 044
031 060
065 084 050 066
042
053
041 046
089 007
068 043
071
077
067
055
054
049
091
080
078
057
090
101
102
092
064
099
082
074
095
087
098
094
Figure 3.3 Substitution Table of Homophonic Cipher
Figure 3.3 illustrates an instance of the substitution table of homophonic cipher. The
top row represents unigrams of the Turkish, while the below row represents
homophones of each unigram.
30
Suppose that the plaintext is FLORYA. The plaintext could be encrypted as one of the
following ciphertexts:
010
084
000
035
075
067
010
026
005
042
052
098
010
043
000
029
021
053
Homophonic cipher is a type of monoalphabetic substitution cipher. A letter could be
shown as several characters. However, a character could symbolize only one plaintext
character. In polyalphabetic cipher, a letter could be represented by several characters
and a character would symbolize several letters throughout encryption. In other
perspective, the encryption alphabet remains constant throughout the encryption process
[16].
exp sym[29]=12, 3, 1, 1, 5, 9, 1, 1, 1, 1, 5, 9, 1, 5, 6, 4, 7, 2, 1, 1, 7, 3, 2, 3, 3, 2, 1, 3, 2
// Expression count of each letter in Turkish Alphabet
num_of_sym=102 // Sum of the expression count of Turkish letters
keyspace=1
b=sym[0]
for from i=0 to 29
keyspace=keyspace*Combination(num_of_sym, b)
num_of_sym=num_of_sym-b
b=sym[i+1]
end for
return keyspace
function Combination (a, b)
dividend=1, denominator=1
for from i=a downto b by -1
dividend = dividend * i
end for
for from i=b downto 1 by -1
denominator = denominator*b
end for
resp = dividend / denominator
return resp
Figure 3.4 Algorithm for Computing the Key Space of Homophonic Cipher for Turkish
31
The key space of homophonic cipher for Turkish is calculated in Figure 3.4. It is a
number larger than 10119. Suppose that the attacker is able to check a possibility per
microsecond, it would take time more than 10105 years to solve ciphertext in worst
case4. Obviously, the encipherment rules out a brute force attack.
It is understood that brute force attacks would not be a solution to break homophonic
cipher if the key space values of well known algorithms are compared. The key space
of the method is overwhelmingly larger than other common algorithms, even most of
modern algorithms, except Blowfish.
Table 3.2 Comparison of Key Space Values of Common Algorithms
Algorithm
Substitution Cipher
Homophonic Cipher
DES
3DES
IDEA
AES
Camellia
Twofish
Serpent
Blowfish
Category
Classical
Classical
Modern
Modern
Modern
Modern
Modern
Modern
Modern
Modern
Key Space
29!
10119
256
2112
2128
2256
2256
2256
2256
2448
Approximate Value
1030
10119
1016
1033
1038
1077
1077
1077
1077
10134
In order to compare the key space of common encryption algorithms, BigDecimal class
of Java programming language is used. Thus, approximate key space values are
retrieved illustrated in Table 3.2.
4
10 119 10 −6
60.60.24.365
> 10105
4.
A New Approach On Attacking Homophonic Cipher
Most frequent n-grams would not help to solve homophonic ciphers. Even if these ngrams are assumed to appear in ciphertext, they would almost be impossible to solve
because of the high expression count.
Homophonic cipher extends the block size of the ciphertext in patches. Moreover, the
block size is variable. That makes the identifying the plaintext difficult. Well known
statistical features of the source language become invalid because of the manipulation
of the ciphetext.
The 100 most common words of Turkish are already illustrated in the section 2.
Expression count of the most common words could contribute to solve homophonic
cipher.
Table 4.1 illustrates the expression count of most common 100 words of
Turkish. It was sorted with respect to the expression count from smallest to greatest.
Nevertheless, making a decision of useful n-grams belonging to the source language
plays pivotal role to solve homophonic ciphers. The unigrams of n-grams should have
low frequencies to be detected easily in homophonic encrypted texts, whereas the ngram itself should have high frequency to be assumed to appear in the plaintext. In
other words, high frequent n-grams should consist of low frequent unigrams [2].
33
Table 4.1 Expression Count of Most Common 100 Words of Turkish within
Homophonic Cipher
Word
O
ġu
Ve
Bu
Hiç
Çok
Gün
Mı
Yok
Çocuk
In
Ya
Mi
Hem
Onu
Son
De
Ki
Kız
ġey
Biz
Da
Ne
Her
En
4.1.
Exp
Count
2
6
9
9
9
10
14
20
30
30
35
36
36
36
42
42
45
45
50
54
54
60
63
63
63
Word
Ġn
Önce
Göre
Bey
Gece
Var
Yıl
Küçük
Uzun
Tek
Çünkü
Tam
Öyle
Ona
Büyük
Oldu
Bir
Ben
Sen
Bunu
Doğru
Türk
Güzel
Gibi
Ġyi
Exp
Count
63
63
63
81
81
84
90
100
126
135
140
144
162
168
180
180
189
189
189
189
210
210
216
243
243
Word
Ġse
Nın
Bütün
Olur
Ġlk
Onun
Ġki
Nin
Ġle
Böyle
ĠĢte
Olduğu
Ġçin
Ama
Daha
Olan
Diye
Eski
Aynı
Bile
Beni
Yeni
Yine
Biri
Bizim
Exp
Count
243
245
252
252
270
294
405
441
486
486
486
540
567
576
720
1008
1215
1215
1260
1458
1701
1701
1701
1701
1944
Word
Dedi
Vardı
Fakat
Hemen
Değil
Adam
Bana
ġimdi
Sonra
KarĢı
BaĢka
Biraz
Ancak
Artık
Benim
Nasıl
Zaman
Kadın
Olduğunu
Kendi
Ġnsan
Kadar
Ġçinde
Türkiye
Olarak
Exp
Count
2025
2100
2160
2268
2430
2880
3024
3240
3528
4200
4320
4536
5040
6300
6804
7560
8064
10500
11340
14175
15876
25200
25515
51030
60480
High Frequent N-grams Consisting of Low Frequent Unigrams
Turkish n-gram frequencies are initially explored in a large corpus of size 13.4 MB to
obtain high frequent n-grams consisting of low frequent unigrams.
Secondly,
expression count of each line within homophonic cipher is computed. Thirdly, sorting
was done with respect to the frequeny values by taking into account the first 300 records
for bigrams, 1500 results for trigrams, 2500 results for tetragrams and pentagrams from
the greatest to smallest and the rest of data was discarded. Finally, it was sorted with
respect to the expression count from the smallest to greatest. N-gram frequencies
indicate frequencies in 11.371.564.
34
Table 4.2 Frequencies and Expression Count of High Frequent Bigrams Consisting of
Low Frequent Unigrams in 11M
Ngr Fre
Exp Ngr Fre
GÖ
GÜ
ÇO
ÖZ
OĞ
OC
ÜÇ
ÇÜ
OP
PO
ĞÜ
ÜĞ
ĞU
UĞ
ÖY
SÖ
CU
PT
UP
BÖ
GU
VU
ÜZ
Üġ
ZÜ
ġÜ
Oġ
ĞI
IĞ
ÇI
CI
IP
PI
DÖ
KÖ
FI
HI
YO
SO
ġT
TÜ
UZ
Uġ
YÜ
BÜ
ÜY
ÜS
TO
BO
OY
1
2
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
6
6
6
6
6
6
6
6
6
6
6
6
6
25203
20124
14880
12477
10648
7324
5469
5186
5075
4765
4516
4463
18753
16907
14744
10196
9701
5061
4701
4683
4374
3907
17636
13030
7025
6549
5093
37718
24106
18112
10287
10041
8685
6918
5975
4036
3786
61044
27989
26972
23620
15172
14641
14156
11348
11253
10146
9312
9184
8640
ÜT
SÜ
OT
PL
ĞL
ÖL
LG
ġU
ÇL
ZU
OS
VL
NC
ÖR
ÖN
ĞR
RG
NG
RÇ
VR
NÇ
MÜ
ÜM
ġM
OM
VE
BU
GE
CE
ĞĠ
GĠ
ST
ĠÇ
ÇĠ
EV
TU
SU
ĠĞ
HE
UY
EC
EĞ
TT
HĠ
ÇE
UT
CĠ
YU
ĠP
VĠ
7852
7729
7353
7068
7029
6801
6372
6102
5262
5205
4774
4745
21614
17778
15278
7347
6210
5692
4136
3925
3916
11630
11563
9568
5460
49863
44624
40841
37156
36283
35787
31918
31429
27377
25568
22533
22168
21975
21182
20367
19480
19472
19323
18821
17736
13198
11387
11219
10803
10524
Exp Ngr Fre
Exp Ngr Fre
Exp Ngr Fre
Exp
6
6
6
6
6
6
6
6
6
6
6
6
7
7
7
7
7
7
7
7
7
8
8
8
8
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
10
10
10
10
10
10
10
10
10
10
10
10
10
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
14
14
14
14
14
14
14
14
15
15
15
15
15
15
15
15
15
15
15
15
15
15
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
20
20
20
20
21
21
21
21
21
21
21
21
21
21
21
21
21
24
24
24
24
24
24
25
25
25
25
25
27
27
27
27
27
27
27
27
27
27
27
27
27
27
27
27
28
28
30
30
30
30
30
35
35
35
35
35
35
35
35
35
36
PE
US
EÇ
FE
EF
EH
ĠH
FĠ
EP
ĠF
SS
ĠC
PĠ
Iġ
OK
KO
DÜ
IZ
ġI
ZI
ÜK
DO
ġK
KÜ
ZD
OD
HA
OL
CA
AH
AP
AĞ
UM
VA
MU
PA
AC
ġL
ÇA
ZL
TM
AV
LÜ
ÜL
AÇ
FA
AF
GA
ĞA
MS
10171
10074
8691
8636
7925
7137
6744
6520
6092
5528
4284
3936
3837
32622
27389
25764
25363
23091
22692
14561
13284
12350
11863
11279
8012
4565
56075
54389
33993
33171
27085
26617
26139
23616
23551
21525
18985
18154
17193
16237
13595
13357
13272
13181
12668
11877
11150
10575
6727
4790
LO
SM
OR
ON
ÜN
ÜR
RÜ
NÜ
Rġ
RO
DU
TI
SI
KT
IY
YI
KU
UK
YD
IS
KS
SK
BI
UD
Ġġ
ĠZ
YL
UL
LU
ZE
ġE
TL
ġĠ
ZĠ
Eġ
EZ
SL
LT
LS
IM
MI
MD
KM
UN
UR
NU
RU
RT
RS
NS
4242
4030
70300
45874
43059
27057
13654
10971
5193
4899
52283
51386
50362
28964
27516
24913
23617
15139
13222
10610
7683
6723
5760
3968
38227
35238
32373
29371
27338
22563
19742
19492
17282
13862
13465
9758
7774
7738
4266
37245
36784
11337
7097
59182
38171
36391
28453
20288
15816
9885
NT
YR
YN
RB
NB
TR
Aġ
AZ
LM
ZA
ġA
ML
DI
IK
KI
KK
ID
BĠ
ĠY
SĠ
YE
TE
TĠ
ET
BE
SE
EY
ES
ĠS
ĠT
YĠ
ĠB
EB
RM
NM
LI
KL
IL
LD
LK
IN
ND
RD
NI
RI
IR
RK
NK
KR
YA
8977
5622
5457
5141
4482
4288
46294
32755
32197
23774
22239
12350
62359
40865
31841
5957
4104
125824
57222
55239
55184
53881
50968
49927
45640
44712
44573
39387
37263
20510
19854
15851
5667
24077
13100
53814
43444
39898
37375
9755
132807
98136
71256
69437
66743
43789
29528
7820
3777
107833
35
Table 4.3 Frequencies and Expression Count of High Frequent Trigrams Consisting of
Low Frequent Unigrams in 11M
Ngr
GÖZ
ÇOC
GÜV
HOC
GÖS
GÖT
ÜĞÜ
ÖZÜ
ÜÇÜ
GÜZ
ÜCÜ
HOġ
KÖP
OCU
OĞU
TOP
SÖZ
ÖTÜ
FÜS
ÖLG
BOĞ
ġÖY
GÖR
ÖNC
ÖĞR
GÖN
ÜġÜ
ÜZÜ
ĞÜM
UĞU
GEÇ
HĠÇ
SÖY
CEĞ
HEP
GEC
BÖY
UCU
ÖST
UYG
YGU
ÇEV
HÇE
CEV
SUÇ
TUĞ
HVE
ÖPE
EVG
VGĠ
Freq
5755
3833
1092
1017
2247
1143
4160
2872
2810
2803
1607
1540
1250
3910
3155
2979
2686
2203
1824
1038
997
982
12199
4016
2452
1184
5781
3851
964
15363
7184
7076
6645
4410
3254
3087
3016
2433
2287
1996
1940
1737
1719
1278
1217
1215
1090
1043
962
954
Exp
2
2
2
2
3
3
4
4
4
4
4
4
5
6
6
6
6
6
6
6
6
6
7
7
7
7
8
8
8
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
Ngr
ÇOK
DOĞ
DÜĞ
KÜÇ
ÇÜK
KOC
KÖġ
IZC
HIZ
ÜTÜ
YÜZ
CAĞ
ÜYO
ÜYÜ
ÖZL
GÜL
ĞUM
HAF
ÖLÜ
OĞL
POL
OTO
HAV
BOġ
ÜġT
OPL
ġTÜ
ÇAĞ
MUH
AHV
ÜSÜ
AHÇ
CUM
VAP
LÜĞ
GÜN
ÖRÜ
ÖNÜ
OĞR
ÇÜN
ÜNC
ĞÜN
ORG
FON
POR
GÜR
RGÜ
DUĞ
TIĞ
PTI
Freq
9685
4452
2915
2321
1907
1906
1290
1094
1063
5629
5561
4672
4299
4106
3266
2851
2715
2525
2404
2295
2079
2061
2005
1984
1937
1739
1615
1244
1233
1213
1051
1029
1026
978
968
8955
4600
3537
3298
2195
2063
1837
1560
1444
1429
1253
1218
10666
4856
3326
Exp
10
10
10
10
10
10
10
10
10
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
14
14
14
14
14
14
14
14
14
14
14
14
15
15
15
Ngr
CUK
YIP
PIY
TIP
KÖY
KÖT
MÜġ
ÜMÜ
ÜġM
MÜZ
ZÜM
ÖYL
UYO
ÜST
BÜT
ġTU
UZU
UġT
BÜY
OYU
OTU
ÖZE
STÜ
ġEH
LUĞ
BOY
UġU
SUZ
ĞLU
ÜSU
ĞĠġ
GĠZ
EFO
ÜVE
OST
BÖL
SYO
GEZ
ÖġE
GUL
UÇL
VĠZ
LUP
CUL
DÜġ
ĞIM
ÜDÜ
DÜZ
KOġ
ÜZD
Freq
3185
1715
1561
1414
1288
1010
2801
2380
1709
1447
959
13810
5892
5059
4849
3803
3780
3615
3577
3519
3383
2459
2345
2272
2258
2202
1990
1927
1873
1827
1520
1499
1372
1366
1336
1255
1195
1141
1115
1084
1080
1025
1023
987
6913
6633
2013
1357
1151
1104
Exp
15
15
15
15
15
15
16
16
16
16
16
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
20
20
20
20
20
20
Ngr
ÜKÜ
ĞUN
ĞRU
UNC
RUP
VUR
ÖRT
RGU
YÖN
GUN
VRU
MUġ
OCA
GAZ
ÜLÜ
HAZ
FAZ
VAġ
ġAH
UġM
MUZ
OĞA
OMU
ZCA
ġAĞ
ÜMS
APO
MÜS
TÜM
IĞI
ÇIK
DIĞ
ICI
KIP
GĠB
SEV
USU
GĠT
UYU
TĠĞ
YEC
TUT
UTU
VET
ÇBĠ
ĠÇB
HĠS
GET
UST
ĠHT
Freq
1016
7798
2722
1857
1662
1636
1431
1275
1235
1102
975
6665
3344
2805
2684
2055
1790
1767
1684
1674
1672
1475
1287
1195
1139
1077
1062
1026
955
22842
11312
11092
1863
1833
11642
5934
5550
4392
4351
4325
3166
3059
2586
2387
2379
2369
2271
2144
1880
1641
Exp
20
21
21
21
21
21
21
21
21
21
21
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
25
25
25
25
25
27
27
27
27
27
27
27
27
27
27
27
27
27
27
27
27
Ngr
ÇTĠ
PSĠ
HTĠ
GĠY
EPS
HEY
TĠH
EÇT
CES
SUS
ÇET
ÖTE
FET
SEF
TTU
UTT
GĠS
TEC
ÜRÜ
ÜNÜ
ġÜN
ZÜN
ÖRM
ZOR
RÜġ
IYO
ġTI
IġT
OKU
LIĞ
YOK
YÜK
SIZ
OKT
SOK
PIL
ÇIL
ġIY
ÖLD
KOY
CIL
LIP
OKS
KUġ
ÜKS
DOS
ĞLI
TIġ
ĞIN
DÖN
Freq
1610
1575
1488
1407
1338
1311
1305
1248
1232
1188
1150
1114
1101
1070
1069
1065
1015
1008
6600
6358
4498
3283
2011
1800
1040
15455
10166
8101
6541
6354
5827
4374
3789
2768
2715
2599
2183
2095
1930
1928
1705
1554
1389
1326
1317
1195
1169
935
12555
4583
Exp
27
27
27
27
27
27
27
27
27
27
27
27
27
27
27
27
27
27
28
28
28
28
28
28
28
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
35
35
36
Table 4.4 Frequencies and Expression Count of High Frequent Tetragrams Consisting
of Low Frequent Unigrams in 11M
Ngr
GÖZÜ
GÜCÜ
ÇOCU
GÖTÜ
OCUĞ
ÇOĞU
GÖST
CUĞU
GÖZL
FOTO
OTOĞ
SÖZÜ
CUMH
GÜÇL
GÖRÜ
ÖRGÜ
PTIĞ
KUVV
ÜĞÜM
ÖZÜM
FÜSU
GÜVE
BUGÜ
HUZU
SOĞU
BÖLG
DÜĞÜ
KÜÇÜ
ÜÇÜK
ÖZÜK
VRUP
YÜZÜ
ÜġTÜ
GÜLÜ
HOCA
LÜĞÜ
HĠÇB
UYGU
GEÇT
HEPS
TUĞU
SEVG
HÇET
BEHÇ
YGUS
GUSU
UVVE
VVET
GÖRM
ÜĞÜN
Fre
1760
628
3833
1132
743
692
2246
699
2267
732
683
633
613
583
4073
909
1419
574
962
608
1797
1092
803
764
678
600
2719
2320
1876
595
609
2595
1607
1314
1017
887
2367
1915
1131
1119
1036
955
807
807
634
600
549
546
1985
1798
Exp
4
4
6
6
6
6
9
9
12
12
12
12
12
12
14
14
15
15
16
16
18
18
18
18
18
18
20
20
20
20
21
24
24
24
24
24
27
27
27
27
27
27
27
27
27
27
27
27
28
28
Ngr
GÜNÜ
ĞÜNÜ
ÖRÜġ
ÖZÜN
ġÜNC
ÖNÜġ
OCUK
KÖTÜ
DOĞU
PIYO
ġTIĞ
OĞUK
ÜMÜZ
GÖRD
GÖND
BÜTÜ
BÜYÜ
GÜZE
UĞUM
ÜSTÜ
OĞLU
TOPL
GEÇM
ĞUMU
ġÖYL
ÖYLÜ
BAHÇ
UHAF
OLCU
HAFT
SÖZL
UMHU
HAYV
BÖLÜ
YOLC
OLUP
OTOB
TOBÜ
OBÜS
DÜġÜ
PMIġ
OĞRU
ÖTÜR
RGÜT
UGÜN
ORGU
TOĞR
OĞUN
ÖRÜY
PORT
Fre
1046
915
893
831
679
611
3087
1007
1002
989
915
595
602
2411
814
4768
3575
2774
2499
2298
1864
1673
1436
1222
982
953
943
935
794
720
677
613
608
593
574
568
559
548
548
4740
567
2540
1182
802
801
784
680
562
560
560
Exp
28
28
28
28
28
28
30
30
30
30
30
30
32
35
35
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
40
40
42
42
42
42
42
42
42
42
42
Ngr
ÖBÜR
DUĞU
DUYG
TTIĞ
KÖPE
ÖFKE
ÖPEK
KTUP
VDĠĞ
YDUĞ
ÖLÜM
MÜġT
OĞAZ
ġIĞI
SÖYL
UġTU
BÖYL
LUĞU
BOYU
ÖLGE
ĞĠġT
SUÇL
VĠZY
ULUĞ
VGĠL
YGUL
ÜġÜN
ÜZÜN
ġÜNÜ
ZÜNÜ
CAĞI
ÜYÜK
ÖLDÜ
ġIYO
KAHV
HIZL
ÇAĞI
YÜZD
ZLIĞ
ÇAKÇ
UĞUN
ĞUNU
ÖNCE
GÖRE
ÖĞRE
GERÇ
GENÇ
ÖREV
PENC
YUNC
Fre
554
10666
1360
1069
899
843
737
580
569
527
1533
1046
635
533
6638
3451
3012
2046
1050
1034
814
767
750
634
628
575
4495
2446
1264
829
4623
2902
1851
1508
1141
953
827
732
544
535
7229
5384
3964
3399
2436
1926
1646
1101
1072
1005
Exp
42
45
45
45
45
45
45
45
45
45
48
48
48
50
54
54
54
54
54
54
54
54
54
54
54
54
56
56
56
56
60
60
60
60
60
60
60
60
60
60
63
63
63
63
63
63
63
63
63
63
Ngr
ÇEVR
URUP
VURU
UCUN
HERH
RUCU
ÖRDÜ
DOĞR
ÇÜNK
DÖNÜ
RDÜĞ
ÖNDÜ
GÜND
NIZC
MUġT
LÜYO
ÇMĠġ
UMUZ
OMUT
OCAS
BOĞA
YÜZL
MÜST
ÜLTÜ
MUYO
OLUġ
UMUġ
TIĞI
ÇIKT
KTIĞ
PISI
TIPK
CISI
DÜġM
MÜDÜ
ġMIġ
CEĞĠ
ECEĞ
GECE
TTĠĞ
GEÇĠ
GĠTT
ÖSTE
HĠSS
GEÇE
TUTU
UTTU
HTĠY
EVGĠ
EHÇE
Fre
804
767
665
587
570
563
2573
2562
1786
1394
1261
1085
902
814
1731
1131
966
942
780
746
700
697
684
649
584
560
524
4806
1764
999
903
727
668
1061
970
879
4351
4324
3002
2865
2546
2324
2286
2062
1655
1144
963
956
954
813
Exp
63
63
63
63
63
63
70
70
70
70
70
70
70
70
72
72
72
72
72
72
72
72
72
72
72
72
72
75
75
75
75
75
75
80
80
80
81
81
81
81
81
81
81
81
81
81
81
81
81
81
37
Table 4.5 Frequencies and Expression Count of High Frequent Pentagrams Consisting
of Low Frequent Unigrams in 11M
Ngr
ÇOCUĞ
FOTOĞ
OCUĞU
GÖZÜK
GÖRÜġ
GÖZÜN
ġOFÖR
ÇOCUK
CUMHU
GÖTÜR
ÖRGÜT
GÖRÜY
GÖVDE
GÖLGE
ÜĞÜNÜ
ÜġÜNC
GÖRMÜ
ÖZÜNÜ
HÜZÜN
GÖREV
GÖRDÜ
ÖRDÜĞ
ĞUMUZ
OTOBÜ
PTIĞI
DÜĞÜM
HÜKÜM
GÖSTE
UYGUS
UVVET
YGUSU
OTOĞR
ÖRÜYO
ÖTÜRÜ
GÖRÜL
SOĞUK
MÜġTÜ
GÜLÜM
ÖLÜMÜ
GÖRÜN
ÖRÜNC
GÖRÜR
KÜÇÜK
GÖZLE
UĞUMU
TUHAF
VĠZYO
CEVAP
ÖYLÜY
HAFĠF
Fre
748
683
666
593
892
472
394
3085
612
1125
802
540
381
433
914
679
446
441
390
1101
2408
981
568
548
1418
803
425
2246
633
543
539
679
540
484
414
581
807
750
702
1592
550
409
1876
1904
1167
866
748
681
644
605
Exp
6
12
18
20
28
28
28
30
36
42
42
42
45
54
56
56
56
56
56
63
70
70
72
72
75
80
80
81
81
81
81
84
84
84
84
90
96
96
96
98
98
98
100
108
108
108
108
108
108
108
Ngr
SÖYLÜ
YOLCU
TOBÜS
UġUYO
ÜġÜNÜ
ÜZÜNÜ
ÖRMÜġ
CAĞIZ
LDÜĞÜ
ÜLKÜC
LKÜCÜ
DÜġTÜ
ÇIKIP
FÜSUN
GÜVEN
OYUNC
BUGÜN
HUZUR
SORGU
SONUC
DUYGU
KUVVE
YDUĞU
UYDUĞ
ÇÜNKÜ
RDÜĞÜ
DÜĞÜN
DÖNÜġ
NDÜĞÜ
ÜĞÜND
BOĞAZ
OĞLUM
PACAĞ
ġTIĞI
IġTIĞ
CILIĞ
BÖLGE
ÖYLEC
UYGUL
ULUĞU
UTSUZ
SUÇLU
VVETL
UYUġT
YUġTU
YÜZÜN
ÜNÜYO
OĞRAF
ġÜNÜY
ÜRÜYO
Fre
601
559
548
380
1264
384
374
443
421
401
401
385
457
1797
1027
896
800
764
465
381
1360
549
527
416
1786
1261
1080
610
517
387
635
396
379
910
480
382
600
579
575
547
500
443
437
414
413
1827
755
732
612
589
Exp
108
108
108
108
112
112
112
120
120
120
120
120
125
126
126
126
126
126
126
126
135
135
135
135
140
140
140
140
140
140
144
144
144
150
150
150
162
162
162
162
162
162
162
162
162
168
168
168
168
168
Ngr
LÜĞÜN
GÜRÜL
RLÜĞÜ
OLDUĞ
BÜYÜK
OCUKL
DUĞUM
APTIĞ
UĞUNU
ÖĞRET
URUCU
UYGUN
TUĞUN
TURUC
ÜLMÜġ
ĞIMIZ
DOĞRU
PIYOR
GÜZEL
MUġTU
OLUYO
YLÜYO
OLCUL
LUĞUM
ÜġÜNM
TTIĞI
KÖPEK
CAĞIM
HĠÇBĠ
GEÇTĠ
HEPSĠ
YECEĞ
SEVGĠ
BEHÇE
EHÇET
HEYEC
STĠHB
TUTTU
ZDIĞI
IġIĞI
BÜTÜN
ÜSTÜN
GÖRME
YORUZ
ONUġU
ġÜNCE
YÜRÜY
ÜYORU
UMHUR
AVRUP
Fre
508
391
386
7706
2902
2023
1672
1405
5192
520
468
420
402
400
380
1273
2536
987
2753
1715
941
600
517
437
701
1068
737
1511
2364
1125
1114
998
954
807
807
770
749
532
499
469
4767
1587
1535
1468
744
679
676
651
613
609
Exp
168
168
168
180
180
180
180
180
189
189
189
189
189
189
192
200
210
210
216
216
216
216
216
216
224
225
225
240
243
243
243
243
243
243
243
243
243
243
250
250
252
252
252
252
252
252
252
252
252
252
Ngr
VRUPA
GÜNEġ
OĞLUN
ġUYOR
ONUġT
LDUĞU
YOKTU
CUKLU
KLUĞU
UKLUĞ
ULDUĞ
YOKSU
OKUSU
OKUYU
DÜġÜN
ÜġÜND
ġÜNDÜ
ÜZÜND
ÖRDÜM
ÜRÜDÜ
ÜDÜRÜ
OLMUġ
ÜLÜMS
TIĞIM
IġIYO
ÇAKÇI
DOKTO
IZLIĞ
ZLIĞI
HIZLI
DUĞUN
RDUĞU
GÖNDE
URDUĞ
UĞUND
NDUĞU
UNDUĞ
CEĞĠM
POLĠS
ġÖYLE
GEÇMĠ
BAHÇE
SÖZLE
SUZLU
BULUġ
GEÇME
MUTSU
USTAF
ÜSTEġ
SAHĠP
Fre
609
583
511
488
468
8212
1241
753
648
571
506
487
409
374
4234
1202
1137
1066
634
516
398
1619
741
1259
731
529
515
449
445
403
5346
911
814
788
778
512
487
1469
1443
982
929
902
630
556
554
507
488
472
472
445
Exp
252
252
252
252
252
270
270
270
270
270
270
270
270
270
280
280
280
280
280
280
280
288
288
300
300
300
300
300
300
300
315
315
315
315
315
315
315
324
324
324
324
324
324
324
324
324
324
324
324
324
38
The bigram gö seems to be one of the most challenging n-grams. It consists of rare
unigrams while it has a high frequency. If a bigram is seen more than one time in the
ciphertext and its frequency is about the frequency of % 0.22 (100x25203/11M), it
could be assumed to correspond to gö. Rougly, the bigram would be uncovered in the
ciphertext of length 873 (2x11M/25203=872.9).
In the literature, the bigram qu is the most common sample way of attacking
homophonic cipher for English [16]. Frequency of the bigram qu is % 0.2. However,
the bigram would be expressed by 3 symbols.
Therefore, it seems that precious
information is obtained for beginning to attack.
The rest of the bigrams could contribute to solve ciphertext but their frequencies are too
close. It seems better to turn back after trying to detect more symbols by using other ngrams.
Table 4.3 contains useful n-grams to solve ciphertext. Though the values are too close
to each other, the trigrams gör and uğu could be evaluated as distinctive because of the
frequency values.
Table 4.4 contains obtrusive values. The tetragram cumh would be expressed by 12
different symbols. However, detecting the tetragram would be easy. The beginning and
ending letter of the tetragram would be replaced with only one symbol. Similarly, same
rules are valid for the tetragrams ptığ and vrup. Moreover, the tetragrams çocu and
görü have distinctive frequencies.
One of the most challenging n-gram seems to be a member of pentagrams.
The
pentagram çocuğ would be expressed by 6 different symbols. More interestingly, three
letters of the tetragram (ç, c, ğ) would be repeated permanently in the ciphertext because
each letter would be replaced with only one symbol. Detecting the rest of the letters (o,
u) would be easier if the other letters are solved. Similarly, the pentagram fotoğ is a
useful n-gram. The first letter and the last letter of the pentagram have a frequency of
%1.
Furthermore, the pentagrams çocuk and gördü have a distinctive frequency.
39
Another point that should not be ignored is that both the pentagrams çocuğ and çocuk
consist of the distinctive tetragram çocu.
Distinctive n-grams exist as seen. It seems more meaningful to begin with looking for
the bigram gö. Then, pentagrams and tetragrams should be attempted to detect. If
pentagrams and tetragrams could be detected in the ciphertext, it provides significant
advantage in the rest of the process. Even if these tetragrams and pentagrams do not
appear in plaintext, distinctive bigrams and trigrams would most probably help to solve
encrypted texts.
Suppose that the following ciphertext is given:
045 044 025 007 076 088 096 092 013 098 081 053 048 097 006 085 071 030 085 077 004 099 075 046
041 046 065 098 062 068 032 002 062 005 013 061 025 008 079 000 025 041 097 098 004 073 084 052
057 037 056 074 066 095 018 054 011 016 062 099 022 080 085 002 006 033 080 073 066 012 056 078
038 020 032 040 050 032 076 079 000 019 030 049 094 080 041 092 018 028 090 042 095 066 060 071
006 072 069 084 014 077 060 056 094 069 033 077 094 081 061 093 051 096 036 078 030 032 029 009
017 098 056 070 026 031 035 036 009 046 050 099 058 088 022 056 060 005 050 008 069 036 054 051
056 014 013 074 004 081 008 001 098 071 057 081 088 062 088 027 036 000 040 097 045 090 052 055
013 046 056 076 007 039 045 095 028 095 077 011 000 035 061 079 047 023 012 078 013 087 028 067
030 063 042 004 054 052 016 041 016 028 097 006 063 091 085 101 079 000 025 008 022 021 070 051
003 072 059 063 027 063 005 043 041 008 025 097 068 033 062 065 089 069 034 074 096 087 001 031
066 034 067 040 075 053 069 032 075 078 021 009 018 070 030 084 087 035 073 091 057 019 007 075
067 036 057 020 062 093 051 016 029 007 018 091 055 036 057 062 050 044 101 043 064 029 054 059
018 024 079 055 036 055 062 090 026 046 013 074 056 037 016 029 095 018 094 096 031 084 049 094
042 032 101 070 018 096 072 086 016 011 007 101 001 064 058 028 054 037 055 006 057 062 027 064
075 074 059 011 000 102 061 051 047 029 049 087 028 047 076 026 092 050 047 059 032 091 071 055
079 074 018 083 028 061 006 085 091 096 032 069 089 022 002 016 075 071 016 038 028 078 096 098
059 089 101 041 005 025 008 039 052 089 051 001 072 018 085 027 063 000 049 039 053 019 032 098
023 039 064 030 037 055 022 055 023 022 055 017 017 046 071 075 031 051 049 012 080 013 082 019
005 058 035 098 028 060 102 045 057 003 085 071 021 098 052 078 004 073 069 032 039 073 071 006
014 051 027 090 076 005 026 022 087 019 032 028 024 071 045 016 071 054 069 007 019 014 034 060
101 062 030 044 101 039 061 030 049 061 026 008 096 097 010 008 004 051 078 029 089 059 073 018
006 072 096 084 046 077 099 018 057 045 005 025 042 097 008 062 008 042 022 097 086 017 008 095
026 056 096 074 002 011 000 028 033 026 031 079 009 060 029 057 051 044 077 041 014 059 023 094
034 082 037 092 077 036 005 025 097 003 008 025 008 018 045 098 069 016 052 091 046 038 085 086
40
063 050 074 036 054 059 079 054 052 024 066 090 076 009 059 020 092 076 073 071 045 098 023 085
036 035 044 034 006 046 042 074 041 044 013 098 045 045 024 019 060 066 001 014 056 093 065 009
026 005 029 093 010 064 077 051 054 081 054 080 003 078 088 029 014 052 014 030 067 086 073 058
022 089 076 030 031 096 023 016 059 085 002 003 087 023 094 099 011 030 009 018 081 061 051 061
101 017 087 091 069 054 022 082 017 097 069 098 091 020 073 026 031 081 090 035 007 056 095 050
084 014 077 083 091 079 016 059 019 005 021 097 020 043 098 091 022 094 041 089 025 031 041 072
091 057 027 049 055 040 001 095 006 098 002 064 030 014 037 024 077 083 071 023 057 038 019 095
028 087 048 032 009 049 099 041 055 075 003 007 048 074 018 041 014 066 007 069 045 057 022 095
084 084 093 021 014 030 030 064 038 044 052 082 027 054 036 094 010 098 066 089 071 006 087 069
014 017 074 041 044 066 047 075 029 032 049 027 092 036 089 071 001 067 066 036 000 058 080 092
065 088 056 072 076 044 011 054 071 003 016 030 092 086 028 053 086 026 031 025 031 075 037 092
075 009 069 031 075 005 080 079 097 050 052 087 069 031 084 047 040 070 027 089 099 019 030 078
071 048 061 026 008 101 056 097 076 053 065 051 098 077 003 047 071 056 097 076 094 056 049 009
077 009 052 012 058 019 031 021 033 071 081 099 080 007 065 093 022 049 046 040 088 075 026 016
102 061 023 008 091 008 091 056 078 101 009 034 093 062 046 011 093 066 007 006 055 035 006 074
010 051 055 027 099 086 034 016 006 046 080 006 024 010 043 014 075 064 066 021 012 002 098 077
037 009 077 023 057 058 063 002 011 012 025 041 070 077 074 010 088 068 023 082 049 088 017 019
098 025 045 031 010 033 023 102 083 013 016 043 012 043 036 009 025 079 070 081 061 102 023 012
058 010 064 037 044 096 011 053 025 079 032 035 057 010 054 013 057 034 047 017 019 094 025 041
032 023 009 084 079 097 059 017 098 071 014 042 011 087 025 079 073 064 036 098 020 050 094 023
039 097 017 011 033 025 001 073 023 093 068 050 024 020 010 064 035 061 001 097 101 011 012 025
045 073 028 060 042 056 014 066 030 093 071 001 016 025 088 086 050 044 021 055 066 067 058 073
030 037 078 040 031 038 094 102 056 051 053 035 070 050 046 075 003 047 066 049 092 080 073 017
099 052 047 030 080 005 026 033 077 073 026 000 096 087 071 020 009 084 067 029 070 050 085 069
014 043 046 042 088 005 056 008 026 049 082 029 089 000 020 057 026 043 064 080 060 007 049 016
062 016 076 099 020 084 088 045 009 043 037 053 029 045 098 056 007 011 047 018 078 017 062 031
051 094 035 089 028 087 025 037 053 077 094 021 091 089 068 044 071 020 017 055 041 005 025 027
061 086 000 043 082 066 004 097 076 053 065 051 067 035 032 048 095 080 048 054 040 099 018 016
002 044 052 091 057 038 093 018 003 000 025 079 097 025 008 052 073 051 037 092 040 003 012 030
063 035 056 060 052 016 058 093 101 059 063 010 008 019 008 093 068 088 081 090 071 060 056 060
021 085 069 075 060 102 027 095 085 062 039 099 051 075 005 058 041 097 060 019 030 098 091 028
061 037 043 008 037 047 077 070 101 101 063 010 061 036 061 045 092 023 064 018 085 002 060 062
006 072 062 037 016 029 037 055 046 029 088 075 060 038 036 054 049 093 066 050 024 050 060 086
017 088 068 073 011 089 056 043 070 028 046 071 003 014 018 090 002 083 101 062 005 013 097 068
084 061 025 097 058 008 058 079 082 068 031 036 073 068 084 031 036 031 021 003 073 062 092 039
026 032 013 094 079 082 072 052 051 074 028 061 043 006 097 102 037 061 079 092 072 075 037 014
081 067 025 049 098 035 048 098 086 031 079 087 072 075 043 046 028 046 052 005 025 037 061 019
093 071 055 050 067 084 094 080 073 079 098 072 021 049 074 020 085 040 056 093 075 046 041 064
079 057 025 083 086 054 056 068 097 086 082 056 084 092 029 045 098 058 096 073 002 036 053 023
41
090 081 095 079 046 000 051 078 066 067 093 051 046 049 057 035 083 091 005 040 020 082 004 081
007 077 010 005 017 000 025 040 092 010 031 062 044 096 007 084 024 048 083 084 019 064 034 016
081 063 075 063 056 048 093 029 044 065 035 053 058 041 067 075 082 059 011 032 030 089 026 092
081 054 026 036 055 000 065 089 002 026 082 080 000 004 053 045 089 018 043 067 035 034 044 000
053 059 071 024 051 044 080 007 071 052 016 020 088 086 017 083 040 045 054 025 099 062 005 013
061 068 026 009 080 056 046 058 020 026 093 081 088 040 081 099 035 083 068 090 039 079 014 071
075 005 065 011 097 101 043 061 025 008 066 061 002 067 021 062 053 025 070 007 049 044 030 005
011 037 094 076 027 092 019 089 101 001 087 091 062 070 056 047 013 082 065 062 033 049 065 098
071 030 032 084 098 080 031 045 008 077 003 097 080 027 087 021 078 036 093 021 087 019 024 030
062 090 056 082 079 102 005 049 012 080 070 059 089 091 006 085 013 063 075 055 017 014 042 022
007 048 097 006 085 101 096 031 002 032 022 069 044 021 101 046 038 095 091 001 005 025 061 050
006 085 091 085 062 005 013 097 068 051 053 077 032 027 098 043 067 021 070 068 005 051 078 081
093 026 027 044 062 053 081 092 011 089 052 084 009 006 057 062 014 101 028 088 080 072 027 085
040 034 046 008 022 061 017 074 030 030 093 025 060 022 017 064 065 006 072 040 063 101 050 064
069 072 079 063 037 079 046 062 005 013 008 068 084 012 102 089 039 073 058 048 078 048 078 037
087 040 089 091 045 009 018 061 017 098 066 022 078 039 012 049 098 040 031 081 007 102 006 085
018 020 005 042 008 091 043 067 035 070 050 089 058 020 000 080 061 091 037 009 042 089 079 047
076 067 021 014 030 048 057 091 003 024 091 093 002 054 101 081 093 102 052 012 069 032 011 031
058 053 056 009 069 087 040 078 040 053 036 020 026 078 029 084 094 080 011 082 086 061 048 007
002 083 027 028 063 075 085 056 001 044 001 014 021 024 003 016 048 033 004 058 016 026 044 080
036 087 062 050 078 084 009 027 032 086 003 044 022 044 019 054 066 084 044 029 093 019 017 046
102 090 039 002 024 052 071 064 038 028 087 019 032 058 056 072 075 001 074 088 037 096 005 096
097 026 085 062 085 059 013 063 036 032 071 073 010 030 053 075 004 024 018 072 025 042 024 017
022 044 018 088 066 099 066 083 036 020 016 025 090 052 051 074 048 083 035 005 068 061 051 030
072 035 044 059 083 058 041 055 079 093 002 099 045 088 002 060 088 066 013 088 075 088 027 006
063 002 074 049 026 060 068 030 074 048 088 042 083 091 013 095 052 083 039 047 079 032 050 073
036 000 077 053 029 011 009 018 073 002 062 016 017 088 071 087 049 020 098 101 032 071 056 032
002 032 021 073 027 041 088 021 055 048 060 080 062 005 013 097 004 076 054 099 040 095 000 056
008 045 097 025 061 034 044 048 012 086 073 066 079 053 045 053 056 070 042 022 032 069 031 056
097 029 045 074 043 024 011 093 048 008 037 008 066 045 008 025 008 007 062 060 058 065 005 022
085 091 054 011 017 038 042 005 038 078 006 092 101 045 067 019 089 075 047 038 020 070 025 073
095 045 045 054 012 019 089 075 049 087 038 005 026 054 011 068 078 080 047 096 000 084 097 091
078 006 072 020 085 029 085 049 050 063 076 017 063 005 030 098 042 095 023 037 074 077 003 016
078 058 096 009 080 012 003 087 038 047 029 043 012 050 014 101 020 000 045 082 075 001 070 050
061 062 082 025 087 082 030 026 047 027 070 076 034 064 023 014 050 024 059 028 087 011 032 101
004 072 052 016 068 000 086 039 097 086 020 008 039 013 047 059 031 050 069 024 052 091 016 038
054 022 028 097 006 085 071 079 053 023 088 028 094 069 055 071 102 063 052 047 043 033 040 032
018 003 047 038 005 026 083 019 006 072 042 085 040 034 024 028 090 029 049 007 065 020 057 006
044 002 079 083 025 090 027 054 069 006 085 059 037 055 102 045 055 023 074 039 044 071 010 092
42
080 096 074 079 074 035 019 093 034 007 037 038 005 043 083 019 049 074 040 093 003 046 096 063
062 085 068 084 063 096 026 044 029 007 066 045 064 072 013 085 021 049 055 056 000 080 096 097
017 008 084 094 066 062 000 013 097 068 026 067 080 003 095 076 062 093 021 074 006 072 017 085
077 050 044 056 037 016 096 005 042 004 008 017 097 051 098 066 062 005 013 097 056 043 067 035
048 074 065 062 099 075 044 034 044 102 022 044 056 049 055 056 005 102 056 097 017 008 084 087
018 062 000 013 061 065 037 094 077 004 085 062 085 056 043 063 056 049 046 040 083 058 079 014
065 005 042 096 061 030 061 043 047 066 072 069 046 043 043 095 004 051 046 044 035 068 055 065
062 005 013 061 068 049 067 080 048 063 075 063 041 063 065 043 016 077 083 101 003 014 041 055
006 057 101 024 084 026 054 004 084 055 068 005 029 096 097 020 061 013 008 000 049 022 047 068
099 036 017 044 040 037 057 035 096 031 069 062 000 013 097 096 049 094 080 032 005 042 030 047
004 028 088 029 068 044 071 030 081 093 080 099 065 054 027 060 091 003 044 059 075 005 056 011
097 091 000 026 053 029 092 004 052 044 030 060 086 027 083 086 065 070 077 011 067 043 065 014
011 095 027 062 000 013 097 068 043 033 029 089 067 101 066 064 037 057 035 005 053 058 058 016
043 044 102 060 018 021 046 020 088 076 020 093 042 003 083 025 060 062 005 013 008 096 051 009
040 052 055 020 027 099 076 063 062 039 099 049 075 005 018 071 085 010 008 036 008 059 052 082
077 032 011 070 091 003 087 058 010 053 002 049 082 011 031 003 087 056 073 002 034 057 065 012
041 031 091 053 075 092 065 026 067 080 089 048 082 096 032 022 051 089 000 037 087 018 049 033
035 082 052 094 096 026 012 042 073 048 087 056 031 022 036 073 069 000 049 098 059 049 078 029
028 093 042 041 094 023 094 096 054 052 070 051 070 059 000 091 023 009 069 099 102 098 101 089
071 041 094 036 054 021 078 011 098 037 006 063 059 045 055 022 065 054 039 028 060 026 054 102
066 067 019 032 049 005 051 098 013 078 096 082 050 012 000 006 063 091 003 014 021 054 101 055
096 054 050 081 099 037 095 040 066 014 068 092 001 053 040 056 070 069 062 000 013 061 025 061
045 000 025 087 013 033 056 038 082 002 094 035 082 056 076 094 027 031 101 073 090 038 049 016
062 024 096 055 101 037 064 029 023 064 102 023 009 026 003 055 028 093 051 095 052 005 040 037
087 077 041 070 077 075 009 023 075 092 096 055 027 087 043 090 091 090 036 017 009 018 028 097
084 097 059 011 024 050 017 049 014 040 054 063 011 030 085 059 064 003 074 076 060 095 035 051
064 102 021 092 002 039 032 076 088 043 065 060 036 020 087 101 028 008 026 086 012 090 035 099
000 043 041 008 025 008 066 008 081 088 069 087 066 019 076 083 095 042 060 059 045 057 093 019
020 067 058 081 061 084 052 005 068 017 061 079 060 034 009 018 074 003 046 028 099 052 094 017
032 018 079 087 001 087 093 019 030 087 101 028 008 037 061 091 019 074 027 030 084 055 035 054
075 005 068 020 008 040 052 078 023 021 033 004 024 050 053 051 060 071 102 063 075 067 006 088
028 054 081 007 080 075 098 069 041 070 076 083 083 077 099 059 088 101 081 046 011 030 016 004
098 029 089 000 019 027 087 059 059 099 023 082 020 079 094 033 023 027 046 017 102 047 011 088
050 090 018 030 000 080 008 018 097 052 003 061 028 054 042 068 016 058 020 081 060 040 083 056
093 039 093 101 041 014 071 053 102 030 009 096 012 026 087 018 048 008 056 014 030 043 055 040
069 016 052 018 074 038 046 003 064 012 052 071 031 006 085 066 001 000 025 022 008 076 000 043
094 091 051 087 035 009 045 092 003 005 025 097 039 075 032 037 045 072 018 063 027 026 044 040
090 068 097 020 049 061 005 051 036 061 058 059 097 017 097 056 049 098 042 081 083 042 021 098
018 009 045 005 025 097 050 006 085 066 037 014 080 054 081 054 080 021 087 101 033
43
If the n-gram based attacking model is performed on the ciphertext above, the following
consequences are obtained:
If the encrypted text is examined, the bigram 006 072 draws attention. It appears 7
times in text of length 3381. Moreover, the frequency of the bigram 006 072
(7x100/3381 = 0.2) is almost equal to the frequency of the bigram gö. Therefore, the
bigram could most probably be the bigram gö.
Another pattern that comes one step forward in the ciphertext is constituted by the
following trigrams:
062
005
013
062
000
013
The pattern appears 14 times in the ciphertext. Moreover, the trigrams specified above
would only continue with the characters 097, 061 and 008 in the ciphertext. The pattern
could only symbolize the tetragram ÇOCU because of the expression count.
The fact is that the tetragram çocu could only continue with the letters k and ğ. In the
encrypted text, the tetragram çocu continues with the characters of 068, 004, 056, 065,
096, and 025.
If the other trigram patterns that contain 025 are examined, the following bigrams are
interesting patterns for an initial investigation:
008
025
008
061
025
061
008
025
061
061
025
008
It had already been detected that the characters 008 and 061 are used to encrypt the
letter u. The pattern specified above would most probably be the trigram uğu.
44
Therefore, it could be said that the character 025 corresponds to the letter ğ and the
characters 068, 004, 056, 065, 096 correspond to the letter k.
K O 080 K U
K O 042 K U
K O 102 K U
K O 029 K U
Detection of the letters (g, ö, ç, o, c, u, ğ, k) reveals some patterns specified above. The
n-gram KORKU could only correspond to the patterns. Therefore, the characters 080,
042, 102, 029 could correspond to the letter R.
Thereafter, the following patterns are detected and solved respectively.
O K U 045 U Ğ U: OKUDUĞU
Ç O C U K 084 U Ğ U: ÇOCUKLUĞU
Ç O C U K L 012 R: ÇOCUKLAR
Ç O C U Ğ U D O Ğ 087 C 033 K: ÇOCUĞUDOĞACAK
Ç O C U K 043 A R: ÇOCUKLAR
Ç O C U K 049 067 R: ÇOCUKLAR
Ç O C U K 026 A R: ÇOCUKLAR
O K U L L 082 R: OKULLAR
Ç O C U K L 009 R: ÇOCUKLAR
K 063 Ç 085 K L 063 K: KÜÇÜKLÜK
Ç O C U K L A 035: ÇOCUKLAR
R Ü 002 G A R: RÜZGAR
O L 041 U Ğ U: OLDUĞU
Ç O C U K L 094 R: ÇOCUKLAR
A K 031 L L A R: AKILLAR
A Ğ L 098 R: AĞLAR
K O R K U 020 U C U: KORKUTUCU
Ü Ç Ü 059 C Ü: ÜÇÜNCÜ
Ö Ğ R 024: ÖĞRE
L A R D 092: LARDA
45
O L 053 R A K: OLARAK
T O R U 091 L A R: TORUNLAR
001 O Ğ U 050 G Ü N Ü: DOĞUMGÜNÜ
T O R U N 037 A R: TORUNLAR
K Ü Ç Ü K L Ü K L 046: KÜÇÜKLÜKLE
O L A N L 078 R: OLANLAR
028 U G Ü N: BUGÜN
D A L L A R D A K 007: DALLARDAKĠ
G Ö Ç L 016 R: GÖÇLER
T O R U N L A R 070 M: TORUNLARIM
Ç O C U K L A 077: ÇOCUKLAR
Ç O C U K 051 A R: ÇOCUKLAR
088 L K O K U L: ĠLKOKUL
G Ü N L 055 R D 055: GÜNLERDE
K Ü Ç Ü K L Ü K L 044 R Ġ: KÜÇÜKLÜKLERĠ
D E Ğ Ġ 076 Ġ K: DEĞĠġĠK
E C 074 K L E R: ECEKLER
075 I L L A R C A: YILLARCA
Ç E ġ 099 T L Ġ: ÇEġĠTLĠ
B E 052 O Ğ L U: BEYOĞLU
G Ü Z E L L 060 K: GÜZELLĠK
G Ö 017 Ü R M E K L E: GÖTÜRMEKLE
30 Ü R K Ġ Y E D E: TÜRKĠYEDE
039 U T L U L U K: MUTLULUK
K U ġ A K L A R 003 047 071 K U ġ A K L A R A: KUġAKLARDANKUġAKLARA
Ġ 019 T A N B U L L U L 047 R: ĠSTANBULLULAR
048 Ü Y Ü D Ü K L E R 083: BÜYÜDÜKLERĠ
Ġ 036 T A 101 B U L: ĠSTANBUL
E 003 E B Ġ Y A T: EDEBĠYAT
R Ü Y A G Ġ B 054: RÜYAGĠBĠ
D O Ğ 022 U ġ O L A N: DOĞMUġOLAN
A C A 081 A: ACABA
S Ġ Y A S 057 T: SĠYASET
B A ġ L A M A N 032 N: BAġLAMANIN
D O Ğ U M Y 089 L D Ö 018 Ü 027 Ü: DOĞUMYILDÖNÜMÜ
46
095 L K K E Z: ĠLKKEZ
023 Ü S R E 034 G E R E D E: HÜSREVGEREDE
B A B 032 A L Ġ: BABIALĠ
D O Ğ 079 U Ğ U: DOĞDUĞU
E R Ġ Y Ġ 038: ERĠYĠP
S 093 N E M A: SĠNEMA
A N N E L E R Ġ N Y E T Ġ 086 T Ġ 040 D Ġ Ğ Ġ: ANNELERĠNYETĠġTĠRDĠĞĠ
T O R U N L A R I M 089 058 T O R U N L A R 089: TORUNLARIMINTORUNLARI
B U L U 066 D U Ğ U: BULUNDUĞU
K O M Ü N Ġ 011 T: KOMÜNĠST
B Ü Y Ü D Ü K L E R Ġ N D 014: BÜYÜDÜKLERĠNDE
R Ü Z G A R 073 N A: RÜZGARINA
B 090 R Ġ N Ġ N: BĠRĠNĠN
069 E Y N E P: ZEYNEP
021 I L D Ö N Ü M Ü: YILDÖNÜMÜ
S E Ç M E N L 064 R: SEÇMENLER
K A L O R Ġ 010 064 R: KALORĠFER
As it is seen, solving the encrypted text is possible on long enough ciphertexts. Hereby,
all the characters of the encrypted text are solved and the following text is obtained:
DEĞĠġĠKACABABUGÜNTÜRKĠYEDEKAÇKIZÇOCUĞUDOĞDUAKILYELKENĠ
NĠSEÇĠMRÜZGARINAKAPTIRMIġDOSTLARDANBĠRĠNĠNGÖZLERĠKAZARAB
UĠLKSATIRATAKILIRSAEMĠNĠMKĠOMUZSĠLKECEKBUDANEBĠÇĠMSORUDĠY
ECEKġĠMDĠBĠRSORUDAHAACABATÜRKĠYEDEBUGÜNÜNDOĞUMYILDÖNÜ
MÜOLDUĞUKAÇKIZVEKADINVARYAZIYAYANITLARINESĠYASETÇĠLERĠN
NESEÇMENLERĠNNEDESEÇĠLECEKLERĠNAKILLARININKÖġESĠNDENBĠLEG
EÇMEYENSORULARLABAġLAMANINNEDENĠBUGÜNKIZIMZEYNEPBAKANI
NDOĞUMYILDÖNÜMÜOLMASIAHMETLEMEHMETTENYILLARCASONRABĠ
RDEDÜNYAYAKIZIMINGELMĠġOLMASIBENDENĠZĠSEVĠNÇTENMUTLULUK
UFUKLARININGÖKLERĠNEDOĞRUUÇURMUġTUĠLKKEZSOBALIDAĠRELERD
ENHAVALARSOĞUDUĞUNDAZEYNEPÜġÜMESĠNDĠYENĠġANTAġINDAHÜS
REVGEREDECADDESĠNDEKĠKALORĠFERLĠBĠRDAĠREYETAġINMIġTIKHENÜ
ZDAHAĠSTANBULUNTANZĠMATUZANTILIBĠRĠKĠMLERĠNDENSOYUTLANM
47
ADIĞIDÖNEMLERDĠGAZETELERĠNHEPSĠBABIALĠDEYDĠBENDENĠZDEMĠLLĠ
YETTEPEYAMĠSAFANINGAZETEDENAYRILMASINDANSONRAKĠKÖġESĠND
ETAġBAġLIĞIYLAYAZIYORDUMYAZILARIMIĠSTANBULUNKUġAKLARDAN
KUġAKLARAYANSIYANBĠRĠKĠMLERĠYLERUHUNUNKANAVĠÇESĠNĠGERGE
FLEMĠġVEGERGEFLEYENYAZARLARHENÜZSAĞDIREFĠKHALĠTSAĞDIFAH
RĠCELALSAĞDIBURHANFELEKSAĞDIREFĠCEVATSAĞDIHALDUNTANERSA
ĞDIESATMAHMUTSAĞDIHĠKMETFERUDUNSAĞDIBĠRKENTĠNDEĞĠġMEYE
NANITLARIPARKLARIMEYDANLARITĠYATROLARILOKANTALARIMÜZELE
RĠOKULLARIOTELLERĠĠLEÇEġĠTLĠDALLARDAKĠSANATÇILARIBAĞLARAY
NIKENTTEDOĞMUġOLANKUġAKLARIBĠRBĠRĠNEZEYNEPĠNDOĞDUĞUYILL
ARDATÜRKĠYENĠNNÜFUSUĠKĠBĠNĠKĠYÜZYĠRMĠÜÇMĠLYONDUĠSTANBULL
ULARINNÜFUSUDAHENÜZĠÇGÖÇLERLEERĠYĠPSĠLĠNMEMĠġTĠKISIKLIBEND
ENĠZĠNÇOCUKLUĞUNUNDAKISIKLISIYDIÇAMLICADAÖYLEBULGURLUDA
ÖYLEBAĞLARBAġIDAÖYLEBEYOĞLUSĠNEMALARIDAÖYLETÜRKĠYEDEDE
ĞĠġĠKKUġAKLARDANKIZSAHĠBĠDEOLANAĠLELERĠNORTAKBĠRFOTOĞRAFI
ÇEKĠLEBĠLSEVEBÜYÜKBĠREKRANDAYANSITILABĠLSEOKIZLAROKADINL
ARVEOANNELERĠNYETĠġTĠRDĠĞĠÇOCUKLARKENTLĠBĠRBĠRĠKĠMDENYOKS
UNLUĞUNUZAYÇAĞIĠLETOSLAġMASINDANÇIKACAKÇALKANTILARIDUR
DURMAYASĠYASETÇĠKADROLARININGÜCÜYETERMĠBUGÜNKIZIMZEYNE
PĠNDOĞUMGÜNÜÇOCUKLARIMALAYIKOLABĠLMEÇABASIYLAGEÇENBĠR
ÖMÜRVEUMUTETTĠĞĠMTEKGÖRÜNMEZÖDÜLDEÇOCUKLARIMINBABALA
RINDANUTANMAMALARIBĠRGÜNTORUNLARIMINTORUNLARIDAġAYETB
ENDENĠZĠNBĠRYAZISINAKAZARARASTLARLARSAġUBĠZĠMBÜYÜKDEDEY
EDEBAKNELERSAÇMALAMIġDEMESĠNLERĠSTERĠMZEYNEPBASINKÖYDEĠ
LKOKULÜÇÜNCÜSINIFTAYKENÖĞRETMENĠNĠNĠSTEĞĠYLEBĠROKULTÖRE
NĠNDEDĠZĠDĠZĠĠNCĠYĠMGÜZELLĠKTEBĠRĠNCĠYĠMADIMISORARSANIZÇETĠN
ALTANINKIZIYIMDĠYEBĠRÇOCUKġĠĠRĠOKUDUĞUVEBAġINDADAKIRMIZIK
URDELESĠBULUNDUĞUĠÇĠNKOMÜNĠSTPROPAGANDASIYAPTIĞIĠDDĠASIYL
APOLĠSKARAKOLUNAGÖTÜRÜLMÜġTÜOTARĠHLERDEANKARADAPARLA
MENTODAYDIMUÇAĞAATLAMIġVEHEMENBASINKÖYEKOġMUġTUMCANI
MZEYNEPĠMBUGÜNDAHĠBAZENRÜYALARINDAPOLĠSGÖRÜRVEBĠRLĠKTE
GEZDĠĞĠMĠZGÜNLERDEHEMENFARKEDERSĠVĠLPOLĠSLERĠDEKÜÇÜKLÜKL
48
ERĠNDEÖCÜYLEKORKUTULANÇOCUKLARDĠġÇĠYEGÖTÜRMEKLEKORKUT
ULANÇOCUKLARBEKÇĠYEVERMEKLEKORKUTULANÇOCUKLARKÜÇÜKLÜ
KLERĠNDEKORKUTULANÖZELLĠKLEERKEKÇOCUKLARBÜYÜDÜKLERĠND
EDEGENELLĠKLEKORKUTUCUOLMAKĠSTERLERKIZÇOCUKLARIORTAKBĠR
KENTBĠRĠKĠMĠNDENYOKSUNOLARAKYETĠġMĠġKIRSALKESĠMÇOCUKLARI
ANNELEROANNELERĠNYETĠġTĠRDĠĞĠÇOCUKLARYETMĠġÜÇMĠLYONNÜFU
SUNYARISINDANFAZLASIDAKIZVEKADINAYAKLARIBAKIMLIOLANLARA
YAKLARIBAKIMSIZOLANLARBĠRDAHAKĠYILINONHAZĠRANINDASĠYASAL
GÜNDEMKĠMBĠLĠRNASILOLACAKAMAOGÜNDEYĠNEKĠMBĠLĠRNEKADARK
IZÇOCUĞUDOĞACAKPAZARAKġAMINIĠPLEÇEKENLERHERHALDEBĠLĠYOR
LARDIRYAHYAKEMALĠNĠSTANBULUNSEMTLERĠÜSTÜNEDEġĠĠRLERYAZM
IġĠLKĠSTANBULġAĠRĠOLDUĞUNUBĠZANSġĠĠRĠNDEĠSTANBULYOKTUDĠVAN
EDEBĠYATINDADAĠSTANBULUNSEMTLERĠYOKTURYAHYAKEMALĠNRÜY
AGĠBĠBĠRYAZDIġĠĠRĠNĠNBESTEKARIOSMANNĠHATDAAHMETRASĠMĠNTOR
UNUYDUBĠRKENTBĠRĠKĠMĠNDENARTAKALANBUKETLERZEYNEPEDEAYN
IGÜNDOĞMUġOLANLARADADOĞUMYILDÖNÜMLERĠKUTLUOLSUNNUTU
KLARBĠRYANADOĞUMGÜNLERĠBĠRYANA
Homophonic cipher comes one step forward in the classical encryption methods
because it generates the ciphertexts consisting of variable block sizes. This makes well
known attacking models invalid. Although, the encryption method contains
vulnerabilities for Turkish, it could clearly be said that the method is stronger than most
of classical methods. Moreover, long ciphertexts are needed to cryptoanalysis. If long
enough and uniform distributed ciphertext is given, distinctive n-grams would most
probably contribute to detect vast majority of the letters of the alphabet. All in all, the
method still maintains its resistance today against to frequency analysis attacks on short
ciphertexts.
5.
Conclusion
The key space of the substitution cipher is enormously larger than one of the most
common modern encryption method DES. However, the block size of the encryption
method remains stable and it is equal to the value of one. That would cause the defeat
against to attacks based on statistical features of the source language.
Nevertheless, the most of modern cryptosystems such as DES and AES are insprired by
the substitution cipher. Moreover, the substitution cipher constitutes the base for the
substitution-permutation networks.
Herein, homophonic cipher is developed as an alternative to the substitution cipher
method.
Homophonic cipher extends the block size of the ciphertext in patches.
Moreover, the block size is variable. This renders plaintext identification diffucult.
Also, well known statistical features of the source language are invalid.
In this work, a novel attacking model for Homophonic cipher in Turkish is developed
while main concepts of cryptology are demonstrated.
Herein, it is copied that Homophonic cipher has a key space wider than the most
modern cryptosystems. All in all, without any hesitation it is figured out that the
homophonic cipher still maintains its resistence today against to frequency analysis
attacks on short ciphertexts. Long ciphertexts are needed to attack encrypted texts.
Meanwhile, the corpus size of the related work presented by Dalkılıç [1] is
overperformed by this study. Therefore, more correct and more consistent results are
obtained. As an additional deliverable, the results obtained towards the solutions of
language based cryptographic problems also contribute to the linguistic studies.
References
[1]
Dalkıllıç, M.E., Dalkılıç, G., “On the Cryptographic Patterns and Frequencies in
Turkish Language”, Advances in Information Systems, 144-153, (2002).
[2]
Serengil, S.I., Akin, M., “Attacking Turkish Texts Encrypted by Homophonic
Cipher”, Proceedings of the 10th WSEAS International Conference on
Electronics, Hardware, Wireless and Optical Communications, 123-126, (2011).
[3]
Hoffstein, J., Pipher, J., Silverman, J., An Introduction to Mathematical
Cryptography, Springer, New York, (2000).
[4]
Menezes, A.J., Oorschot, P.C.V. et al, Handbook of Applied Cryptography,
CRC, New York, (1997).
[5]
Delf, H., Knebl, H., Introduction to Cryptography, Springer, New York, (2001).
[6]
Stallings, W., Cryptography and Network Security Principles and Practice,
Prentice Hall, New York, (2005).
[7]
Acharya, B., Rath, G. S. et al, “Novel Methods of Generating Self-Invertible
Matrix for Hill Cipher Algorithm”, International Journal of Security, 1(1), 1421, (2007).
[8]
Eisenberg, M., “Hill Ciphers and Modular Linear Algebra”, Mimeographed
Notes, University of Massachusetts, 1-19, (1999).
[9]
Acharya, B., Jena, D. et al, “Invertible, Involutory and Permutation Matrix
Generation Methods for Hill Cipher System”, International Journal of Security,
410-414, (2007).
[10]
Dalkılıç, M. E., Gungor, C., “An Interactive Cryptanalysis Algorithm for the
Vigenere Cipher”, Advances in Information Systems, 341-351, (2000).
[11]
Pommerening, K., “Kasiski’s Test: Couldn’t the Repetitions be by Accident”,
Cryptologia, 30(4), 346-352, (2006).
[12]
Penzhorn, W., “A Fast Homophonic Coding Algorithm Based on Arithmetic
Coding”, IEEE Transactions on Information Theory, 45(6), 2083-2091, (1999).
51
[13]
Penzhorn, W.T., Els, W.C., “A Universal Homophonic Coding Algorithm Based
on Arithmetic Coding”, Communications and Signal Processing, 45(6), 20832091, (1994).
[14]
Rocha, V., Massey, J., “On the Entropy Bound for Optimum Homophonic
Substitution”, Information Theory, 93-94, (1997).
[15]
Ryabko, B., Fionov, A., “Efficient Homophonic Coding”, 45(6), 2083-2091,
Information Theory, (1999).
[16]
Singh, S., The Code Book: The Secret History of Codes and Code-breaking,
Anchor, New York, (1999).
[17]
Günther, C., Boveri, A. et al,
“A Universal Algorithm for Homophonic
Coding”, Advances in Cryptography, 405-414, (1988).
[18]
Jendal, H., Kuhn, Y., et al, “An Information-Theoretic Treatment of
Homophonic Substitution”, Advances in Cryptology, 382-394, (1998).
[19]
Sgarro, A., “Equivocations for Homophonic Ciphers”, Advances in Cryptology,
51-61, (1985).
[20]
Hammer, C., “Second Order Homophonic Ciphers”, 12(1), Cryptologia, 11-20,
(1988).
[21]
Hammer, C., “Higher Order Homophonic Ciphers”, 5(4), Cryptologia, 231-242,
(1981).
[22]
King, J. C., Bahler, D. R., “A Framework for the Study of Homophonic Ciphers
in Classical Encryption and Genetic Systems”, Cryptologia, 17(1), 45-54,
(1993).
[23]
King, J. C., Bahler, D. R., “An Algorithmic Solution of Sequential Homophonic
Ciphers”, Cryptologia, 17(2), 148-165, (1993).
[24]
Ravi, S., Knight, K., “Bayesian Inference for Zodiac and Other Homophonic
Ciphers”, Human Language Technologies, (2011).
Appendix
In this work, the corpus of size 13.4 MB is used to obtain the Turkish n-gram
frequencies. Also, the corpus consists of the sources specified below:
1. 120 articles of a columnist, Çetin Altan, from the Turkish daily newspaper Milliyet
published between 20.01.2010 - 04.07.2010. (Available at www.milliyet.com.tr )
2. 37 novels of 9 authors as listed in Table A.1.
53
Table A.1 List of Novels Used in the Corpus
Index
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
27
28
29
30
31
32
33
34
35
36
37
Author
Ahmet Altan
Ahmet Altan
Ahmet Altan
Ahmet Altan
Ahmet Altan
Aziz Nesin
Aziz Nesin
Aziz Nesin
Aziz Nesin
Aziz Nesin
Aziz Nesin
Aziz Nesin
Aziz Nesin
Aziz Nesin
Aziz Nesin
Çetin Altan
Gülse Birsel
Gülse Birsel
Gülse Birsel
Orhan Kemal
Orhan Kemal
Orhan Pamuk
Orhan Pamuk
Orhan Pamuk
Orhan Pamuk
Orhan Pamuk
Orhan Pamuk
Orhan Pamuk
Orhan Pamuk
Orhan Pamuk
Rıfat Ilgaz
Soner Yalçın
Soner Yalçın
Soner Yalçın
Soner Yalçın
Yılmaz Erdoğan
Yılmaz Erdoğan
Novel
Ġçimizde Bir Yer
Kırar Göğsüne Bastırırken
Aldatmak
Kristal Denizaltı
Sudaki Ġz
Anıtı Dikilen Sinek
Borçlu Olduklarımız
Tatlı BetüĢ
Rıfat Bey Neden KaĢınıyor
Bay Düdük
Memleketin Birinde
Damda Deli Var
Ġstanbul’un Halleri
Sizin Memlekette EĢĢek Yokmu
Gerçeğin Masalı
Viski
Yolculuk Nereye HemĢerim
Hala Ciddiyim
Gayet Ciddiyim
Cemile
Baba Evi
Masumiyet Müzesi
Babamın Bavulu
Hatıralar ve ġehir
Kar
Benim Adım Kırmızı
Yeni Hayat
Kara Kitap
Beyaz Kale
Sessiz Ev
Hababam Sınıfı
Bay Pipo
Reis
Beco
BinbaĢı Ersever’in Ġtirafları
Hijyenik AĢklar
Hüsünbaz SeviĢmeler
Publishing Year
2004
2003
2002
2001
1985
1982
1976
1974
1965
1958
1958
1956
1974
2005
2004
2003
1952
1949
2008
2006
2003
2002
1998
1994
1990
1985
1983
1957
1999
1997
1996
1994
2003
2001
Biographical Sketch
Serengil was born in Istanbul on November 24th, 1986. In 2003, he graduated from
Kadikoy Intas Lisesi in Istanbul.
He began his undergraduate studies in 2004 at
Istanbul Commerce University Computer Engineering Department.
In 2009, he
received his BSc degree in Computer Engineering from Istanbul Commerce University.
He enrolled in MSc studies in Galatasaray University Computer Engineering
Department same year. He is currently pursuing his MSc degree. Presently, he is
working as a Software Developer at Softtech, which is a subsidiary compay of Isbank
Group since August 2010. Also, he is the co-author of the paper entitled “Attacking
Turkish Texts encrypted by Homophonic Cipher” which was published in the
Proceedings of the 10th WSEAS International Conference on Electronics, Hardware,
Wireless and Optical Communications held at Cambridge, UK in February 20-22, 2011.