1. Lecture 2 2012 Classical Encryption Techniques Dr. Nermin Hamza

2. Introduction Cryptography
Cryptography is the science of writing in- secret code and is an ancient art .
The first documented use of cryptography in writing dates back to circa 1900 B.C. by Egyptian.

3. Introduction (cont’d)
Cryptography
DAVID KAHN at said at “coder breaker” :
Cryptology was born among the Arabs.
They were the first to discover and write down the methods of cryptanalysis
وقد نشر مجمع اللغة العربية ، بدمشق الجزء الأول من الكتاب ”علم التعمية و استخراج المعمى ”، سنة ١٩٨٧ ونشر الجزء الثاني سنة ١٩٩7
للدكتور : محمد مراياتي ويحيى ميرعلم و محمد حسان الطيان

4. Requirements two requirements for secure use of symmetric encryption:
a strong encryption algorithm
a secret key known only to sender / receiver
mathematically have:
Y = EK(X)
X = DK(Y)
assume encryption algorithm is known
implies a secure channel to distribute key

5. Some Basic Terminology
plaintext - original message
ciphertext - coded message
cipher-algorithm : for transforming plaintext to ciphertext
key - info used in cipher known only to sender/receiver
encipher (encrypt) - converting plaintext to ciphertext
decipher (decrypt) - recovering ciphertext from plaintext

6. Encryption Diagram Encryption algorithm Decryption algorithm
Plain Text
Cipher Text
Plain Text
Key
Key

7. Cryptography characterize cryptographic system by: number of keys used
single-key or private / two-key or public
type of encryption operations used
substitution / transposition / product
way in which plaintext is processed
block / stream

8. Cryptography types:
Symmetric cipher
Asymmetric cipher

9. Also called Secret Key Cryptography (SKC):
Symmetric cryptography :
Also called Secret Key Cryptography (SKC):
Uses a single key for both encryption and decryption
Plain Text
Plain Text
Cipher Text

10. Also called Public Key Cryptography (PKC):
Asymmetric Cryptography :
Also called Public Key Cryptography (PKC):
Uses one key for encryption and another for decryption
Plain Text
Cipher Text
Plain Text

11. Symmetric Encryption or conventional / private-key / single-key
sender and recipient share a common key
all classical encryption algorithms are private-key
was only type prior to invention of public- key in 1970’s
and by far most widely used

12. Some Basic Terminology
cryptography - study of encryption principles/methods
cryptanalysis (codebreaking) - study of principles/ methods of deciphering ciphertext without knowing key
cryptology - field of both cryptography and cryptanalysis

13. Cryptanalysis objective to recover key not just message
general approaches:
cryptanalytic attack
rely on the nature of the algorithm plus perhaps some knowledge of the general characteristics of the plaintext or even some sample plaintext- ciphertext pairs.
Brute-force attack
try every possible key on a piece of cipher text until an intelligible translation into plaintext is obtained.
Typically objective is to recover the key in use rather then simply to recover the plaintext of a single ciphertext.
There are two general approaches:
Cryptanalytic attacks rely on the nature of the algorithm plus perhaps some knowledge of the general characteristics of the plaintext or even some sample plaintext-ciphertext pairs.
Brute-force attacks try every possible key on a piece of ciphertext until an intelligible translation into plaintext is obtained. On average,half of all possible keys must be tried to achieve success.

14. Cryptanalytic Attacks
ciphertext only
only knows algorithm & ciphertext
known plaintext
know/suspect plaintext & ciphertext
chosen plaintext
select plaintext and obtain ciphertext
chosen ciphertext
select ciphertext and obtain plaintext
chosen text
select plaintext or ciphertext to en/decrypt

15. Brute Force Search always possible to simply try every key
most basic attack, proportional to key size
assume either know / recognise plaintext
Key Size (bits)
Number of Alternative Keys
Time required at 1 decryption/µs
Time required at decryptions/µs 32
232 = 4.3  109
231 µs = 35.8 minutes
2.15 milliseconds 56
256 = 7.2  1016
255 µs = 1142 years
10.01 hours
128
2128 = 3.4  1038
2127 µs = 5.4  years
5.4  1018 years
168
2168 = 3.7  1050
2167 µs = 5.9  years
5.9  1030 years
26 characters (permutation)
26! = 4  1026
2  1026 µs =  1012 years
6.4  106 years
A brute-force attack involves trying every possible key until an intelligible translation of the ciphertext into plaintext is obtained. On average, half of all possible keys must be tried to achieve success. Stallings Table 2.2 shows how much time is required to conduct a brute-force attack, for various common key sizes (DES is 56, AES is 128, Triple-DES is 168, plus general mono-alphabetic cipher), where either a single system or a million parallel systems, are used.

16. The main two basic techniques
Substitution
Transposition

17. Substitution Ciphers

18. Classical Substitution Ciphers
where letters of plaintext are replaced by other letters or by numbers or symbols
or if plaintext is viewed as a sequence of bits, then substitution involves replacing plaintext bit patterns with cipher text bit patterns

19. Caesar Cipher earliest known substitution cipher by Julius Caesar
first attested use in military affairs
replaces each letter by 3rd letter on
example:
M e e t m e a f t e r t h e t o g a p a r t y
P H H W P H D I W H U W K H W R J D S D U W B

20. Caesar Cipher then have Caesar cipher as: c = E(p) = (p + k) mod (26)
p = D(c) = (c – k) mod (26)

21. Caesar Cipher can define transformation as:
a b c d e f g h i j k l m n o p q r s t u v w x y z
D E F G H I J K L M N O P Q R S T U V W X Y Z A B C
mathematically give each letter a number
a b c d e f g h i j k l m n o p q r s t u v w x y z
then have Caesar cipher as:
c = E(p) = (p + 3) mod (26)
If p= a= 0 ,
E(a) = (0+3) mod 26 = 3 = D

22. a b c d e f g h i j k l m n o p q r s t u v w x y z a b c d e f g h i j k l m n o p q r s t u v w x y z 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

23. Caesar Example
Let k= 10
Encrypt the following “Hello”

24. Caesar Example Let k= 10 Encrypt the following “Hello” H E L L O
(MOD 26)
R O V V Y

25. Caesar Example
Let k= 9
Encrypt the following “SUN”

26. Caesar Example Let k= 9 Encrypt the following “SUN” S U N 18 20 13
(MOD 26)
B D W

27. Caesar Example Let the cipher text = “IFMMP” and k =1
What is the plain text?
P= (C-1) mod 26
P = Hello

28. Cryptanalysis of Caesar Cipher
only have 26 possible ciphers
A maps to A,B,..Z
could simply try each in turn
a brute force search
given ciphertext, just try all shifts of letters
do need to recognize when have plaintext
eg. break ciphertext "GCUA VQ DTGCM"

29. Example for fun G C U A V Q D T M W O P K X N B L Y H R Z I S J E F

30. Monoalphabetic Cipher
rather than just shifting the alphabet
could shuffle (jumble) the letters arbitrarily
each plaintext letter maps to a different random ciphertext letter
hence key is 26 letters long
Plain: abcdefghijklmnopqrstuvwxyz
Cipher: DKVQFIBJWPESCXHTMYAUOLRGZN
Plaintext: ifwewishtoreplaceletters
Ciphertext: WIRFRWAJUHYFTSDVFSFUUFYA
With only 25 possible keys, the Caesar cipher is far from secure. A dramatic increase in the key space can be achieved by allowing an arbitrary substitution, where the translation alphabet can be any permutation of the 26 alphabetic characters.
See example translation alphabet, and an encrypted message using it.

31. Monoalphabetic Cipher Security
Could be another equation :
(a.i +b ) mod 26

32. Monoalphabetic Cipher Security
now have a total of 26! = 4 x 1026 keys
with so many keys, might think is secure
but would be !!!WRONG!!!
problem is language characteristics

33. Language Redundancy and Cryptanalysis
human languages are redundant
eg "th lrd s m shphrd shll nt wnt"
letters are not equally commonly used
in English E is by far the most common letter
followed by T,R,N,I,O,A,S
other letters like Z,J,K,Q,X are fairly rare
have tables of single, double & triple letter frequencies for various languages

34. English Letter Frequencies
Note that all human languages have varying letter frequencies, though the number of letters and their frequencies varies. Stallings Figure 2.5 shows English letter frequencies. Seberry & Pieprzyk, "Cryptography - An Introduction to Computer Security", Prentice-Hall 1989, Appendix A has letter frequency graphs for 20 languages (most European & Japanese & Malay).

35. Use in Cryptanalysis compare counts/plots against known values
if caesar cipher look for common peaks/troughs
peaks at: A-E-I triple, NO pair, RST triple
troughs at: JK, X-Z
for monoalphabetic must identify each letter tables of common double/triple letters help

36. Polyalphabetic Ciphers
polyalphabetic substitution ciphers
improve security using multiple cipher alphabets
make cryptanalysis harder with more alphabets to guess and flatter frequency distribution
use a key to select which alphabet is used for each letter of the message
use each alphabet in turn
repeat from start after end of key is reached

37. Vigenère Cipher simplest polyalphabetic substitution cipher
effectively multiple caesar ciphers
key is multiple letters long K = k1 k2 ... kd
ith letter specifies ith alphabet to use
use each alphabet in turn
repeat from start after d letters in message
decryption simply works in reverse
The best known, and one of the simplest, such algorithms is referred to as the Vigenère cipher, where the set of related monoalphabetic substitution rules consists of the 26 Caesar ciphers, with shifts of 0 through 25. Each cipher is denoted by a key letter, which is the ciphertext letter that substitutes for the plaintext letter ‘a’, and which are each used in turn, as shown next.

38. Steps of Vigenère Cipher
1- write the plaintext out
2- Write your keyword across the top of the text you want to encipher, repeating it as many times as necessary.
3- encrypt the corresponding plaintext letter
4- eg using keyword deceptive
key: deceptivedeceptivedeceptive
plaintext: wearediscoveredsaveyourself
ciphertext:ZICVTWQNGRZGVTWAVZHCQYGLMG J
Discuss this simple example from text Stallings section 2.2.

39. 5- For each letter, look at the letter of the keyword above it ,and find that row in the Vigenere table.
6- Then find the column of your plaintext letter
7- Finally, trace down that column until you reach the row you found before and write down the letter in the cell where they intersect

40. Example D and W  Z key: d e c e p t ivedeceptivedeceptive
plaintext: w e a r e d iscoveredsaveyourself
ciphertext: Z I C V T W QNGRZGVTWAVZHCQYGLMGJ

42. Let key = MEC
Plain text :
We need more supplies fast

43. We need more supplies fast
Let key = MEC
Plain text :
We need more supplies fast
Keyword: M E C M E C M E C M E C M E C M E C M E C M
Plaintext: w e n e e d m o r e s u p p l i e s f a s t

44. A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

45. We need more supplies fast
Let key = MEC
Plain text :
We need more supplies fast
Keyword: M E C M E C M E C M E C M E C M E C M E C M
Plaintext: w e n e e d m o r e s u p p l i e s f a s t
Ciphertext: I I P Q I F Y S T Q W W B T N U I U R E U F

46. Security of Vigenère Ciphers
have multiple ciphertext letters for each plaintext letter
hence letter frequencies are obscured
but not totally lost

47. Play Fair
The keyword written into five-by-five square , omitting repeated letters and combining I and J in one cell.
Key: MANCHESTER

48. Example of play fair M A N C H E S T R B D F G I/J K L O P Q U V W X YZ

49. Example of play fair matrix
“playfair example" as the key

50. Example of play fair matrix
“Monarchy” R A N O M D B Y H C K
I/J G F E T S Q P L Z X W V U

51. Play Fair
Break the message into two-letter group. If both letters are the same : insert X between them. If only one letter add X letter
PLAIN: “THIS SECRET MESSAGE IS ENCRYPTED”

52. Steps
IF The letters in the same row, replace them with the letters to their immediate right respectively
Ex: AR => RM R A N O M D B Y H C K
I/J G F E T S Q P L Z X W V U

53. Steps
IF The letters in the same column take the below letters MU => CM R A N O M D B Y H C K
I/J G F E T S Q P L Z X W V U

54. Steps
If the two letters are located at opposite corner of the rectangle., is replaced by the letter that lies in its own row and the column occupied by the other plain text. HS=> BP R A N O M D B Y H C K
I/J G F E T S Q P L Z X W V U

55. SOLVE Key is “playfair Example”
Encrypt: “Hide the gold in the tree stump”

56. P L A Y F I R E X M B C D G H K N O Q S T U V W Z
HI DE TH EG OL DI NT HE TR EX ES TU MP
BM OD ZB XD NA BE KU DM UI XM MO UV IF

57. Play Fair
And then : take 2 letter from the plain text two by two and locate the letter at opposite corner of the rectangle:
TH BN M A N C H E S T R B D F G
I/J K L O P Q U V W X Y Z M A N C H E S T R B D F G
I/J K L O P Q U V W X Y Z

58. IF The letters in the same row, replace them with the letters to their immediate right respectively
SE TS M A N C H E S T R B D F G
I/J K L O P Q U V W X Y Z

59. IF The letters in the same column take the below letters CR RID F G
I/J K L O P Q U V W X Y Z

60. Solution
Solve

61. One-Time Pad
if a truly random key as long as the message is used, the cipher will be secure
called a One-Time pad
is unbreakable since ciphertext bears no statistical relationship to the plaintext
since for any plaintext & any ciphertext there exists a key mapping one to other
can only use the key once though
problems in generation & safe distribution of key

62. Transposition Ciphers

63. Transposition Ciphers
now consider classical transposition or permutation ciphers
these hide the message by rearranging the letter order
without altering the actual letters used
can recognise these since have the same frequency distribution as the original text

64. Rail Fence cipher
write message letters out diagonally over a number of rows
then read off cipher row by row
eg. write message out as:
m e m a t r h t g p r y
e t e f e t e o a a t
giving ciphertext
MEMATRHTGPRYETEFETEOAAT
The simplest such cipher is the rail fence technique, in which the plaintext is written down as a sequence of diagonals and then read off as a sequence of rows.
The example message is: "meet me after the toga party" with a rail fence of depth 2.
This sort of thing would be trivial to cryptanalyze.

65. Reverse cipher Write the message backwards Ex:
Plain: I came I saw I conq uered
Cipher: d ereu q noci w asie maci