1. Elementary Cryptography
Chapter 2
Elementary Cryptography
Department of Computer Science, Umm Al-Qura University University year: 1435/1436
Computer Security Systems
Lecturer :H.Ben Othmen

2. Computer Security Systems
Outline
Concepts of encryption
Cryptanalysis: how encryption systems are "broken"
Symmetric (secret key) encryption and the DES and AES algorithms
Asymmetric (public key) encryption and the RSA algorithm
Key exchange protocols and certificates
Digital signatures
Cryptographic hash functions
1435/1436
Computer Security Systems

3. Computer Security Systems
Introduction
Study of algorithms and protocols used to preserve confidentiality of information and ensuring its integrity.
It forms the basis of most security measures:
Secure Internet exchanges,
confidentiality of banking,
protection of trade secrets,
protection of medical confidentiality,
protection of computer systems against intrusion,
Through the electronic signature:
identification of correspondents,
Guarantee of integrity of documents.
1435/1436
Computer Security Systems

4. Computer Security Systems
Terminology
Encryption is the process of encoding a message
Decryption is the reverse process, transforming an encrypted message back into its normal
Encode the original message to hide its meaning
Decode it to reveal the original message
The original form of a message is known as plaintext
The encrypted form is called ciphertext
encode = encrypt= encipher
decode=decrypt = decipher
1435/1436
Computer Security Systems

5. Computer Security Systems
Terminology
P: plaintext message / P = <p1, p2, …, pn> (as a sequence of individual characters)
C: ciphertext message / C = <c1, c2, …, cm>
For example
the plaintext message "I want cookies" can be denoted as the message string <I, ,w,a,n,t, , c,o,o,k,i,e,s>.
It can be transformed into ciphertext <c1, c2, …, c14>,
the encryption algorithm tells us how the transformation is done.
Figure 2.1. Encryption
1435/1436
Computer Security Systems

6. Computer Security Systems
Terminology
using the following formal notation to describe the transformations between plaintext and ciphertext.
For example, we write C = E(P) and P = D(C), where:
C represents the ciphertext,
E is the encryption rule,
P is the plaintext,
D is the decryption rule.
What we seek is a cryptosystem for which P = D(E(P)).
In other words, we want to be able to convert the message to protect it from an intruder, but we also want to be able to get the original message
1435/1436
Computer Security Systems

7. Computer Security Systems
Encryption Algorithms
The cryptosystem involves a set of rules for how to encrypt the plaintext and how to decrypt the ciphertext
Algorithms: The encryption and decryption rules
K (key) is a device used by the algorithm
The resulting ciphertext depends on the original plaintext message, the algorithm, and the key value.
dependence : C = E(K, P).
E is a set of encryption algorithms
key K selects one specific algorithm from the set
1435/1436
Computer Security Systems

8. Computer Security Systems
Encryption Algorithms
Symmetric encryption
The encryption and decryption keys are the same
P = D(K, E(K,P))
D and E are mirror-image processes
Asymmetric encryption
The encryption and decryption keys come in pairs
A decryption key, KD, inverts the encryption of key KE
P = D(KD, E(KE,P))
An encryption scheme that does not require the use of a key is called a keyless cipher.
1435/1436
Computer Security Systems

9. Computer Security Systems
Encryption with Keys
Fig2.2. Encryption with Keys
1435/1436
Computer Security Systems

10. Computer Security Systems
Cryptology
A key gives us flexibility in using an encryption scheme
We can create different encryptions of one plaintext message just by changing the key
Cryptography: means hidden writing, and it refers to the practice of using encryption to conceal text
Encryption has been used for centuries to protect diplomatic and military communications, sometimes without full success
1435/1436
Computer Security Systems

11. Computer Security Systems
Cryptology
a cryptographer and a cryptanalyst attempt to translate coded material back to its original form.
a cryptographer works on behalf of a legitimate sender or receiver
a cryptanalyst works on behalf of an unauthorized interceptor (A cryptanalyst is an expert in cryptanalysis)
cryptology is the research into and study of encryption and decryption; it includes both cryptography and cryptanalysis.
Cryptology = cryptography+ cryptanalysis
1435/1436
Computer Security Systems

12. Computer Security Systems
Cryptanalysis
break a single message
recognize patterns in encrypted messages, to be able to break subsequent ones by applying a straightforward decryption algorithm
infer some meaning without even breaking the encryption (communication was short or long)
deduce the key, to break subsequent messages easily
find weaknesses in the implementation or environment of use of encryption
find general weaknesses in an encryption algorithm, without necessarily having intercepted any messages
1435/1436
Computer Security Systems

13. Computer Security Systems
Substitution : Shift (Caesar) Cipher
The Caesar Cipher:
Rules => Ci = E(pi)= pi + k mod 26
Pi = D(ci) = ci– k mod 26
Examples:
1) k=3 (Rot 3)
P= TREATY IMPOSSIBLE
C= w u h d w b l p s r v v l e o h
2) ROT13:
Why did the chicken cross the road?
Gb trg gb gur bgure fvqr!
Letter: A B …… Y Z
Code : 0 1 …… 24 25
Can we do arithmetic on
letters?
Example: A+2=C, N+1=O
Y-1=X, etc.
Rot 3: “rotate by 3 places”
1435/1436
Computer Security Systems

14. Outer: plaintext Inner: ciphertext
The Caesar cipher
Outer: plaintext
Inner: ciphertext
1435/1436
Computer Security Systems

15. Computer Security Systems
The Caesar cipher
K=3
1435/1436
Computer Security Systems

16. Computer Security Systems
Substitutions :Keyword Mixed Alphabet
Rule
1) pick a keyword
2) spell it without duplicates
3) then, fill in the rest of the alphabet in order
Example: keyword VACATION
P: 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
C: V A C T I O N B D E F G H J K L M P Q R S U W X Y Z
Q: Encrypt “I should be sailing” as: DQBK SGTA
IQVD GDJN
1435/1436
Computer Security Systems

17. Computer Security Systems
Substitutions : Vernam Cipher
a type of one-time pad devised by Gilbert Vernam
The basic encryption involves an arbitrarily long non repeating sequence of numbers that are combined with the plaintext.
1435/1436
Computer Security Systems

18. Computer Security Systems
Substitutions : Vernam Cipher
The encryption is done by adding the key to the message modulo 2, bit by bit.
This process is often called exclusive or (XOR).
1435/1436
Computer Security Systems

19. Example: Key : XMCKL Message: HELLO
Substitutions : Vernam Cipher
Example:
Key : XMCKL
Message: HELLO H E L O
message (plaintext) +
7(H)
4(E)
11(L)
14(O)
message
23(X)
12(M)
2(C)
10(K)
Key 30 16 13 21 25
Message+key
16(Q)
13(N)
21(V)
25(Z)
Message+key (mod 26) Q N V Z
Ciphertext
1435/1436
Computer Security Systems

20. Computer Security Systems
Substitution : Vigenere Cipher
Vigenere cipher is a method of encrypting alphabetic text by using a series of different Caesar ciphers based on the letters of a keyword.
The Vigenere square or Vigenere table
1435/1436
Computer Security Systems

21. Computer Security Systems
Substitution : Vigenere Cipher
Example:
The person sending the message chooses a keyword and repeats it until it matches the length of the plaintext.
P= ATTACKATDAWN
keyword :LEMON
Method
A:the first letter of the plaintext,
L: the first letter of the key
A is paired with L
use row L and column A of the Vigenere square
X? : the first letter of the Ciphertext
X= row L ∩ column A
Plaintext: ATTACKATDAWN
Key: LEMONLEMONLE
Ciphertext: LXFOPVEFRNHR
1435/1436
Computer Security Systems

22. Computer Security Systems
Transpositions (Permutations)
A transposition is an encryption in which the letters of the message are rearranged
With transposition, the cryptography aims for diffusion, widely spreading the information from the message or the key across the ciphertext
A transposition is also known as a permutation.
1435/1436
Computer Security Systems

23. Computer Security Systems
Columnar Transpositions
The following set of characters is a five-column transposition
The plaintext characters are
written in rows of five and arranged one row after another
c1 c2 c3 c4 c5
c6 c7 c8 c9 c10
c11 c12 etc
Figure 2.4. Columnar Transposition
1435/1436
Computer Security Systems

24. Computer Security Systems
Columnar Transpositions- Example
Plaintext : THIS IS A MESSAGE TO SHOW HOW A COLUMNAR TRANSPOSITION WORKS T H I S A M E G O W C L U N R P K
Ciphertext:
tssoh oaniw haaso lrsto imghw
utpir seeoa mrook istwc nasns
Note : if the message length is not a multiple of the length of a row, the last columns will be one or more letters short. When this happens, we sometimes use an infrequent letter, such as X, to fill in any short
1435/1436
Computer Security Systems

25. Computer Security Systems
Symmetric and Asymmetric Encryption Systems
Two basic kinds of encryptions are:
Symmetric
Secret key
Symmetric algorithms use one key, which works for both
encryption and decryption
Authenticity is ensured
n users who want to communicate in pairs need n * (n - 1)/2 keys.
key distribution
Asymmetric
Two keys: -public key
-private key
1435/1436
Computer Security Systems

26. Computer Security Systems
DES
DES: Data Encryption Standard
a system developed for the U.S. government
DES algorithm: key is 64 bits
Uses basic techniques of encryption
confusion (substitutions)
diffusion (permutations)
Same process 16 times/block
Uses standard arithmetic and logical operators
1435/1436
Computer Security Systems

27. Computer Security Systems
DES algorithm
The DES algorithm
Fractioning of the text into 64-bit (8 octet) blocks
Initial permutation of blocks
Breakdown of the blocks into two parts: left and right, named L and R
Permutation and substitution steps repeated 16 times (called rounds)
Re-joining of the left and right parts then inverse initial permutation.
The function expects a 64-bit key as input. However, only 56 of these bits are ever used; the other 8 bits can be used as parity bits or simply set arbitrarily.
1435/1436
Computer Security Systems

28. Computer Security Systems
Fig 2..General Depiction of DES Encryption Algorithm
1435/1436
Computer Security Systems

29. Computer Security Systems
DES
Left-hand side:
The processing of the plaintext proceeds in three phases
First, the plaintext (64-bit) passes through an initial permutation (IP) that rearranges the bits to produce the permuted input
This is followed by a phase consisting of 16 rounds of the same function (permutation and substitution functions)
The output of the last (sixteenth) round consists of 64 bits that are a function of the input plaintext and the key.
1435/1436
Computer Security Systems

30. Computer Security Systems
DES
The left and right halves of the output are swapped to produce the preoutput
Finally, the preoutput is passed through a permutation (IP-1) that is the inverse of the initial permutation function, to produce the 64-bit ciphertext
The right-hand:
The key is passed through a permutation function for each of the 16 rounds, a subkey (Ki) is produced by the combination of a left circular shift and a permutation
1435/1436
Computer Security Systems

31. Computer Security Systems
DES
The key is ciphered on 64 bits and made of 16 blocks of 4 bits, generally denoted k1 to k16 . Given that "only" 56 bits are actually used for encrypting, there can be 2^56 (or 7.2*10^16 ) different keys
The permutation function is the same for each round, but a different subkey is produced
1435/1436
Computer Security Systems

32. The First phase: Initial Permutation
DES: Initial Permutation
The First phase: Initial Permutation
After round 16: Inverse Initial Permutation (IP-1)
Description :
put bit 58 into the 1st position,
put 50 into the 2nd position,
………….
At the end of the iterations, the two blocks L16 and R16 are re-joined, then subject to inverse initial permutation
1435/1436
Computer Security Systems

33. Computer Security Systems
Figure 2.. Single Round of DES Algorithm
1435/1436
Computer Security Systems

34. Computer Security Systems
DES-Expansion Permutation (E)
1435/1436
Computer Security Systems

35. Computer Security Systems
DES-Calculation of F(R, K)
1435/1436
Computer Security Systems

36. Computer Security Systems
DES: S Boxes
Each box defines a substitution
– 6-bit input
– 4-bit output
1435/1436
Computer Security Systems

37. Computer Security Systems
DES: S Boxes
Example: S box 1
bit 1 and 6 define the row.
bit 2-5 define col.
Example:
bit 1,6 = 01 → row 1
bit 2,3,4,5 = 1001 → col 9
output = 6, i.e. 0110
1435/1436
Computer Security Systems

38. Computer Security Systems
Permutation function (P) 16 7 20 21 29 12 28 17 1 15 23 26 5 18 31 10 2 8 24 14 32 27 3 9 19 13 30 6 22 11 4 25
1435/1436
Computer Security Systems

39. Computer Security Systems
DES: Keys
PC1: just a simple permutation
(output = 56 bit) selected by Pc1
key split in half each half 28 bits
Both halves are shifted lift either 1 or 2 bits (depending on round)
result of shift fed to PC2
bits are permuted and 48 of the 56 bits chosen for Subkey 1 28 28
1435/1436
Computer Security Systems

40. Computer Security Systems
The Triple Data Encryption Standard (Triple DES)
Triple DES Operation
For each block:
encrypt with key 1
decrypt with key 2
i.e. C= E(K3, D(K2, E(K1, P)))
C: ciphertext
P: plaintext
E[K, X] encryption of X using key K
D[K, Y] decryption of Y using key K
1435/1436
Computer Security Systems

41. Computer Security Systems
The Triple Data Encryption Standard (Triple DES)
Key Length (3DES) = 3*56 = 168
1435/1436
Computer Security Systems

42. Computer Security Systems
1435/1436
Computer Security Systems

43. Computer Security Systems
Bibliography
Security in Computing, Fourth Edition By Charles P. Pfleeger - Pfleeger Consulting Group, Shari Law rence Pfleeger
cryptography-and-network-security-principles-and-practices-4th-ed-william-stallings
1435/1436
Computer Security Systems