RC CNS unit 2.pptx types of algorithms in cns

UNIT -II
Symmetric Encryption
Mathematics of Symmetric Key Cryptography,
Introduction to Modern Symmetric Key Ciphers,
Data Encryption Standard,
Advanced Encryption Standard.

Unit -2
Cryptography : Cryptography is a technique of securing information and
communications through use of codes. Thus preventing unauthorized access to
information. The prefix “crypt” means “hidden” and suffix graph means “writing”.
Cryptography Types
Symmetric Key Cryptography:
The sender and receiver of message use a single common key to encrypt and
decrypt messages.
Asymmetric Key Cryptography:
A pair of keys is used to encrypt and decrypt information. A public key is used for
encryption and a private key is used for decryption. Even if the public key
y is known by everyone the intended receiver can only decode it because he alone
knows the private key.
Hash Functions:
There is no usage of any key in this algorithm. A hash value with fixed length is
calculated as per the plain text which makes it impossible for contents of plain text to be
recovered..

Mathematics of Symmetric Key Cryptography
Algebraic Structures:
• Cryptography requires set of integers and specific
operations that are defined for those sets. The combination
of the set and the operations that are applied to the
elements of the set is called an algebraic structure.

Group
• A group (G) is indicated by {G, }. It is a group of elements with a binary
∙
operation that satisfies four properties. The properties of Group are
′ ∙ ′
as follows −
• Closure − If a and b are elements of G, therefore c = a b is also an
∙
element of set G. This can define that the result of using the operations
on any two elements in the set is another element in the set.
• Associativity − If a, b, and c are element of G, therefore (a b) c = a (b
∙ ∙ ∙
c), means it does not substance in which order it can use the
∙
operations on higher than two elements.
• Identity − For all a in G, there occur an element e in G including e a = a
∙
e = a.
∙
• Inverse − For each a in G, there occur an element a’ known as the
inverse of a such that a a = a a = e.
∙ ′ ′ ∙
• A group is an abelian group if it satisfies the following four properties
more one additional property of commutativity.
• Commutativity − For all a and b in G, we have a b = b a.
∙ ∙

Ring
• A ring R is indicated by {R, +, x}. It is a set of elements with two binary
operations, known as addition and multiplication including for all a, b,
c in R the following axioms are kept −
• R is an abelian group regarding addition that is R satisfies properties
A1 through A5. In the method of additive group, it indicates the
identity element as 0 and the inverse of a as − a.
• (M1): Closure under multiplication − If and b belong to R, then ab is
also in R.
• (M2): Associativity of Multiplication − a(bc)=(ab)c for all a, b, c in R.
• (M3): Distributive Laws −
• a(b+c)=ab + ac for all a, b, c in R
• (a+b)c=ac+bc for all a, b, c in R
• (M4): Commutative of Multiplication − ab=ba for all a, b in R.
• (M5): Multiplicative identity − There is an element 1 in R including
a1=1a for all a in R.
• (M6): No zero divisors − If a, b in R and ab = 0, therefore a = 0 or b =
0.

Field
• A field F is indicated by {F, +, x}. It is a set of
elements with two binary operations known
as addition and multiplication, including for all
a, b, c in F the following axioms are kept −
• F1 is an integer domain that is F satisfies
axioms A1 through A5 and M1 through M6.
• (M7): Multiplication inverse − For each a in F,
except 0, there is an element a−1
in F such that
aa−1
= (a−1
)a=1.

Informal Definitions
• A GROUP is a set in which you can perform one operation
(usually addition or multiplication mod n for us) with some
nice properties.
• Groups have properties which are useful for many
cryptographic operations
• A RING is a set equipped with two operations, called
addition and multiplication. A RING is a GROUP under
addition and satisfies some of the properties of a group for
multiplication.
• A FIELD is a GROUP under both addition and multiplication.

Comparison of Group, Ring and Field:

Symmetric Key Cipher
• The sender and receiver of message use a single
common key to encrypt and decrypt messages.

If P is the plaintext, C is the ciphertext, and K is the key,
• We assume that Bob creates P1; we prove that P1 =
P:
• Figure Locking and unlocking with the same key

• Kerckhoff’s Principle
Based on Kerckhoff’s principle, one should always
assume that the adversary, Eve, knows the
encryption/decryption algorithm. The resistance of
the cipher to attack must be based only on the
secrecy of the key
• Cryptanalysis
As cryptography is the science and art of creating
secret codes, cryptanalysis is the science and art of
breaking those codes

RC CNS unit 2.pptx types of algorithms in cns

• Cipher text-Only Attack
Figure Ciphertext-only attack
In Ciphertext-Only Attack , the attacker knows only some cipher text. He try to
find corresponding key and plain text using various methods.
Brute-Force attack: Attacker tries all possible keys. We assume that he knows key
domain
Statistical attack: The cryptanalyst can benefit from some inherent charactersistics
of the plain text language to perform statistical attack. Example: Letter E is most
frequently used character in English.

• Chosen-Plaintext Attack
Figure Chosen-plaintext attack
This is similar to known-plaintext attack, but plaintext/cipher text
pairs have been choosen by the attacker . This can happen when
attacker has access to Alice computer. She can choose some
plaintext and interpret ciphertext.

• Known-Plaintext Attack
• Figure Known-plaintext attack
In this attack, he know some cipher text and plain text pairs
that were sent previously by Alice to Bob. Attacker has kept
both cipher text and plain text to use them to break the next
secrete message.

• Chosen-Ciphertext Attack
Figure Chosen-Ciphertext attack
This is similar to Chosen Plaintext attack except eve
chooses some ciphertext and decrypt it to from a
cipher/plain text pairs.
This can happen when Eve has access to Bob computer.

Categories of Traditional Ciphers
– SUBSTITUTION CIPHERS
• A substitution cipher replaces one character with
another
– TRANSPOSITION CIPHERS
• A Transposition cipher reorders symbols

SUBSTITUTION CIPHERS
• A substitution cipher replaces one symbol with
another. Substitution ciphers can be categorized as
either monoalphabetic ciphers or polyalphabetic
ciphers.
• A substitution cipher replaces one symbol with
another.
Note:
A substitution cipher replaces one symbol with another.
Monoalphabetic Ciphers:
In monoalphabetic substitution, the relationship
between a symbol in the plaintext to a symbol in the
ciphertext is always one-to-one.

Example 1
• The following shows a plaintext and its corresponding
ciphertext. The cipher is probably
• monoalphabetic because both l’s (els) are encrypted as
O’s.
Example 2
• The following shows a plaintext and its corresponding
ciphertext. The cipher is not monoalphabetic because each
l (el) is encrypted by a different character. The first l (el) is
encrypted with N;the second as Z

Additive Cipher
The simplest monoalphabetic cipher is the additive
cipher. This cipher is sometimes called a shift cipher
and sometimes a Caesar cipher, but the term
additive cipher better reveals its mathematical
nature.
Figure Plaintext and ciphertext in Z26

When the cipher is additive, the plaintext, ciphertext, and key are integers in Z 26.
Example:
Use the additive cipher with key = 15 to encrypt the message “hello”.
Solution
We apply the encryption algorithm to the plaintext, character by character:

Example:
Use the additive cipher with key = 15 to decrypt the
message “WTAAD”.
Solution
We apply the decryption algorithm to the plaintext character by character:

Caesar cipher
• Here is an example of how to use the Caesar cipher to
encrypt the message “HELLO” with a shift of 3:
• Write down the plaintext message: HELLO
• Choose a shift value. In this case, we will use a shift of 3.
• Replace each letter in the plaintext message with the letter
that is three positions to the right in the alphabet.
• H becomes K (shift 3 from H)
• E becomes H (shift 3 from E)
• L becomes O (shift 3 from L)
• L becomes O (shift 3 from L)
• O becomes R (shift 3 from O)

• Hiding some data is known as encryption.
When plain text is encrypted it becomes
unreadable and is known as ciphertext. In a
Substitution cipher, any character of plain text
from the given fixed set of characters is
substituted by some other character from the
same set depending on a key. For example
with a shift of 1, A would be replaced by B, B
would become C, and so on.

• Finite Fields:
• A finite field, a field with a finite number of elements.
The finite fields are usually called Galois fields and
denoted as GF(pn
).
• Note: A Galois field, GF(pn
), is a finite field with pn
elements where p is prime.
• GF(p) Fields: When n=1, we have GF(p) field. T is field
can be the set Z, (0,1,2,p-1), with two operations
addition and multiplication. Each element has an
additive inverse and that nonzero elements have a
multiplicative inverse for prime p.
• Example for GF(p) Field: A very common field in this
category is GF(2) with the set {0,1} and two operations
addition and multiplication a shown below:

NOTE: Addition is same as to XOR and multiplication is AND operation

• GF(2n
) Fields:-
• GF(2n
) is a Finite Field with 2n
elements. The
elements in this set are n-bit words. For
example, if n = 3, the set is: { 000, 001, 010,
011, 100, 101, 110, 111 }
• Example: if n = 2, then GF(22
) field in which
the set has four 2-bit words:
• { 00, 01, 10, 11 }.

Why GF(2n
)?
• Generally computer stores positive integers as n-bit words, can
be 8-bit, 16-bit, 32-bit, 64-bit. This means that range of
words(integers) is 0 to 2n
-1. So, the modulus is 2n
• We have two choices if we use a field structure 1) using GF(p) or
GF(2 n
)
• If we use GF(p) with the set Zp, where p is the largest prime
number less than 2n
. This is ineffiecient, if we use integers from
p to2n
-1.
• If n=3, the largest prime less than 23
is 7. This means that we can
not use integer 7,8.
•
If we GF(2n
) with the set 2n
elements. The elements in this set
are n-bit words. Example: If n=3, , the set is
{000,001,010,011,100,101,110,111}

Polynomials
• The data is shown as n-bit words in the computers
that satisfy the properties in GF(2n
) . These n-bit
words are easily represented by Polynomial of
degree n-1.
• A polynomial of degree n-1 is an expression of the
form: Where xi
is called the ith term and ai is
called coefficient of the ith term.

Note: Polynomials representing n-bit words use two fields: GF(2)
for Coefficients and GF(2n
) for terms.

Modulus:
• Addition of two polynomials never creates a
polynomial out of the set. Multiplication of two
polynomials may create a polynomial with
degrees more than n-1. This means that we need
to divide the result by a modulus and keep only
the remainder.
• A Prime Polynomial cannot be factored into a
polynomial with degree of less than n. Such
polynomials are referred to as Irreducible
polynomials.

Operations on Polynomials: Addition:
• Addition and Subtraction operations on polynomials are the
same operation.
• The addition operation for polynomials with coefficient in GF(2)
is add the coefficients of the corresponding term in GF(2).
• Adding two polynomials of degree n-1 always create a
polynomial with degree n-1, which means that we do not need
to reduce the result using the modulus.
• Additive Identity: The additive identity in a polynomial is a zero
polynomial ( a polynomial with all coefficients set to zero).
• Additive inverse: The additive inverse of a polynomial with
coefficients in GF(2) is the polynomial itself. This means that the
subtraction operation is the same as the addition operation.

• Shift Cipher and Caesar Cipher
Historically, additive ciphers are called shift ciphers. Julius
Caesar used an additive cipher to communicate with his
officers. For this reason, additive ciphers are sometimes
referred to as the Caesar cipher. Caesar used a key of 3 for
his communications.
• Additive ciphers are sometimes referred to as shift ciphers
or Caesar cipher

• Example1: What is the key domain for any multiplicative
cipher?
• Solution: The key needs to be in Z26*. This set has only 12
members: 1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23, 25.
• Example2 : We use a multiplicative cipher to encrypt the
message “hello” with a key of 7. The ciphertext is “XCZZU”.

• Affine Ciphers:
Combine additve and multiplicative Ciphers
• Example1: The affine cipher uses a pair of keys in
which the first key is from Z26* and the second is
from Z26.
• The size of the key domain is 26 × 12 = 312.
• Example2:
Use an affine cipher to encrypt the message “hello”
with the key pair (7, 2).

• Monoalphabetic Substitution Cipher
• Because additive, multiplicative, and affine ciphers have
small key domains, they are very vulnerable to brute-force
attack.
• A better solution is to create a mapping between each
plaintext character and the corresponding ciphertext
character. Alice and Bob can agree on a table showing the
mapping for each character.
• Figure An example key for monoalphabetic substitution
cipher

• We can use the key in Figure to encrypt the
message
The cipher text is

• Polyalphabetic Ciphers
• In polyalphabetic substitution, each occurrence of a
character may have a different substitute. The
relationship between a character in the plaintext to
a character in the ciphertext is one-to-many.
• Example ‘a’ can be enciphered as ‘D’ in the
beginning of the text, but as ‘N’ at the middle.
• Polyalphabetic has advantage of hiding the letter
frequency

• Example: Autokey Cipher
Example: Assume that Alice and Bob agreed to use
an autokey cipher with initial key value k1 = 12.
Now Alice wants to send Bob the message “Attack
is today”. Enciphering is done character

• TRANSPOSITION CIPHERS
• A transposition cipher does not substitute one symbol for
another, instead it changes the location of the symbols. A
symbol in the first position may appaer in the tenth position
of the cipher. A symbol in the eighth position may appear in
the first osition of the cipher.
• Note: A transposition cipher reorders symbols
• Keyless Transposition Ciphers
• Simple transposition ciphers, which were used in the past,
are keyless.
• Example 1:
• A good example of a keyless cipher using the first method is
the rail fence cipher. The ciphertext is created reading the
pattern row by row. For example, to send the message “
Meet me at the park” to Bob, Alice writes

She then creates the ciphertext “MEMATEAKETETHPR”.

Example 2:
• Alice and Bob can agree on the number of
columns and use the second method. Alice
writes the same plaintext, row by row, in a table
of four columns
She then creates the ciphertext “MMTAEEHREAEKTTP” by
transmitting the characters column by column. Bob receives
the cipher text and follows the reverse process to get plain
text

• The cipher in previous example is actually a
transposition cipher. The following shows the
permutation of each character in the plaintext
into the ciphertext based on the positions.
The second character in the plaintext has moved to the
fifth position in the ciphertext; the third character has
moved to the ninth position; and so on.Although the
characters are permuted, there is a pattern in the
permutation: (01, 05, 09, 13), (02, 06, 10, 13), (03, 07, 11,
15), and (4, 8, 12). In each section, the difference
between the two adjacent numbers is 4.

• Keyed Transposition Ciphers
• The keyless ciphers permute the characters by using
writing plaintext in one way and reading it in another way
The permutation is done on the whole plaintext to create
the whole ciphertext.
• Another method is to divide the plaintext into groups of
predetermined size, called blocks, and then use a key to
permute the characters in each block separately.
• Example
Alice needs to send the message “Enemy attacks
tonight” to Bob..

• The key used for encryption and decryption is a
permutation key, which shows how the character
are permuted
The permutation yields

• Combining Two Approaches for better result
• Encryption or decryption is done in 3 steps:
• Text is written into row by row
• Permutation is done by reordering columns
• New table is read column by column

Stream Ciphers and Block Ciphers
Stream Ciphers : A stream cipher is one that
encrypts a digital data stream one bit or one byte at
a time. Examples of classical stream ciphers are the
auto keyed Vigenère cipher and the Vernam cipher.

Block Ciphers
• A block cipher is one in which a block of plaintext is
treated as a whole and used to produce a cipher
text block of equal length.
• A block size of 64 or 128 bits is used.

Modern Block Ciphers
A symmetric-key modern block cipher encrypts an n-bit
block of plaintext or decrypts an n-bit block of cipher text.
The encryption or decryption algorithm uses a k-bit key. The
Decryption algorithm must be the inverse of the encryption
algorithm and must use the same secrete key.

• Components of a Modern Block Cipher
Modern block ciphers normally are keyed substitution
ciphers in which the key allows only partial mappings
from the possible inputs to the possible outputs. It
uses P-Boxes,S-Boxes.

P-Boxes
• P-Boxes(also called as D-Box means Diffusion box)
• A P-box (permutation box) parallels the traditional
transposition cipher for characters. It transposes
bits.
Three types of P boxes

Example
• Figure shows all 6 possible mappings of a 3 × 3
P-box.

• Straight P-Boxes
• TableExample of a permutation table for a straight
P-box(64x64) At output of P-Box:
• Input 58 goes to 1st
position, input 50 goes to 2nd
position, input 42 to 3rd
position,….

Product Ciphers
• Shannon introduced the concept of a product
cipher. A product cipher is a complex cipher
combining substitution, permutation, and other
components .
• Combination of S-box and P-box transformation—a
product cipher. Two classes of product ciphers:
• Feistel ciphers, Example DES(data encryption
standard)
• Non-feistel Ciphers, Example AES(Advanced
Encryption system)

Diffusion
• The idea of diffusion is to hide the relationship
between the cipher text and the plain text.
Confusion
• The idea of confusion is to hide the relationship
between the cipher text and the key.
Rounds
• Diffusion and confusion can be achieved using
iterated product ciphers where each iteration is a
combination of S-boxes, P-boxes, and other
components.

Feistel Cipher Structure:
• Feistel Cipher is not a specific scheme of block cipher. It is a
design model from which many different block ciphers are
derived.
• DES is just one example of a Feistel Cipher.
• A cryptographic system based on Feistel cipher structure uses
the same algorithm for both encryption and decryption.
• The input block to each round is divided into two halves that
can be denoted as L and R for the left half and the right half.
• In each round, the right half of the block, R, goes through
unchanged. But the left half, L, goes through an operation
that depends on R and the encryption key. First, we apply an
encrypting function ‘f’ that takes two input − the key K and R.
The function produces the output f(R,K). Then, we XOR the
output of the mathematical function with L

Block Cipher Design Principles
• Block size: Larger block sizes mean greater security (all other things
being equal) but reduced encryption/decryption speed for a given
algorithm. The greater security is achieved by greater diffusion. Key
size: Larger key size means greater security but may decrease
encryption/ decryption speed. The greater security is achieved by
greater resistance to brute-force attacks and greater confusion
• Number of rounds: The essence of the Feistel cipher is that a single
round offers inadequate security but that 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 F: Again, greater complexity generally means
greater resistance to cryptanalysis. Diffusion And Confusion:- The
terms diffusion and confusion were introduced by Claude Shannon
to capture the two basic building blocks (Plain Text & Cipher Text)
for any cryptographic system.

Data Encryption Standard (DES)
• The Data Encryption Standard (DES) is a symmetric-key block cipher
published by the National Institute of Standards and Technology
(NIST) in 1997.
• DES is an implementation of a Feistel Cipher. It uses 16 round Feistel
structure. The block size is 64 -bit. key length is 64-bit, DES has an
effective key length of 56 bits, since 8 of the 64 bits of the key are not
used by the encryption algorithm (function as check bits only).

• DES Symmetric key Block Cipher algorithm.
DES follows Feistel cipher structure.
• Plain Text Block Size : 64
• Bits Cipher Text Size :64 Bits
• Master Key Size : 64 / 56
• Bits No. Of Rounds 16
• Round Key / Subkey Size: 48 Bits.

Initial Permutation & Inverse Initial Permutation
The initial permutation and its inverse are defined by tables,
as shown in Tables. The tables are to be interpreted as follows.
• The input to a table consists of 64 bits numbered from 1 to
64.
• The 64 entries in the permutation table contain a
permutation of the numbers from 1 to 64.
• Each entry in the permutation table indicates the position of
a numbered input bit in the output, which also consists of
64 bits.
• The initial and final permutations are straight Permutation
boxes (P-boxes) that are inverses of each other.
Note: Initial Permutation & Inverse Initial Permutations have
no cryptography significance in DES.

In output
At 1st
place 58
At 2nd
place 50
At 3rd
place 42 .

• In output
• At 1st
place 40
• At 2nd
place 8
• At 3rd
place 48 ..

Rounds
• The left and right halves of each 64- bit intermediate value are treated as separate
32-bit quantities, labeled L (left) and R (right).
• As in any classic Feistel cipher, the overall processing at each round can be
summarized in the following formulas:
• The round key Ki is 48 bits. The R input is 32 bits. This R input is first expanded to
48 bits by using a table that defines a permutation plus an expansion that involves
duplication of 16 of the R bits.
• The resulting 48 bits are XORed with Ki. This 48-bit result passes through a
substitution function that produces a 32-bit output, which is permuted as defined
by Table.
• The role of the S-boxes in the function F is illustrated in Figure 3.7.The substitution
consists of a set of eight S-boxes, each of which accepts 6 bits as input and
produces 4 bits as output. These transformations are defined in Table 3.3, which is
interpreted as follows: The first and last bits of the input to box Si form a 2-bit
binary number to select one of four substitutions defined by the four rows in the
table for Si. The middle four bits select one of the sixteen columns. The decimal
value in the cell selected by the row and column is then converted to its 4-bit
representation to produce the output. For example, in S1, for input 011001, the
row is 01 (row 1) and the column is 1100 (column 12). The value in row 1, column
12 is 9, so the output is 1001.

• P-Boxes
• P-Boxes(also called ad D-Box means Diffusion
box)
• A P-box (permutation box) parallels the
traditional transposition cipher for characters.
It transposes bits.
Three types of P-boxes

DES Weaknesses Analysis
• Weakness in Cipher Design:
• It is not clear why the designers of DES used the initial
and final permutations; these have no security benefits.
• In the expansion permutation, the first and fourth bits
of every 4-bit series are repeated.
• Weakness in Cipher Key:
• o DES Key size is 56 bits. To do Brute force attack on
a given ciphertext block, the adversary needs to check
256
keys.
• With available technology it is possible to check 1
million keys per second
•

• The Data Encryption Standard (DES) is an older encryption algorithm that was widely used in the past but
has since been replaced by more secure algorithms like AES. Here's a simple explanation of how DES
works:
• Basic Idea: DES takes a block of plaintext (unencrypted text) and transforms it into ciphertext (encrypted
text) using a secret key. This process makes it difficult for unauthorized users to understand the original
message.
• Block Cipher: DES operates on blocks of data, typically 64 bits in size. If the input message is not a multiple
of 64 bits, padding is used to make it fit.
• Key Size: DES uses a 56-bit key. This key is used both for encryption and decryption. However, due to
advances in computing power, a 56-bit key is now considered relatively insecure.
• Substitution-Permutation Network (SPN): Similar to AES, DES uses a series of rounds called a
Substitution-Permutation Network. Each round involves substituting and permuting bits of the data
according to the key.
• Rounds: DES performs 16 rounds of encryption, with each round using a different subkey derived from the
main encryption key.
• Confusion and Diffusion: Like AES, DES relies on confusion (making the relationship between the plaintext
and ciphertext complex) and diffusion (spreading the influence of each plaintext bit across many
ciphertext bits) to enhance security.
• Security: While DES was once considered secure, advances in computing power have made it vulnerable
to brute-force attacks. Today, it's generally recommended to use stronger encryption algorithms like AES
with longer key lengths.
• In summary, DES is an older encryption standard that transforms plaintext into ciphertext using a 56-bit
key and a series of rounds. While it was widely used in the past, it's now considered relatively insecure
compared to modern encryption standards.

• Triple – DES
• Triple DES was developed in 1999 by IBM – by a
team led by Walter Tuchman. DES prevents a
meet-in- the-middle attack. 3- DES has a 168-bit
key and enciphers blocks of 64 bits.
• 3-DES with 2 Keys:

• The encryption-decryption process is as
follows −
• Encrypt the plaintext blocks using single DES
with key K1. Now decrypt the output of step 1
using single DES with key K2.
• Finally, encrypt the output of step 2 using
single DES with key K3. The output of step 3 is
the ciphertext.
• Decryption of a ciphertext is a reverse process.
User first decrypt using K3, then encrypt with
K2, and finally decrypt with K1

• Advanced Encryption Standard (AES) is a widely used encryption algorithm that helps keep
information secure when it's being transmitted or stored. Here's a simple explanation of how it
works:
• Basic Idea: AES takes a block of plaintext (unencrypted text) and transforms it into ciphertext
(encrypted text) using a secret key. This makes it unreadable to anyone who doesn't have the
key.
• Key Size: AES supports three different key sizes: 128-bit, 192-bit, and 256-bit. The larger the
key size, the more secure the encryption, because it makes it harder for attackers to guess the
key.
• Substitution-Permutation Network: AES operates through a series of steps called a
Substitution-Permutation Network (SPN). In simple terms, it shuffles and substitutes bits of
data in a precise way, making it very difficult to reverse-engineer without the key.
• Rounds: AES processes data in multiple rounds, with each round consisting of several steps,
including substitution, permutation, and mixing of data. The number of rounds depends on the
key size: 10 rounds for 128-bit keys, 12 rounds for 192-bit keys, and 14 rounds for 256-bit keys.
• Confusion and Diffusion: AES achieves security through two main principles: confusion and
diffusion. Confusion means that even a small change in the key should produce a significantly
different ciphertext. Diffusion means that each bit of the plaintext affects many bits of the
ciphertext, spreading out the influence of each bit.
• Security: AES has been extensively studied and tested by cryptographers, and it's considered
highly secure when used with a strong key. However, like any encryption algorithm, its security
ultimately depends on the strength of the key and how well it's implemented.
AES is a powerful and widely trusted encryption standard that helps keep sensitive information
safe from unauthorized access.

Advanced Encryption Standard (AES Algorithm)
• The Advanced Encryption Standard (AES) was published by the National Institute of Standards
and Technology (NIST) in 2001.
• AES is a symmetric block cipher that is intended to replace DES.
The features of AES are as follows −
• Symmetric key symmetric block cipher
• 128-bit data, 128/192/256-bit keys
• Stronger and faster than Triple-DES
• Provide full specification and design details
• Software implementable in C and Java
• AES is an iterative rather than Feistel cipher. It is based on ‘substitution–permutation
network’. It comprises of a series of linked operations, some of which involve replacing inputs
by specific outputs (substitutions) and others involve shuffling bits around (permutations).
• Interestingly, AES performs all its computations on bytes rather than bits. Hence, AES treats
the 128 bits of a plaintext block as 16 bytes. These 16 bytes are arranged in four columns and
four rows for processing as a matrix.
• Unlike DES, the number of rounds in AES is variable and depends on the length of the key.
• AES uses 10 rounds for 128-bit keys, 12 rounds for 192-bit keys and 14 rounds for 256-bit
keys. Each of these rounds uses a different 128-bit round key, which is calculated from the
original AES key.

ROUNDS
• Unlike DES, the number of rounds in AES is variable and depends on
the length of the keyAES uses
• 10 rounds for 128-bit keys,
• 12 rounds for 192-bit keys and
• 14 rounds for 256-bit keys.
• Each of these rounds uses a different 128-bit round key, which is
calculated from the original AES key.

AES Transformations:
There are four transformation functions used in AES
Cipher at each round.
• Substitute Bytes Transformation
• ShiftRows Transformation
• MixColumns Transformation
• AddRoundKey Transformation

Byte Substitution (SubBytes)
The 16 input bytes are substituted by values as specified in a table (S-box) given in
design.
Each input byte of State is mapped into a new byte in the following way:The leftmost 4
bits of the byte are used as a row value(in hexadecimal form) and the rightmost 4 bits
are used as a column value(in hexadecimal form) in S-boxtable.
For example, the hexadecimal value {95} references row 9, column 5 of the S-box,
which contains the value {2A}. Accordingly, the value {95} is mapped into the value {2A}.

• ShiftRows Transformation:
In this transformation bytes are permuted(shifted).
– In the Encryption, the tranformation is called Shiftrows
and the shifting is to the left.
– The number of shifts depends on the row
number(0,1,2,or 3) of the state matrix as shown below:

• The following is an example of ShiftRows.
The inverse shift row transformation, called
InvShiftRows, performs the circular shifts in the
opposite direction for each of the last three rows,
with a 1-byte circular right shift for the second row,
and so on.

MixColumns Transformation:
• Mixing is the transformaton that changes bits inside byte.
• This operation takes 4 bytes(a column) and by multiplying it
with a constant matrix then mixes them that produces new
bytes.
• MixColumn: operates on each column individually. Each
byte of a column is mapped into a new value.
• It takes a column from state and multiply it with a constant
square matrix.
• The byte values are represented as polynomials with
coefficients in GF(2) and mulitplications are done in GF(28
)

Constant matrices for multiplications:

AddRoundKey Transformation:
To make the ciphertext more secrete, we add cipher key
to the data in a state. AddRoundKey is same as to
MixColumns but performs addition operation instead of
multiplication.
The following is an example of AddRoundKey:
The first matrix is State, and the second matrix is the round key.

ANALYSIS OF AES
Security
• AES was designed after DES. Most of the known attacks on DES were
already tested on AES.
• Brute-Force Attack
• AES is definitely more secure than DES due to the larger-size key.
• Statistical Attacks
• Numerous tests have failed to do statistical analysis of the ciphertext.
• Differential and Linear Attacks
• There are no differential and linear attacks on AES as yet.
Implementation
• AES can be implemented in software, hardware, and firmware. The
implementation can use table lookup process or routines that use a well-
defined algebraic structure.
Simplicity and Cost
• The algorithms used in AES are so simple that they can be easily
implemented using cheap processors and a minimum amount of memory.

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