Computer security module 1

Cryptography and Network Security
Deepak John
SJCET-Pala

 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
• 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

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:
 security attack
 security mechanism
 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
 Unauthorized reading of messages
 Traffic analysis
 Passive attacks are very difficult to detect
 Message transmission apparently normal
 No alteration of the data

Active Attacks
 Active attacks try to alter system resources or affect their
operation
 Modification of data, or creation of false data
 Four categories
 Masquerade
 Replay
 Modification of messages
 Denial of service: preventing normal use
 A specific target or entire network
 Difficult to prevent
 The goal is to detect and recover

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)
Security Mechanisms (X.800)
• specific security mechanisms: incorporated into appropriate
protocol layer
• pervasive security mechanisms: not specific to any protocol
layer

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.

Security Services (X.800)
 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

 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
 using this model requires us to:
1. select appropriate gatekeeper functions to identify users
2. implement security controls to ensure only authorised
users access designated information or resources

Fundamentals of Abstract Algebra

Group
 A group G is a set of elements and some generic operation/s,
with some certain relations:
 Axioms:
 A1 (Closure) If {a,b} G, then (a.b)G
 A2 (Associative) law:(a·b)·c = a·(b·c)
 A3 (has identity) e: e·a = a·e = a
 A4 (has inverses) a’: a·a’= e
 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:
 closure :If a and b belong to R, then ab is also in R. (M1)
 Associative:a(bc) = (ab)c for all a, b, c in R. (M2)
 distributive over addition:(a(b+c) = ab + ac) (M3)
 Commutative: ab = ba for all a, b in R. (M4)
 Multiplicative identity: There is an element 1 in R such
that a1 = 1a = a for all a in R. (M5)
 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)

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
 eg. 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

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
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:
Addition Multiplication

Finding Multiplicative Inverse in GF(p)
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

 Ex: Inverse of 550 in GF(1759)
Q A1 A2 A3 B1 B2 B3
— 1 0 1759 0 1 550
3 0 1 550 1 –3 109
5 1 –3 109 –5 16 5
21 –5 16 5 106 –339 4
1 106 –339 4 –111 355 1

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:
 a strong encryption algorithm
 a secret key known only to sender / receiver
Classical Encryption Techniques

 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

Model of conventional cryptosystem

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 output block for each input
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:
 Ciphertext-only attack
 Known-plaintext attack
 Chosen-plaintext attack
 Chosen-ciphertext attack

Ciphertext-only attack
 only know algorithm & ciphertext
 An encryption scheme is completely insecure if it cannot
resist ciphertext-only attacks.
known plaintext
 Know plaintext & ciphertext
chosen plaintext
 select plaintext and obtain ciphertext
chosen ciphertext
 select ciphertext and obtain plaintext

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
 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

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

Monoalphabetic Cipher Security
 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 ciphertext
 compare this distribution against the known one

Example Cryptanalysis
 Given ciphertext:
UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZ
VUEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZUHSX
EPYEPOPDZSZUFPOMBZWPFUPZHMDJUDTMOHMQ
 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

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"

Security of Playfair Cipher
 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.
56

Security of Vigenère Ciphers
 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
 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.
The keyword written as a matrix.
The key matrix

• 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 algebraic rules of matrix multiplication.

 So we get
 we have to reduce the resultant column vector modulo 26.
 Repeating this procedure gives us a final ciphertext of
"APADJ TFTWLFJ".

 Message P =“ACTDOG”, use m=3
 Break into two blocks: “ACT”, and “DOG”
 For the first block “ACT” is the vector 'A' is 0, 'C' is 2 and
'T' is 19, the vector: x=
 Encryption key is a 3*3 matrix: K=
 The cipher text of the first block is:
c = K∙x
c =‘POH’

 If the first block plaintext is ‘CAT’
 x =
 c=K ∙ x
 c= ‘FIN’
 Cryptanalysis: - hard with ciphertext-only
- easy with known plaintext:

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.
 where K is the key matrix, d is the determinant of the key
matrix and adj(K) is the adjugate matrix of K.
 Where
General method to calculate the inverse key matrix.

Example:
 keyword :hill , ciphertext :"APADJ TFTWLFJ".
 Multiplicative Inverse of the Determinant
The keyword written as a matrix. The key matrix
Algebraic method to calculate the determinant of a 2 x 2 matrix.
 Once we have found this value, we need to take the number
modulo 26.

Calculating the determinant of our 2 x 2 key matrix.
 now have to find the multiplicative inverse of the
determinant working modulo 26. That is, the number
between 1 and 25 that gives an answer of 1 when we
multiply it by the determinant. So, in this case, we are
looking for the number that we need to multiply 15 by to
get an answer of 1 modulo 26.
 ie

 By trail and error we found that the multiplicative inverse of
the determinant modulo 26 is 7.
 The adjugate matrix is a matrix of the same size as the
original. That is, we swap the top left and bottom right
numbers in the key matrix, and change the sign of the the
top right and bottom left numbers. Algebraically this is
given below.
The adjugate matrix of a 2 x 2 matrix.

 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.

 To get the inverse key matrix, we now multiply the inverse
determinant (that was 7 in our case) by each of the elements
of the adjugate matrix . Then we take each of these answers
modulo 26.
 Ie
Multiplying the multiplicative inverse of the determinant by the adjugate
to get the inverse key matrix.

 convert the ciphertext into column vectors and multiply the
inverse matrix by each column vector in turn, take the
results modulo 26 and convert these back into letters to get
the plaintext.
 After multiplying inverse key matrix with ciphertext
column vector, We get back our plaintext of "short
example".

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.
Plaintext
Blocks of
plaintext
Requires padding
with extra bits.

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

Feistel Cipher 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

Feistel Cipher 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.
 subkey 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
 Input: 2w bits (L0, R0)
 L1 = R0
 R1= L0 xor F(R0, K1) K1 is the first subkey

• Encryption:
L1 = R0 R1 = L0⊕f1(R0,K0)
L2 = R1 R2 = L1⊕f2(R1,K1)
Ln+1 = Rn Rn+1 = Ln⊕fn(Rn, Kn)
R1L1
RnLn

• Decryption:
Rn = Ln+1 Ln = Rn+1⊕fn(Ln+1 ,Kn)
R0 = L1; L0 = R1⊕f0(L1 ,K0)
Rn Ln
R1
L1

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

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

Initial Permutation IP
 first step of the data
computation
 reorders the input data bits
• 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.

DES Round Structure
 uses two 32-bit L & R halves
Li = Ri–1
Ri = Li–1  F(Ri–1, Ki)

 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.
 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
DES F Function
Expansion table

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

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

 K=64 bit
 K1….K16=48 bits
 C,D=28 bits
 Ci=LSi(Ci-1)
Di=LSi(Di-1)
Ki=PC-2(CiDi)

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.
 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

Computer security module 1

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Computer security module 1