1. Chapter Two: Classic Cryptography

2. Index Introduction A.1 Cryptosystems A.2 Terminology
B. Classic Cipher (Substitution Cipher)
B.1 Caesar Cipher
B 2 Tap Code
B.3 Pigpen Cipher
B 4 Vigenere Cipher
B 5 Book Cipher
C. Cryptanalysis of Substitution Cipher
C.1 Brute force cryptanalysis
C.2 Frequency Distribution Analysis
D. Calculation of Modulo operation
E. One-Time Pad
F. Classic Cipher( Transposition Cipher)
F.1 Route Cipher
F.2 Rail Fence Cipher
F.3 Column Cipher

3. Cryptosystems A. Ciphers B. Classic B.1 Substitution
e.g., Caesar Cipher
B.2 Transposition
e.g., Route Cipher
B.3 Hybrid
C. Modern
C.1 Symmetric
(Private Key)
Stream Cipher e.g., RC4, A5/1
Block Cipher e.g., DES, AES
C.2 Asymmetric
(Public Key)
e.g., RSA
C.3 Hybrid

4. A. Terminology
Cryptology is the art and science of making and breaking “secret codes.”
Cryptography is the making of “secret codes.”
Cryptanalysis is the breaking of “secret codes.”
Crypto is a synonym for any or all of the above (and more).
Cipher (صفر) is an algorithm for performing encryption and decryption — a series of well-defined steps that can be followed as a procedure.

5. Terminology
Encryption is the process of encoding a message so that its meaning is not obvious
Equivalent terms: encode, encipher
Decryption is the reverse process, transforming an encrypted message back into its normal, original form
Equivalent terms: decode, decipher
Encrypt
Plaintext
Ciphertext
Decrypt

6. Terminology
Encryption/decryptions algorithms often use a device called a key, so that the resulting ciphertext depends on the original plaintext message, the algorithm, and the key value
An encryption scheme that does not require the use of a key is called a keyless cipher
The cryptosystem involves a set of rules for how to encrypt the plaintext and how to decrypt the ciphertext
Encrypt
Plaintext
Ciphertext
Decrypt

7. Terminology Plaintext: message to be encrypted
Ciphertext: encrypted message
DK(EK(P)) = P

8. Terminology
Symmetric uses same key for encryption and decryption process.
To encrypt: C = E(K, P)
To decrypt: P = D (K, E(K,P))
Asymmetric uses different key for encryption and decryption process.
To encrypt: C = E (KE,P)
To decrypt: P = D (KD, E (KE,P))

9. B. Classic Cipher
Substitution Ciphers: exchange one letter (or more) with another letter/number/symbol/sound/art
A mono-alphabetic cipher uses fixed substitution over the entire message,
A poly-alphabetic cipher uses a number of substitutions at different times in the message
Transposition Ciphers: re-arrange the order of the letters

10. B.1. Substitution Ciphers 1. Caesar Cipher
Idea: each letter or group of letters is replaced by another letter or group of letters
Caesar cipher – circularly shift by 3 letters
a -> D, b -> E, … z -> C
More generally, shift by k letters, k is the key

11. B.1. Substitution Ciphers 1. Caesar Cipher
It is monoalphabetic cipher uses addition modulo 26
The message must be a sequence of letters, each letter is identified with a number:
The key k is a number in the range 1 … 25.
Advantages and Disadvantages:
The Caesar cipher is quite simple
The ability of predict the entire algorithm using small piece of ciphertext

12. B.1. Substitution Ciphers 1. Caesar Cipher (Algorithms)
Encryption/decryption involve ± k to each letter (mod 26). So the general Caesar algorithm is
Ci= Ek(Mi) = E(Mi, k) = (Mi+k) mod 26
Mi= Dk(Ci) = D(Ci, k) = (Ci-k) mod 26
For example,
Plaintext : treaty impossible
Key : ± 3
Ciphertext: wuhdwb lpsrvvleoh
That is, Ci=E[Mi , 3] = Mi+3 mod 26

13. B.1. Substitution Ciphers 1. Caesar Cipher
It is the simplest monoalphabetic cipher. Caesar cipher using the shift parameter as the key:

14. Example: Caeser Cipher (Encryption)

15. Example: Caesar Cipher (Decryption)

16. Example: Caesar cipher (Encryption)
Use the Caesar cipher with key=15 to encrypt the message “hello”
Ciphertext: WTAAD

17. Example: Caesar Cipher (Decryption)
Use the Caesar cipher with key=15 to decrypt the message “WTAAD”
Ciphertext: hello

18. Questions Review
Q1. Use the Caesar cipher to find the plaintext and the key from the ciphertext:
Ciphertext : ugehmlwj kwumjalq
Q2. Use the Caesar cipher with key=3 to encrypt the next message:
Plaintext: the quick brown fox jumps over the lazy dog

19. B.1. Substitution Ciphers 2. Tap Code
Each letter is replaced by a number of beeps

20. Substitution Cipher Pigpen Cipher
Each letter is replaced by an art

21. B.1. Substitution Ciphers 3. Vigenère Cipher
Polyalphabetic ciphers flatten the frequency distribution of the plaintext considerably.
Vigenère Cipher is an example of polyalphabetic ciphers - use different monoalphabetic substitutions as one proceeds through the plaintext message.
For example:
Plaintext (M) meet me at ten
Key (K) badb ad ba dba
Ciphertext(C) nehu mh bt wfn
where C = M+K mod 26

22. B.1. Substitution Ciphers 3. Vigenère Cipher
Vigenère Tableau

23. B.1. Substitution 3.Vigenere algorithm
This is a Polyalphabetic Cipher that uses Caesar Cipher with more than one key.

24. B.1. Substitution 3.Vigenere algorithm
- We can notice from the above example that four keys are used for encryption
and decryption.
- Keys range from 1 to 25.
- Four keys are used in the above example (5,9,18 and 24)
- Encryption is done by using first key ( i.e. 5) to encrypt first letter A, Second
letter B is encrypted using key =9 and C is encrypted using key 18 and a letter
D is encrypted using key= 24.
- When we used all keys the process is repeated and a second round is made. So
when we reach letter E, we encrypt it again using key = 5 and letter F is
encrypted using key=9 and etc…
- To decrypt the cipher, we should know what the letters that each key encrypts
is. This is can be done by using array of letter indexes (i.e. Key = 5 encrypts
letter in indexes 0, 4,8,12 ….
- The Excel sheet will spread to the students and they should try it by adjusting
some parameters keys.

25. Question Review
Q1:Use the Vigenere cipher with key=lemon to encrypt the message “attackatdawn”

26. B.1. Substitution Ciphers 4. Book Cipher
Any book can provide a key
The key is formed from the letter of the text
Steps:
select a passage (Key)
“the page cannot be found”
match the plaintext with selected text.
Plaintext  “MACHINES CANNOT THINK”
encode plaintext using Vigenere table

27. B.1. Substitution Ciphers Cryptanalysis
Brute force cryptanalysis: would have to try 26! permutations of a particular ciphertext message.
Students can guess the key by using brute force technique. - For example in the above
program, the key was set to 3.

28. Brute force cryptanalysis (cont)
Try key = 0, the decrypted cipher will be:
Try key = 1, the decrypted cipher will be:
Try key = 2, the decrypted cipher will be:
Try key = 3, the decrypted cipher will be:
Matched!!
So key =3

29. B.1. Substitution Ciphers Cryptanalysis (cont)
2. Frequency Distribution Analysis: In practice, it is not difficult to determine the key using frequencies of letters, pairs of letter etc., or by guessing a probable word or phrase
Most frequently occurred
Letters: e, t, o, a, n, …
Digrams: th, in, er, re, an, …
Trigrams: the, ing, and, ion, ent
Words: the, of, and, to, a, in, that,

30. B.1. Substitution Ciphers 7. One-Time Pads

31. B.1. Substitution Ciphers 7. One-Time Pads (using Bits)
One-time pad: construct an unbreakable cipher
Choose a random bit string as the key
Convert the plaintext into a bit string
Compute the XOR of these two strings, bit by bit
The resulting ciphertext cannot be broken, because in a sufficiently large sample of ciphertext, each letter will occur equally often, as will every diagram, every trigram, and so on
=> There is simply no information in the message because all possible plaintexts of the given length are equally likely
The Vernam Cipher is a type of one-time pad devised by Gilbert Vernam for AT&T

32. Calculation of MOD operation
Calculate the following mod:
E.g., (5) mod 21 =5
(30) mod 21
= (9) mod 21 =9

33. Calculation Negative MOD
Modula always return non-negative number: Calculate the following mod E.g., (-57) mod 21 = (-36) mod 21 = (-15) mod 21 = (6) mod 21 =6

34. B.1. Substitution Ciphers 7. One-Time Pads (using ASCII Code)
Plaintext V E R N A M C I P H
Numeric Equivalent 21 4 17 13 12 2 8 15 7
+ Random Number 76 48 16 82 44 3 58 11 60 5 47 88
= Sum 97 52 33 95 19 75 51
105
= mod 26 18 23 25 1
Ciphertext t a h r s p i x m z b
To decrypt: (Ci – Ki) mod 26
Note on rules of mod on negative number: “The mod function is defined as the amount by which a number exceeds the largest integer multiple of the divisor that is not greater than that number” (
Modula op always return non-negative number
E.g., (19-76) mod 26 = (-57) mod 26 = (-78+21) mod 26 = 21
Ciphertext t a h r s p i x m z b
Numeric Equivalent 19 7 17 18 15 8 23 12 25 1
- One-time pad 76 48 16 82 44 3 58 11 60 5 47 88
= Difference
-57
-48 -9
-65
-26
-50
-37
-22
-87
= mod 26 21 4 13 2
Plaintext V E R N A M C I P H

35. B.1. Substitution Ciphers 7. One-Time Pads
Observations:
The repeated letter comes from different plaintext letters
Duplicate ciphertext letters are generally unrelated when this encryption algorithm is used => there is no information in the message to be exploited
Disadvantages
The key cannot be memorized, both sender and receiver must carry a written copy with them
Total amount of data can be transmitted is limited by the amount of key available
Aabsolute synchronisation is between sender and receiver, otherwise, it fails completely to protect message integrity)

36. B.2. Transposition Ciphers
Transposition cipher – reorders (rearrange) symbols but does not disguise them. It is also called permutation
With transposition, the cryptography aims for diffusion
Widely spreading the information from the message or the key across the ciphertext
Transpositions try to break established patterns

37. B.2. Transposition Ciphers 1. Route Cipher

38. B.2. Transposition Ciphers 2. Rail Fence Cipher

39. B.2. Transposition Ciphers 3. Columnar Transposition
Plaintext written in rows
Number of columns = key length
Key is used to number the columns
Ciphertext reads out by columns, starting with column whose key letter is lowest

40. B.2. Transposition Ciphers 3. Columnar Transposition
For example:
Plaintext (M): WE ARE DISCOVERED FLEE AT ONCE
Key (K):
Ciphertext(C): EVLNE ACDTK ESEAQ ROFOJ DEECU WIREE

41. Example:Columnar cipher
Ciphertext(C): EVLNX ACDTX ESEAX ROFOX DEECX
WIREE
Key:
Plaintext (M): WE ARE DISCOVERED FLEE AT ONCE

42. Question review Q1. Encrypt the following plaintext using Columnar
transposition:
We are going to university every day
Use your Last name as keyword
Q2.use the rail fence Cipher (3 rails) to encode the following plaintext
Plaintext: We are going to university every day

43. Question review
Q3. They are 4! = 24 possible combinations for the substations. Here some sample:
Q4 . By using brute force we must try all 24 choices until we break the cipher.

44. Terms and Concepts Encryption & Decryption Plaintext & Ciphertext
Algorithm & Cipher
Cryptology
Cryptography & Cryptanalysis
Key
Substitution & Transposition
Monoalphabetic Ciphers & Polyalphabetic Ciphers