1. Computer and Network Security
CSEN 1001
Computer and Network Security
Amr El Mougy
Alaa Gohar
Heba Anwar

2. Lecture (2)
Cryptographic Tools

3. Early History
Egypt (Old Kingdom), ca. 1900BC. Use of non-standard hieroglyphs (probably not a serious attempt at secret communication)
Mesopotamia, ca. 1500BC. Encrypted recipe for pottery glaze on clay tablet
Hebrew, ca. 500BC. Monoalphabetic substitution cipher used by scholars

4. Not so Early History
800AD. Early description of frequency analysis for breaking substitution ciphers (credited to Arab mathematician Al- Kindi, 801–873). Works about cryptanalysis of single- and polyalphabetic ciphers
Ahmad al-Qalqashandi 1355–1418 List of ciphers in his encyclopedia contains a cipher with multiple substitutions for each letter; frequency tables for letters to aid cryptanalysis
1467: Leon Battista Alberti (“father of Western cryptology”) describes the polyalphabetic cipher

5. Recent History
WWII heavy use of rotor machines for complex polyalphabetic substitution ciphers
The “Enigma” machine:

6. Recent History
The time of WWII brought massive advances in cryptography as well as cryptanalysis
In the 20th century, mathematical cryptography was developed
Works by Claude Shannon. Any theoretically unbreakable cipher must have keys which are at least as long as the plaintext and used only once (one-time pad)
Publication of the Data Encryption Standard in 1970
1976 Ground-breaking paper: Whitfield Diffie and Martin Hellman. “New Directions in Cryptography” solves key exchange problem and sparks development of asymmetric key algorithms

7. Cryptographic Tools
Cryptographic algorithms important element in security services
Review various types of elements
symmetric encryption
public-key (asymmetric) encryption
digital signatures and key management
secure hash functions
Example is to encrypt stored data
Characterize cryptographic system by:
Type of encryption operations used
substitution / transposition / product
Number of keys used
single-key or private / two-key or public
Way in which plaintext is processed
block / stream

8. Symmetric Encryption 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

9. Public Key Encryption

10. 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

11. Attacking Symmetric Encryption
Cryptanalysis
rely on the nature of the algorithm
plus some knowledge of plaintext characteristics
even some sample plaintext-ciphertext pairs
exploits characteristics of algorithm to deduce specific plaintext or key
Brute-force attack
try all possible keys on some ciphertext until get an intelligible translation into plaintext

12. Cryptanalysis Attacks
Ciphertext only
only know algorithm & ciphertext, is statistical, know or can identify plaintext
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

13. Encryption Schemes
An encryption scheme is unconditionally secure if the ciphertext generated by the scheme does not contain enough information to determine uniquely the corresponding plaintext, no matter how much ciphertext is available
An encryption scheme is said to be computationally secure if:
The cost of breaking the cipher exceeds the value of the encrypted information
The time required to break the cipher exceeds the useful lifetime of the information

14. Exhaustive Key Search

15. 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 ciphertext bit patterns

16. Caesar Cipher
Earliest known substitution cipher (invented by Julius Caesar)
First attested use in military affairs
Replaces each letter by 3rd letter down in the alphabet. Example:
Meet me after the toga party
PHHW PH DIWHU WKH WRJD SDUWB
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 + k) mod (26)
p = D(c) = (c – k) mod (26)

17. Breaking 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
Compression reduces chance of breaking

18. Monoalphabetic Cipher
Rather than just shifting the alphabet, 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
Now have a total of 26! = 4 x 1026 keys
With so many keys, might think is secure
But would be !!!WRONG!!!

19. Breaking the Monoalphabetic Cipher
Given ciphertext:
UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZ
VUEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZUHSX
EPYEPOPDZSZUFPOMBZWPFUPZHMDJUDTMOHMQ

20. Breaking the Monoalphabetic Cipher
Human languages are redundant, eg “secrty s awsm"
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

21. Breaking the Monoalphabetic Cipher
Key concept - monoalphabetic substitution ciphers do not change relative letter frequencies
Discovered by Arabian scientists in 9th century
Calculate letter frequencies for ciphertext
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

22. Breaking the Monoalphabetic Cipher
Given ciphertext:
UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZ
VUEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZUHSX
EPYEPOPDZSZUFPOMBZWPFUPZHMDJUDTMOHMQ
Count relative letter frequencies
Guess P & Z are e and t
Guess ZW is “th” and hence ZWP is “the”. Frequency of two-letter combinations is known as digrams
Proceeding with trial and error finally get:
it was disclosed yesterday that several informal but
direct contacts have been made with political
representatives of the viet cong in moscow

23. “pack my box with five dozen liquor jugs”
Problem 1
In the English language, a sentence that contains all 26 letters of the alphabet is called a perfect pangram. These sentences may have important use in some cryptography algorithms. Specify a good use of a perfect pangram for any cryptography algorithm (hint: think of the monoalphabetic cipher).
Using the answer in part (a), use the following perfect pangram:
“pack my box with five dozen liquor jugs”
To encrypt the statement: “I am going to graduate very soon” using the cipher you chose in part (a).
Is the encryption algorithm that you used considered secure? Why?
Solution
For the monoalphabetic cipher, a perfect pangram can be used as the key.
First construct the substitution table
Then perform the substitution to be: XPHBVXFBNVBZPKLPNMQMZJEVVF
c) It is vulnerable to frequency analysis, so it is not secure. 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 P A C K M Y B O X W I T H F V E D N L Q U R J S

24. Problem 2
The following cipher texts have been encrypted using Caesar cipher, find out the original text:
m xlmro, xlivijsvi m ibmwx
Solution
Caesar Cipher is broken either with brute force or frequency analysis.
Using Frequency Analysis, the letter ‘m’ is repeated, and single letter words are scarce in English; examples are ‘a’ and ‘I’.
To decipher the rest of the text, we find the shift needed to turn ‘m’ to ‘a’ and ‘m’ to ‘I’, whichever produces a meaningful sentence is the correct shift.
Fours shifts backwards are needed to turn ‘m’ to ‘I’, continuing to shift each of the letters of the cipher text 4 shifts backwards produces the decrypted text:
I think, therefore I exist

25. Problem 3
The following ciphertext was produced using a Caesar cipher. Break the encryption to obtain the plaintext. Note that the most commonly occurring letter in the English language is “e” and the second most commonly occurring letter is “t”.
MAX YTNEM, WXTK UKNMNL, EBXL GHM BG HNK LMTKL UNM BG HNKLXEOXL
Solution
By analyzing the ciphertext, the most commonly occurring letter is M, followed by X. If we assume that M is equivalent to e and X is equivalent to t we do not get a meaningful phrase. Thus, we can estimate that M = t and X = e. Analysis confirms that this is a shift of 19 letters in both substitutions. Using this same shift for all letters gives the plaintext
The fault, dear Brutus is lies not in our stars but in ourselves

26. Playfair Cipher
Not even the large number of keys in a monoalphabetic cipher provides security
One approach to improving security was to encrypt multiple letters
The Playfair Cipher is an example
Invented by Charles Wheatstone in 1854, but named after his friend Baron Playfair
A 5X5 matrix of letters based on a keyword
Fill in letters of keyword (without duplicates)
Fill rest of matrix with other letters
eg. using the keyword MONARCHY M O N A R C H Y B D E F G
I/J K L P Q S T U V W X Z

27. Encrypting and Decrypting
Plaintext is encrypted two letters at a time
If a pair is a repeated letter, insert filler like 'X’
If both letters fall in the same row, replace each with letter to right (wrapping back to start from end). Ex: ar becomes RM
If both letters fall in the same column, replace each with the letter below it (again wrapping to top from bottom). Ex: mu becomes CM
Otherwise each letter is replaced by the letter in the same row and in the column of the other letter of the pair. Ex: hs becomes BP

28. Security of Playfair Security much improved over monoalphabetic
Since have 26 x 26 = 676 digrams
Would need a 676 entry frequency table to analyse (verses 26 for a monoalphabetic), and correspondingly more ciphertext
Was widely used for many years
eg. by US & British military in WW1
It can be broken, given a few hundred letters
Since still has much of plaintext structure

29. Problem 4 Solution Encryption table
Encrypt the following phrase with the Playfair cipher. The key is “children”
Too cool for school
Solution
Encryption table
Letters will be encrypted as: to oc ox ol fo rs ch ox ol
Thus, the ciphertext is: um fd kz md gf np hi kz md C h
i/j l d r e n a b f g k m o p q s t u v w x y z

30. Polyalphabetic Cipher
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

31. 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
Write the plaintext out. Write the keyword repeated above it
Use each key letter as a Caesar cipher key. Encrypt the corresponding plaintext letter
eg using keyword deceptive
key:
plaintext:
ciphertext: d e c p t i v w a r s o y u l f Z I C V T W Q N G R A H Y L M J

32. Plaintext
Key

33. Breaking the Vigenère Cipher
Have multiple ciphertext letters for each plaintext letter
Hence letter frequencies are obscured, but not totally lost
Start with letter frequencies
see if look like monoalphabetic or not
If not, then need to determine number of alphabets, since then can attach each
Kasiski method developed by Babbage/Kasiski is a way of breaking Vigenere
Repetitions in ciphertext give clues to period, so find same plaintext an exact period apart which results in the same ciphertext
Of course, could also be random fluke
eg repeated “VTW” in previous example suggests size of 3 or 9
Then attack each monoalphabetic cipher individually using same techniques as before

34. Problem 5 Solution a) Plain text: Key : Result :
a) Encrypt “Attack Now” using Vigenère cipher, with the keyword “Play” using tabula recta.
b) Perform an examination to find the length of the key that was used to produce the following Vigenère cipher text.
io ygx wewq ss tswmw nzl eytluonnr. vs wewq ss hzo aj acw ysamdi yo mw eytluojd.
Solution
a) Plain text:
Key :
Result : p l a y t c k n o w P E T Y R V N M L
b) First, we find repetitions of sequences in the cipher:
io ygx wewq ss tswmw nzl eytluonnr. vs wewq ss hzo aj acw ysamdi yo mw eytluojd.
The distances between repetitions are 25 characters and 35 characters respectively.
Using prime factorization:
25 = 5 *5
35 = 5*7
Therefore the gcd = 5
This indicates a key length of 5.

35. Problem 6
Assume that Vigenere cipher was used to convert the following plaintext into ciphertext:
If the sequence of characters TICRMQUIRTJR was found twice in the ciphertext, once starting at the 10th character position and again starting at the 241st character position (numbering starts from 1), we can use the Kasiski method to estimate that the key length can be multiples of
241 – 10 = 231 = 3*7*11
Thus, we estimate that the length of the key is 3, 7 or 11 characters. Discover the key.
Plaintext c r y p t o g a h
Ciphertext T I C R M Q U J

36. Solution 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 51 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
At position 10, the shift is
T – c = 19 – 2 = 17 = r
Similarly, the remaining letters give the corresponding keyword: rrectcorrect
This is obviously not periodic with period 3 or 11, while period 7 is possible. A keyword of length 7 starts at position 15, resulting in the keyword: correct

37. One-time Pad
A random key as long as the message is used to encrypt and decrypt a single message
The key is then discarded, never to be used again
The output bears no statistical relationship to the plaintext
Given any plaintext of equal length to the ciphertext, there is a key that produces that plaintext. Therefore, if you did an exhaustive search of all possible keys, you would end up with many legible plaintexts, with no way of knowing which was the intended plaintext
ciphertext: ANKYODKYUREPFJBYOJDSPLREYIUNOFDOIUERFPLUYTS
key: pxlmvmsydofuyrvzwc tnlebnecvgdupahfzzlmnyih
plaintext: mr mustard with the candlestick in the hall
key: mfugpmiydgaxgoufhklllmhsqdqogtewbqfgyovuhwt
plaintext: miss scarlet with the knife in the library
Large number of keys need to be used. Key distribution is a big problem

38. 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
Simplest transposition cipher is the 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

39. Row Transposition Ciphers
A more complex transposition
Write letters of message out in rows over a specified number of columns, then reorder the columns according to some key before reading off the rows
Key:
Plaintext:
Ciphertext: TTNAAPTMTSUOAODWCOIXKNLYPETZ
Ciphers using substitutions or transpositions are not secure because of language characteristics
Hence consider using several ciphers in succession to make harder, but:
two substitutions make a more complex substitution
two transpositions make more complex transposition
but a substitution followed by a transposition makes a new much harder cipher 4 3 1 2 5 6 7 a t c k P o s n e d u i l w m x y Z

40. Rotor Machines
Before modern ciphers, rotor machines were most common complex ciphers in use
Widely used in WW2
German Enigma, Allied Hagelin, Japanese Purple
Implemented a very complex, varying substitution cipher
Used a series of cylinders, each giving one substitution, which rotated and changed after each letter was encrypted
With 3 cylinders have 263=17576 alphabets

41. Rotor Machines

42. Note
The material in this lecture can be found in Chapter 2, Cryptography and network security. Everything except “Hill cipher” has been covered.