Network and Computer security

MODULE I MCA-501 Computer Security ADMN 2012-‘15
Dept. of Computer Science And Applications, SJCET, Palai Page 1
INTRODUCTION
Computer security is the effort to create a secure computing platform, designed so that agents (users or
programs) cannot perform actions that they are not allowed to perform, but can perform the actions that
they are allowed to.
Some general Terms
 Plain text : Original message(Message to be send)
 Cipher Text : Message after transformation.
 Encryption/Enciphering : Conversion of plain text to cipher text
 Decryption/Deciphering : Conversion of cipher text to plain text
 Cryptography: Area of Study about encryption and decryption
 Cipher/Cryptographic System: Entire system of encryption/decryption.
 Cryptanalysis : Cryptanalysis is the art of breaking codes and ciphers
 Cryptology : Study of Cryptography and cryptanalysis.
Definitions
 Computer Security - generic name for the collection of tools designed to protect data and to prevent
hackers
 Network Security - measures to protect data during their transmission
 Internet Security - measures to protect data during their transmission over a collection of
interconnected networks
Key Security Concepts
Fig 1.1 Key security concepts

• Confidentiality is roughly equivalent to privacy
• Integrity involves maintaining the consistency, accuracy, and trustworthiness of data over its entire
life cycle.
Computer Security Challenges
1. not simple
2. must consider potential attacks
3. involve algorithms and secret info
4. must decide where to deploy mechanisms
5. battle of wits between attacker / admin
6. not perceived on benefit until fails
7. requires regular monitoring
8. regarded as impediment to using system
Computer security is not as simple as it might first appear to the novice. The requirements
seem to be straightforward, but the mechanisms used to meet those requirements can be quite
complex and subtle. In developing a particular security mechanism or algorithm, one must always
consider potential attacks (often unexpected) on those security features. Having designed various
security mechanisms, it is necessary to decide where to use them. Security mechanisms typically
involve more than a particular algorithm or protocol, but also require participants to have secret
information, leading to issues of creation, distribution, and protection of that secret information.
Computer security is essentially a battle of wits between a perpetrator who tries to find holes and
the designer or administrator who tries to close them. There is a natural tendency on the part of
users and system managers to perceive little benefit from security investment until a security failure
occurs. Security requires regular monitoring, difficult in today's short-term environment. Security is
still too often an afterthought - incorporated after the design is complete. Many users / security
administrators view strong security as an impediment to efficient and user-friendly operation of an
information system or use of information.
OSI SECURITY ARCHITECTURE
 ITU-T X.800 “Security Architecture for OSI”
 Defines a systematic way of defining and providing security requirements.
Aspects of Security
Consider 3 aspects of information security:
i. security attack
ii. security mechanism
iii. security service

Security Attack
 any action that compromises the security of information owned by an organization
 often threat & attack used to mean same thing
 have a wide range of attacks
 can focus of generic types of attacks
 passive
 active
Passive Attacks
 Passive attacks do not affect system resources
 Two types of passive attacks
a. Unauthorized reading of messages
b. Traffic analysis
 Passive attacks are very difficult to detect
 Message transmission apparently normal
 No alteration of the data
Fig 1.2 Passive Attacks

Active Attacks
 Active attacks try to alter system resources or affect their operation
 Modification of data, or creation of false data
 Four categories
a. Masquerade
b. Replay
c. Modification of messages
d. Denial of service: preventing normal use
 Difficult to prevent
 The goal is to detect and recover
Fig 1.3 masquerade
Fig 1.4 Replay

Fig 1.5 modification of message
Security Mechanism
 Are designed to detect, prevent, or recover from a security attack
 no single mechanism that will support all services required
 however one particular element underlies many of the security mechanisms in use(cryptographic
techniques)
Example: X.800
• specific security mechanisms: incorporated into appropriate protocol layer
• pervasive security mechanisms: not specific to any protocol layer
Fig 1.6 specific security mechanisms

Fig 1.7 pervasive security mechanisms
Security Service
 enhance security of data processing systems and information transfers of an organization
 using one or more security mechanisms
Example
 X.800: defines a service provided by a protocol layer of communicating open systems, which
ensures adequate security of the systems or of data transfers.
 Authentication - assurance that the communicating entity is the one claimed
 Access Control - prevention of the unauthorized use of a resource
 Data Confidentiality –protection of data from unauthorized disclosure
 Data Integrity - assurance that data received is as sent by an authorized entity
 Non-Repudiation - protection against denial by one of the parties in a communication
 Availability – resource accessible/usable
Model for Network Security
Fig 1.8 model for network security

 using this model requires us to:
1. design a suitable algorithm for the security transformation
2. generate the secret information (keys) used by the algorithm
3. develop methods to distribute and share the secret information
4. specify a protocol enabling the principals to use the transformation and secret information
for a security service
Model for Network Access Security
Fig 1.9 model for network access security
The security mechanisms needed to cope with unwanted access fall into two broad categories. The
first category might be termed a gatekeeper function. It includes password-based login procedures that are
designed to deny access to all but authorized users and screening logic that is designed to detect and reject
worms, viruses, and other similar attacks. Once either an unwanted user or unwanted software gains access,
the second line of defense consists of a variety of internal controls that monitor activity and analyze stored
information in an attempt to detect the presence of unwanted intruders.
FUNDAMENTALS OF ABSTRACT ALGEBRA
Group
 A group G is a set of elements and some generic operation/s, with some certain relations:
 Axioms:
1. A1 (Closure) If {a,b} G, then (a.b)G
2. A2 (Associative) law:(a·b)·c = a·(b·c)
3. A3 (has identity) e: e·a = a·e = a
4. A4 (has inverses) a’: a·a’= e
5. A5 (has commutative) a·b = b·a,
 A G is a finite group if has a finite number of elements

 A G is abelian if it is commutative,
Cyclic Group
 a group G is cyclic if every element of G is a power of some fixed element a  G ie b = ak
for some
a and every b in group (k is an integer).a is said to be a generator of the group
Ring
 a set of “numbers” denoted by {R,+,X} with two operations (addition and multiplication) which
form:
 an abelian group with addition operation (R satisfies axioms A1-A5)
 and multiplication:
1. Closure: If a and b belong to R, then ab is also in R. (M1)
2. Associative: a (bc) = (ab) c for all a, b, c in R. (M2)
3. distributive over addition:(a(b+c) = ab + ac) (M3)
4. Commutative: ab = ba for all a, b in R. (M4)
5. Multiplicative identity: There is an element 1 in R such that a1 = 1a = a for all a in R.
(M5)
6. No zero divisors: If a, b in R and ab = 0, then either a = 0 or b = 0
(M6)
 if multiplication operation is commutative, it forms a commutative ring
 if multiplication operation has an identity and no zero divisors, it forms an integral domain
Field
 a set of numbers denoted by
{F,+,X}
 with two operations which form:
 abelian group for addition(F satisfies axioms A1-A5)
 abelian group for multiplication (F satisfies axioms A1-M6 ignoring 0)
Fig 1.10 heirachy of field

Modular Arithmetic
The Modulus
 If ‘a’ is an integer and ‘n’ is a positive integer, we define “a mod n” to be the remainder when ‘a’ is
divided by n. The integer ‘n’ is called the modulus.
 Two integers ‘a’ and ‘b’ are said to be congruent modulo n, if (a mod n) = (b mod n).
 This can be written as a ≡ b (mod n)
i.e. when divided by n, a & b have same remainder
 e.g. 100 ≡ 34 mod 11
Modulo 8 Addition Example
+ 0 1 2 3 4 5 6 7
0 0 1 2 3 4 5 6 7
1 1 2 3 4 5 6 7 0
2 2 3 4 5 6 7 0 1
3 3 4 5 6 7 0 1 2
4 4 5 6 7 0 1 2 3
5 5 6 7 0 1 2 3 4
6 6 7 0 1 2 3 4 5
7 7 0 1 2 3 4 5 6
Fig 1.11 Modulo 8 Addition example
Fig 1.12 properties of modular arithmetic

Fig 1.13 examples for modular arithmetic properties
Euclidean Algorithm
 an efficient way to find the GCD(a,b)
 uses theorem that:
 GCD(a,b) = GCD(b, a mod b)
 The algorithm assumes a > b > 0.
EUCLID (a,b)
1. A = a; B = b
2. If B = 0 return A = gcd (a, b)
3. R = A mod B
4. A = B
5. B = R
6. goto 2
Fig 1.14 Euclidean algorithm progression
FINITE FIELDS OF THE FORM GF(p) Galois Fields
 order of a finite field (number of elements in the field) must be a power of a prime .known as
Galois Fields
 GF(p) is the set of integers {0,1, … , p-1} with arithmetic operations modulo prime p.
 The simplest finite field is GF(2). Its arithmetic operations are easily summarized:

Fig 1.15 GF arithmetic operations addition and multiplication
Finding Multiplicative Inverse in GF(p)
An important problem is to find multiplicative inverses in such finite fields. Extend the Euclidean
algorithm to find them as shown.it uses the following concept.
if GCD(a,b) = 1 = ax + by then x is inverse of a mod b (or mod y)
EXTENDED EUCLID (m, b)
1. (A1, A2, A3) = (1, 0, m);
(B1, B2, B3)= (0, 1, b)
2. If B3 = 0
Return A3 = gcd (m, b); no inverse
3. If B3 = 1
Return B3 = gcd (m, b); B2 = b–1
mod m
4. Q = A3 div B3
5. (T1, T2, T3) = (A1 – Q B1, A2 – Q B2, A3 – Q B3)
6. (A1, A2, A3) = (B1, B2, B3)
7. (B1, B2, B3) = (T1, T2, T3)
8. goto 2
Fig 1.16 extended Euclidean algorithm example
Addition Multiplication

POLYNOMIAL ARITHMETIC
 can compute using polynomials
f(x) = anxn
+ an-1xn-1
+ … + a1x + a0 = ∑ aixi
 several alternatives available
 ordinary polynomial arithmetic using the basic rules of algebra
 poly arithmetic with coefs mod p
 poly arithmetic with coefs mod p and polynomials mod m(x)
Ordinary Polynomial Arithmetic
 add or subtract corresponding coefficients
 multiply all terms by each other
 eg
Let f(x) = x3
+ x2
+ 2 and g(x) = x2
– x + 1
f(x) + g(x) = x3
+ 2x2
– x + 3
f(x) – g(x) = x3
+ x + 1
f(x) x g(x) = x5
+ 3x2
– 2x + 2
Fig 1.17 examples for ordinary polynomial arithmetic

Polynomial Arithmetic with Modulo Coefficients
• • If each distinct polynomial is considered to be an element of the set, then that set is a ring
• When polynomial arithmetic is performed on polynomials over a field, then division is possible
• Note: this does not mean that exact division is possible
• If we attempt to perform polynomial division over a coefficient set that is not a field,
we find that division is not always defined
• Even if the coefficient set is a field, polynomial division is not necessarily exact
• With the understanding that remainders are allowed, we can say that polynomial
division is possible if the coefficient set is a field
Fig 1.18 examples of Polynomial Arithmetic with Modulo Coefficients

Polynomial Division
• We can write any polynomial in the form:
f(x) = q(x) g(x) + r(x)
• r(x) can be interpreted as being a remainder
• So r(x) = f(x) mod g(x)
• If there is no remainder we can say g(x) divides f(x)
• Written as g(x) | f(x)
• We can say that g(x) is a factor of f(x)
• Or g(x) is a divisor of f(x)
• A polynomial f(x) over a field F is called irreducible if and only if f(x) cannot be expressed as a
product of two polynomials, both over F, and both of degree lower than that of f(x)
• An irreducible polynomial is also called a prime polynomial
Polynomial GCD
• The polynomial c(x) is said to be the greatest common divisor of a(x) and b(x) if the following are
true:
• c(x) divides both a(x) and b(x)
• Any divisor of a(x) and b(x) is a divisor of c(x)
• An equivalent definition is:
• gcd[a(x), b(x)] is the polynomial of maximum degree that divides both a(x) and b(x)
• The Euclidean algorithm can be extended to find the greatest common divisor of two polynomials
whose coefficients are elements of a field
Computational Considerations
• Since coefficients are 0 or 1, they can represent any such polynomial as a bit string
• Addition becomes XOR of these bit strings
• Multiplication is shift and XOR
• cf long-hand multiplication
• Modulo reduction is done by repeatedly substituting highest power with remainder of irreducible
polynomial (also shift and XOR)
•
CLASSICAL ENCRYPTION TECHNIQUES
Symmetric Encryption
 or conventional / private-key / single-key
 sender and recipient share a common key

 all classical encryption algorithms are private-key
Requirements
Two requirements for secure use of symmetric encryption:
1. a strong encryption algorithm
2. a secret key known only to sender / receiver
Fig 1.19 symmetric cipher model
Detail the five ingredients of the symmetric cipher model
- plaintext - original message
- encryption algorithm – performs substitutions/transformations on plaintext
- secret key – control exact substitutions/transformations used in encryption algorithm
- ciphertext - scrambled message
- decryption algorithm – inverse of encryption algorithm
 Mathematically:
Y = E(K, X) X = D(K, Y)
X = plaintext
Y = ciphertext
K = secret key
E = encryption algorithm
D = decryption algorithm
Both E and D are known to public

Fig 1.20 conventional crypto system
Cryptography
 characterize cryptographic system by:
i. Type of encryption operations used
ii. Number of keys used
iii. Way in which plaintext is processed
i. Type of encryption operations used
Substitution: each element in the plaintext is mapped into another element,
Transposition: elements in the plaintext are rearranged.
Product: using multiple stages of substitutions and transpositions
ii. Number of keys used
Single-key or private / two-key or public
iii. Way in which plaintext is processed
Block: processes the input one block of elements at a time, producing an o/p block for each i/p block.
Stream: processes the input elements continuously, producing output one element at a time, as it goes
along.
Cryptanalysis
 objective to recover key not just message
 general approaches:
 cryptanalytic attack
 brute-force attack
i. Cryptanalytic Attacks

Classified by how much information needed by the attacker:
a. Ciphertext-only attack- only know algorithm & ciphertext
b. Known-plaintext attack- Know plaintext & ciphertext
c. Chosen-plaintext attack - select plaintext and obtain ciphertext
d. Chosen-ciphertext attack - select ciphertext and obtain plaintext
ii. Brute Force Search
 most basic attack, proportional to key size
 always possible to simply try every key
 An attacker has an encrypted message .They know that this file contains data they want to
see, and they know that there’s an encryption key that unlocks it. To decrypt it, they can
begin to try every single possible password and see if that results in a decrypted file.
Classical Substitution Ciphers
 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
Caesar Cipher
 earliest known substitution cipher by Julius Caesar
 replaces each letter by 3rd letter on
 example:
meet me after the toga party
PHHW PH DIWHU WKH WRJD SDUWB
 Mathematically, map letters to numbers:
a, b, c, ..., x, y, z
0, 1, 2, ..., 23, 24, 25
 Then the general Caesar cipher is:
c = EK(p) = (p + k) mod 26
p = DK(c) = (c – k) mod 26
Cryptanalysis of Caesar Cipher
 only have 26 possible ciphers
 could simply try each in turn
 a brute force search
 given ciphertext, just try all shifts of letters

Monoalphabetic Cipher
 rather than just shifting the alphabet could shuffle 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
Cryptanalysis
 Now we have a total of 26! = 4 x 1026
keys.
 With so many keys, it is secure against brute-force attacks.
 But not secure against some cryptanalytic attacks.
 Problem is language characteristics.
Language Statistics and Cryptanalysis
 Human languages are not random.
 Letters are not equally frequently 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.
 There are tables of single, double & triple letter frequencies for various languages
 To attack, we
 calculate letter frequencies for cipher text
 compare this distribution against the known one
Example: Given cipher text:
UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZVUEPHZHMDZSHZOWS
FPAPPDTSVPQUZWYMXUZUHSXEPYEPOPDZSZUFPOMBZWPFUPZHMDJUDTMOHMQ
 Count relative letter frequencies
 Guess {P, Z} = {e, t}
 Of double letters, ZW has highest frequency, so guess ZW = th and hence ZWP = the
 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

Playfair Cipher
 Not even the large number of keys in a monoalphabetic cipher provides security.
 One approach to improving security is to encrypt multiple letters at a time.
 The Playfair Cipher is the best known such cipher.
 Invented by Charles Wheatstone in 1854, but named after his friend Baron Playfair.
Playfair Key Matrix
 Use a 5 x 5 matrix.
 The matrix is constructed by filling in the letters of the keyword without duplicates from left to
right and from top to bottom.
 Fill the rest of matrix with other letters in alphabetic order.
 E.g., key = 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
Fig 1.21 playfair key matrix
Encrypting and Decrypting
 plaintext encrypted two letters at a time:
1. If a pair is a repeated letter, insert a filler like 'X',
eg. "balloon" encrypts as "ba lx lo on"
2. If both letters fall in the same row, replace each with letter to right (wrapping back to start from end),
eg. “ar" encrypts as "RM"
3. If both letters fall in the same column, replace each with the letter below it (again wrapping to top from
bottom),
eg. “mu" encrypts to "CM"
4. Otherwise each letter is replaced by the one in its row in the column of the other letter of the pair,
eg. “hs” encrypts to "BP", and “ea" to "IM" or "JM"

Cryptanalysis
 Equivalent to a monoalphabetic cipher with an alphabet of 26 x 26 = 676 characters or diagrams.
 would need a 676 entry frequency table to analyse
 Was widely used for many decades
 eg. by US & British military in WW1 and early WW2
Polyalphabetic Ciphers
 A sequence of monoalphabetic ciphers (M1, M2, M3... Mk) is used in turn to encrypt letters.
 A key determines which sequence of ciphers to use.
 Each plaintext letter has multiple corresponding ciphertext letters.
 This makes cryptanalysis harder since the letter frequency distribution will be flatter
 repeat from start after end of key is reached
Vigenère Cipher
 Simplest polyalphabetic substitution cipher
 Consider the set of all Caesar ciphers:
{ Ca, Cb, Cc, ..., Cz }
 Key: e.g. security
 Encrypt each letter using Cs, Ce, Cc, Cu, Cr, Ci, Ct, Cy in turn.
 Repeat from start after Cy.
 Decryption simply works in reverse.
Fig 1.22 example of vignere cipher

Crytanalysis
 There are multiple ciphertext letters corresponding to each plaintext letter.
 To break Vigenere cipher:
1. Try to guess the key length.
2. If key length is N, the cipher consists of N Caesar ciphers. Plaintext letters are encoded by
the same cipher.
3. Attack each individual cipher
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 has 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
 problems in generation & safe distribution of key
Transposition Ciphers
 Also called permutation ciphers.
 these hide the message by rearranging the letter order.
 without altering the actual letters used
Rail Fence cipher
 write message letters out diagonally over a number of rows
 Key: the number of Rails
 Ciphertext: read off cipher row by row.
 eg. write message out as:
defend the east wall
Fig 1.23 rail cipher
 Obtained ciphertext
DNETLEEDHESWLXFTAAX

Row Transposition Ciphers
 a more complex transposition
 write letters of message in a rectangle in rows over a specified number of columns (related to the
length of the key) and read out message column by column
 then reorder the columns according to some key before reading off the rows
Key: 3 4 2 1 5 6 7
Plaintext: a t t a c k p
o s t p o n e
d u n t i l t
w o a m x y z
Ciphertext: TTNAAPTMTSUOAODWCOIXKNLYPETZ
Product Ciphers
 Uses a sequence of substitutions and transpositions
 Harder to break than just substitutions or transpositions
 this is bridge from classical to modern ciphers.
Rotor Machines
 before modern ciphers, rotor machines were most common product cipher.
 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
Steganography
 Hide a message in another message.
 E.g., hide your plaintext in a graphic image
 Each pixel has 3 bytes specifying the RGB color
 The least significant bits of pixels can be changed w/o greatly affecting the
image quality
 So can hide messages in these LSBs
 Advantage: hiding existence of messages
 Drawback: high overhead

Hill Cipher
 Multiletter or block cipher developed by Lester Hill in 1929,based on matrix
multiplication
 Key: an invertible m x m matrix (where m is the block length)
 Encryption
• first turn our keyword into a key matrix
• turn the plaintext into a column vector.
• then perform matrix multiplication modulo the length of the alphabet (i.e. 26) on each
vector.
• These vectors are then converted back into letters to produce the ciphertext
Example
• plaintext : “short example”, keyword : hill use 2 x 2 matrix.
• turn the keyword into a matrix.
• With the keyword in a matrix, we need to convert this into a key matrix. We do this
by converting each letter into a number by its position in the alphabet (starting at 0).
So, A = 0, B = 1, C= 2, D = 3, etc.
 Convert plaintext to column vectors.
• Convert the plaintext column vectors to plaintext matrix by replacing each letter by its appropriate
number.
• Multiply the key matrix by each column vector in turn.
The keyword written as a matrix.
The key matrix
The algebraic rules of matrix multiplication.

Example:
Decryption
To decrypt a ciphertext encoded using the Hill Cipher, we first multiply the inverse key matrix (K-1) with
each column vectors that the ciphertext is split into, take the results modulo the length of the alphabet, and
finally convert the numbers back to letters.
General method to calculate the inverse key matrix.
Where K is the key matrix, d is the determinant of the key matrix and adj(K) is the adjugate matrix of K.
Where

 Once we have these values we will need to take each of them modulo 26 (in particular, we need to
add 26 to the negative values to get a number between 0 and 25). For our example we get the matrix
below.
The adjugate matrix of the key matrix.

BLOCK CIPHERS
 In a block cipher:
 Plaintext and ciphertext have fixed length b (e.g., 128 bits)
 A plaintext of length n is partitioned into a sequence of m blocks, P[0], …, P[m1], where n
 bm  n + b
 Each message is divided into a sequence of blocks and encrypted or decrypted in terms of its
blocks.
Fig 1.24 Block ciphering

Claude Shannon and Substitution-Permutation Ciphers
 Claude Shannon introduced idea of (S-P) networks in 1949 .form basis of modern block ciphers
 based on the two primitive cryptographic operations :
Substitution (S-box): Replace n bits by another n bits
Permutation (P-box): Bits are rearranged. No bits are added/removed.
 provide confusion & diffusion of message & key
 diffusion – dissipates statistical structure of plaintext over bulk of ciphertext
 confusion – makes relationship between ciphertext and key as complex as possible
Structure
 Horst Feistel devised the feistel cipher
 based on concept of invertible product cipher
 partitions input block into two halves
 Perform a substitution on left data half based on a function of right half & subkey (Round
Function).
 Then permutation by swapping halves
 Practical implementation of Shannon’s S-P net concept.
 Repeat this round of S-P many times
Design Elements
 Block size: Larger block sizes mean greater security but reduced encryption/decryption speed for a
given algorithm.
Ex: 64,128bits
 Key size: Larger key size means greater security but may decrease encryption/ decryption speed.
 Number of rounds: multiple rounds offer increasing security. A typical size is 16 rounds.
 Sub key generation algorithm: Greater complexity in this algorithm should lead to greater difficulty
of cryptanalysis.
 Round function: greater resistance to cryptanalysis.
 Fast software encryption/decryption: the speed of execution of the algorithm becomes a concern.
 ease of analysis
Encryption:
L1 = R0 R1 = L0⊕f1 (R0, K0)
L2 = R1 R2 = L1⊕f2 (R1, K1)
Ln+1 = Rn Rn+1 = Ln⊕fn (Rn, Kn)

Fig 1.25 Fiestal encryption and decryption
Decryption:
Rn = Ln+1 Ln = Rn+1⊕fn (Ln+1, KN)
R0 = L1; L0 = R1⊕f0(L1 ,K0)
Data Encryption Standard (DES)
 Features:
– Block size = 64 bits
– Key size = 56 bits (in reality, 64 bits, but 8 are used as parity-check bits for error control, see next slide)
– Number of rounds = 16
– 16 intermediary keys, each 48 bits
Fig 1.26 DES
Key length in DES
 In the DES specification, the key length is 64 bit:
 8 bytes; in each byte, the 8th bit is a parity-check bit

Fig 1.27 DES key
DES Encryption
Fig 1.28 DES Encryption
Initial Permutation IP
 first step of the data computation
 reorders the input data bits

Fig 1.29 permutation table for initial permutation
• This table specifies the input permutation on a 64-bit block.
• The meaning is as follows:
 The first bit of the output is taken from the 58th bit of the input;
 The second bit from the 50th bit, and so on, with the last bit of the output taken from the 7th bit of
the input.
Final Permutation (IP-1
)
 The final permutation is the inverse of the initial permutation;
 That is, the output of the Final Permutation has bit 40 as its first bit, bit 8 as its second bit, and so
on, until bit 25 as the last bit of the output.
Fig 1.30 final permutation table
DES Round Structure
 uses two 32-bit L & R halves
Li = Ri–1
Ri = Li–1  F(Ri–1, Ki)
Fig 1.31 DES Single round structure

DES F Function
 F takes 32-bit R half and 48-bit subkey
 E is an expansion function which takes a block of 32 bits as input and produces a block of 48 bits as
output.it uses the expansion table
 16 bits appear twice, in the expansion
 48 bit added to subkey using XOR
 And the result is passes through 8 S-boxes to get 32-bit result
 finally permutes using 32-bit P
Fig 1.32 expansion table
Fig 1.33 DES F Function structure
Substitution Boxes S
 Each of the unique selection functions S1,S2,...,S8, takes a 6-bit block as input and yields a 4-bit
block as output
Fig 1.34 S-Box structure

DES Key Schedule
 forms subkeys used in each round consists of:
• Initial permutation of the key (PC1) which selects 56-bits in two 28-bit halves
• 16 stages consisting of:
 rotating each half separately
 Give the shifted output to next round and permuting them by PC2 for use in function f, selecting
24-bits from each half
Fig 1.35 DES key generation

DES Decryption
 Decryption uses the same algorithm as encryption, except that the subkeys K1, K2…K16 are
applied in reversed order.
Avalanche effect
 A desirable property of any encryption algorithm is that a small change in either plaintext or key
should produce significant changes in the ciphertext. DES exhibits a strong avalanche effect
Strength of DES
 Key Size: 56-bit keys have 256
values, brute force search looked hard.
 Timing Attacks: is one in which information about the key or the plaintext is obtained by observing
how long it takes a given implementation to perform decryptions on various ciphertexts. DES
appears to be fairly resistant to a successful timing attack.
 Nature of the DES Algorithm
Cryptanalysis of DES
 Weak Keys: encrypting twice with a weak key K produces the original plaintext.
EK (EK(x))=x
for all weak keys should be avoided at key generation. Four weak keys in DES
 Semi-weak keys: which only produce two different subkeys, each used eight times in the algorithm.
We can refer to them as K1 and K2.They have the property that
EK1(EK2(x))=x
Differential Cryptanalysis (Biham-Shamir)
• This is a chosen plaintext attack, assumes than an attacker knows (Plaintext, Ciphertext) pairs
• involves comparing the XOR of 2 plaintexts to the XOR of the 2 corresponding ciphertexts
• Difference ΔP = P1⊕P2, ΔC = C1⊕C2
• Distribution of ΔC’s given ΔP may reveal information about the key (certain key bits)
• After finding several bits, use brute-force for the rest of the bits to find the key.
• DES was resistant to differential cryptanalysis. S-boxes were designed to resist differential cryptanalysis.
 K=64 bit
 K1….K16=48 bits
 C,D=28 bits
 Ci=LSi(Ci-1)
Di=LSi(Di-1)
Ki=PC-2(CiDi)

• Against 16-round DES, attack requires 247 chosen plaintexts.Differential cryptanalys is not effective
against DES in practice
Linear Cryptanalysis of DES
 another recent development
 also a statistical method
 must be iterated over rounds, with decreasing probabilities
 developed by Matsui et al in early 90's
 based on finding linear approximations
 can attack DES with 243
known plaintexts, easier but still in practise infeasible

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