Module 2.pptx

CYBER SECURITY AND CRYPTOGRAPHY
S3. MCA
Module 2
Prepared By
SEETHAL PRINCE E
Asst. Professor
CSE

Block Ciphers and Stream Cipher
• Stream Cipher:
• Encrypts Digital Data Stream 1 bit or 1 byte at a time.
• Eg: Vigenere Cipher, Vernam Cipher
• Block Cipher
• A block of plaintext is treated as a whole and used to produce cipher text
block of equal length.
• Typically a block size of 64 or 128 bits is used.

Block Cipher Design Principles - Feistel Structure
• The plaintext is divided into 2 equal halves (Left and Right).
• Right Half is applied to a function(Round Function).
• The output from this function is XORed with Left half.
• Output of this XOR operation and Right half is swapped to make the
new left and right.
• This entire process is called a ROUND.
• This process is repeated to make multi rounds and thus encryption is
made stronger

Fiestel Encryption
• The inputs to the encryption algorithm are a plaintext block of length
2w bits and a key K .
• The plaintext block is divided into two halves L0 and R0
• The two halves of the data pass through n rounds of processing and
then combine to produce the ciphertext block.
• Each round i has Li-1 and Ri-1 derived from the previous round as
inputs, as well as a subkey Ki derived from the overall K.
• In general, the subkeys Ki are different from K and from each other.

Cont..
• All rounds have the same structure. A substitution is performed on
the left half of the data.
• This is done by applying a round function F to the right half of the
data and then taking the exclusive-OR of the output of that function
and the left half of the data.
• The round function has the same general structure for each round but
is parameterized by the round subkey .

Fiestel Decryption
• Use the ciphertext as input to the algorithm, but use the subkeys in
reverse order.
• That is, use Kn in the first round, Kn-1 in the second round, and so on,
until K1 is used in the last round.
• We need not implement two different algorithms; one for encryption
and one for decryption.

Feistel network depends on the choice of the following parameters and
design
• Block size: Larger block sizes mean greater security but, reduced
encryption/decryption speed for a given algorithm. Traditionally, a
block size of 64 bits has been considered.
• 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. Key sizes of 64 bits or less are
now widely considered to be inadequate, and 128 bits has become a
common size.

Cont…
• 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: Greater complexity generally means greater
resistance to cryptanalysis.

Modes Of Operation
To apply a block cipher in a variety of applications, five modes of
operation have been defined:
1. Electronic Code Book Mode
2. Cipher Block Chaining Mode
3. Cipher Feedback Mode
4. Output Feedback Mode
5. Counter Mode

1. Electronic Code Book Mode
• The simplest mode is the electronic codebook (ECB) mode, in which
plaintext is handled one block at a time and each block of plaintext is
encrypted using the same key.

2. Cipher Block Chaining
• In this scheme, the input to the encryption algorithm is the XOR of
the current plaintext block and the preceding ciphertext block
• Same key is used for each block.
• To produce the first block of ciphertext, an initialization vector (IV) is
XORed with the first block of plaintext.
• On decryption, the IV is XORed with the output of the decryption
algorithm to recover the first block of plaintext.
• The IV is a data block that is that same size as the cipher block.

Note: In both Encryption and Decryption Cipher block is chained.

3. Cipher Feedback Mode
• The input to the encryption function is a s-bit shift register that is
initially set to some initialization vector (IV).
• The leftmost (most significant) s bits of the output of the encryption
function are XORed with the first segment of plaintext to produce the
first unit of ciphertext , which is then transmitted.
• The contents of the shift register are shifted left by s bits, and C1 is
placed in the rightmost (least significant) s bits of the shift register.
• This process continues until all plaintext units have been encrypted.

Note:
• Not the plaintext but, output of the shift register is Encrypted using the Key
• Common value of s=8

• For decryption, the same scheme is used, except that the received
ciphertext unit is XORed with the output of the encryption function
to produce the plaintext unit.
• Note that it is the encryption function that is used, not the decryption
function.

4. Output Feedback Mode
• The output feedback (OFB) mode is similar in structure to that of CFB.
• The output of the encryption function is fed back to the shift register
in OFB.
• OFB mode operates on full blocks of plaintext and ciphertext.

Cont..
• OFB mode requires an initialization vector.
• Nonce: unique to each execution of the encryption operation.
• Advanatge: bit errors in transmission do not propagate.
• Disadvantage: more vulnerable to a message stream modification
attack.

5. Counter Mode
• A counter equal to the plaintext block size is used.
• Counter value must be different for each plaintext block.
• It is initialized to some value and then incremented by 1 for each
subsequent block.
• For encryption, the counter is encrypted and then XORed with the
plaintext block to produce the ciphertext block.
• There is no chaining.
• For decryption, the same sequence of counter values is used, with
each encrypted counter XORed with a ciphertext block to recover the
corresponding plaintext block.

DES – Data Encryption Standard
• The most widely used encryption scheme is based on the Data
Encryption Standard (DES) adopted in 1977 by the National Bureau of
Standards.
• Data are encrypted in 64-bit blocks using a 56-bit key.
• The algorithm transforms 64-bit input in a series of steps into a 64-bit
output.
• The same steps, with the same key, are used to reverse the
encryption(ie; decryption)
• Uses Feistel Structure principles.

Cont.
• There are two inputs to the encryption function:
• the plaintext to be encrypted
• the key.
• The plaintext must be 64 bits in length and the key is 56 bits in length.
(Actually, 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.)

Cont.
• At the left-hand side of the figure, we can see that the processing of
the plaintext
• First, the 64-bit plaintext passes through an initial permutation (IP) that
rearranges the bits to produce the permuted input.
• This is followed by a phase consisting of sixteen rounds of the same function,
which involves both 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.
• The left and right halves of the output are swapped to produce the
preoutput.
• Finally, the preoutput is passed through a permutation that is the inverse of
the initial permutation function, to produce the 64-bit ciphertext.

Cont.
• The right-hand portion of Figure shows the way in which the 56-bit
key is used.
• Initially, the key is passed through a permutation function.
• Then, for each of the sixteen rounds, a subkey (Ki) is produced by the
combination of a left circular shift and a permutation.
• The permutation function is the same for each round, but a different subkey
is produced because of the repeated shifts of the key bits.

Cont.
• The left and right halves of each 64-bit input is treated as separate
32-bit quantities, L (left) and R (right).
• The round key is 48 bits.
• The input is 32 bits.
• This input is first expanded to 48 bits.
• This is XORed with Ki.
• This 48-bit result passes through a substitution function that
produces a 32-bit output.
• This is permuted again.

Cont.
• The role of the S-boxes in the function F is illustrated in Figure.
• The substitution consists of a set of eight S-boxes, each of which
accepts 6 bits as input and produces 4 bits as output.

Cont.
• Key Generation
• A 64-bit key is used as input to the algorithm.
• The key is first subjected to a permutation.
• The resulting 56-bit key is then treated as two 28-bit quantities, labeled C0
and D0.
• At each round, Ci-1 and Di-1 are separately subjected to a circular left shift.
• These shifted values serve as input to the next round.
• They also serve as input to the part labeled Permuted Choice Two which
produces a 48-bit output that serves as input to the function F(R,K).
• DES Decryption
• As with any Feistel cipher, decryption uses the same algorithm as encryption,
except that the application of the subkeys is reversed.

AES – Advanced Encryption Standard
• Strongest encryption algorithm.
• Symmetric key block cipher.
• Block size is 128 bits (plaintext and Cipher text)
Rounds No. of bits in key
10 128
12 192
14 256

Cont.
• Input is in the form of 4x4 matrix
• ie; 16 bytes = 128 bits

Cont.
• No. of keys = No. of rounds +1
• States :- 4x4 matrix , stores intermediate results
• Each Round has four different stages
• Substitute bytes: Uses an S-box to perform a
byte-by-byte substitution of the block
• ShiftRows: A simple permutation
• MixColumns: A substitution that makes use of
arithmetic over
• AddRoundKey: A simple bitwise XOR of the
current block with a portion of the expanded key
• Last round has only 3 stages, MixColums is not in
nth round.

Cont.
• Substitution Bytes:
• Also called as SubBytes.
• Is a simple table lookup.
• Each individual byte of State is mapped into a new byte.

Cont.
• Shift Rows Transformation
Row 1 : 0 or no shift
Row 2: 1 byte shift
Row 3: 2 byte shift
Row 4: 3 byte shift

Cont.
• MixColums
• A constant matrix of size 4x4 is used .
• Each word (column) is taken, multiplied with
constant 4x4 matrix.
• Product word is placed in the corresponding
position of output matrix.
• This stage is not performed in the last round.

Cont.
• Add Round Key
• 128 bits of State are bitwise XORed with the 128 bits of the round key.
• AES Decryption : It is the reverse of Encryption process.
• Key is used in reverse order.

MULTIPLE ENCRYPTION AND TRIPLE DES
• Considering the vulnerabilities in DES, there has been considerable
interest in finding an alternative.
• One approach is to design a completely new algorithm, of which AES
is a prime example.
• Another alternative, which would preserve the existing investment in
software and equipment, is to use multiple encryption with DES and
multiple keys.

Double DES
• The simplest form of multiple encryption has two encryption stages
and two keys
• Given a plaintext and two encryption keys, cipher text is generated as:
C = E(K2, E(K1, P))
• Decryption requires that the keys be applied in reverse order
P = D(K1, D(K2, C))
• But, his is vulnerable to
meet-in-the-middle
attack

Triple DES with Two Keys
• It’s a triple encryption method that uses only two keys.
• The function follows an encrypt-decrypt-encrypt (EDE) sequence.
• C = E(K1, D(K2, E(K1, P)))
• P = D(K1, E(K2, D(K1, C))).
• 3DES with two keys is a relatively popular alternative to DES

PRINCIPLES OF PUBLIC-KEY CRYPTOSYSTEMS
• Asymmetric algorithms rely on one key for encryption and a different
but related key for decryption.
• It is computationally infeasible to determine the decryption key given
only knowledge of the cryptographic algorithm and the encryption
key.

A public-key encryption scheme has 5 ingredients
• Plaintext: This is the readable message or data that is fed into the
algorithm as input.
• Encryption algorithm: The encryption algorithm performs various
transformations on the plaintext.
• Public and private keys: This is a pair of keys that have been selected so
that if one is used for encryption, the other is used for decryption.The exact
transformations performed by the algorithm depend on the public or
private key that is provided as input.
• Ciphertext: This is the scrambled message produced as output. It depends
on the plaintext and the key. For a given message, two different keys will
produce two different ciphertexts.
• Decryption algorithm: This algorithm accepts the ciphertext and the
matching key and produces the original plaintext.

Steps:
1. Each user generates a pair of keys to be used for the encryption and
decryption of messages.
2. Each user places one of the two keys in a public register or other
accessible file. This is the public key. The companion key is kept. Each
user maintains a collection of public keys obtained from others.
3. If Bob wishes to send a confidential message to Alice, Bob encrypts
the message using Alice’s public key.
4. When Alice receives the message, she decrypts it using her private
key. No other recipient can decrypt the message because only Alice
knows Alice’s private key.

Ensuring
secrecy/confidentiality in
public key cryptography
• Encryption : using public key
• Decryption : using private
key
• How?
• As receiver decrypts the
cipher text using his private
key, only the authorized
receiver can do the
decryption.

Ensuring authentication in
• Encryption : using private key
• Decryption : using public key
• How?
• As the sender encrypts the plaintext
using his private key, at the receiver
end it can be assured that the cipher
text comes from that particular sender..
• The entire message serves as s digital
signature of the sender.

Ensuring both confidentiality and authentication in

RSA [Rivest-Shamir-Adleman]
• The RSA scheme is a block cipher in which the plaintext and
ciphertext are integers between 0 and n - 1 for some n.
• Encryption and decryption are of the following form, for some
plaintext block M and ciphertext block C.
• Public Key: (e,n)
• Private Key: (d,n)

Steps:
1. Select two prime numbers, p and q.
2. Calculate n = pq.
3. Calculate f(n) = (p - 1)(q - 1).
4. Select e such that e is relatively prime to f(n) and less than f(n)
5. Determine d such that, de ≡ 1 mod f(n)
de mod f(n) = 1

RSA Example
• Choose p = 3 and q = 11
• Compute n = p * q = 3 * 11 = 33
• Compute φ(n) = (p - 1) * (q - 1) = 2 * 10 = 20
• Choose e such that 1 < e < φ(n) and e and φ (n) are coprime. Let e = 3
• Compute a value for d such that (d * e) % φ(n) = 1. One solution is d = 7
• Public key is (e, n) => (3, 33)
• Private key is (d, n) => (7, 33)

M=19
Encryption:
Cipher Text, C = Me mod n
= 193 mod 33
= 6859 mod 33
= 28
Decryption: M = Cd mod n
= 287 mod 33
= (282*282 *282*281) mod 33 = (25*25*25*28) mod 33
= 437500 mod 33
= 19 = M

Key Management
• There are 2 distinct aspect to use public key:
• The distribution of public key
• The use of public – key encryption to distribute secret keys

Distribution of Public Keys
• Several techniques have been proposed for the distribution of public
keys:
1. Public Announcement
2. Publically available directory
3. Public-key authority
4. Public-key certificates

1. Public Announcement of Public Keys
• Point of public-key encryption should be that the public key is public.
• Any party can send his or her public key to any other participant or
broadcast the key to the community at large.
• Disadvantage is that anyone can forge such a public announcement.

2. Public Key Directory
Allice 011101011101
Bob 0011000101001
Bimal 0001111100110
…. ….
• If the directory is made available to everybody, an attacker can change the
values which will disturb the entire system.
• Solution: Hire a trusted authority responsible to maintain this file.
• Bottle neck problem at the authority happens.

3. Public Key Authority
• Each participant knows a public key for the authority, with only the
authority knowing the corresponding private key.
• This may cause bottle neck in the system.
• Because, every user will be trying to contact the authority.

4. Public Key Certificates
• Another approach is to use certificates that can be used by
participants to exchange keys without contacting a public-key
authority.
• Each participant will get a certificate made ready from the authority.
• Each certificate will have id of the user, timestamp, public key of user
along with the authorities signature.
• So, when 2 parties has to communicate, they send their certificates to
each other.

Diffie Hellman Key Exchange Algorithm
• Not an encryption algorithm
• Used to exchange secret/symmetric key.
• Done using Assymetric Encryption

Steps:
1. Select a Prime Number –> q
2. Select a number α : α < q and α is primitive root of q
[if α modp, α2 modp, α3 modp….. α p-1 mod p gives the answers 1,2,3…p-1 we call α as primitive root of p]
3. Assume XA : Private key of user A, XA <q
4. Calculate YA: Public key of user A, YA= α XA mod q
5. Assume XB : Private key of user B, XB < q
6. Calculate YB : Public key of user B, YB = α XB mod q
7.Calculation of Secret Key at SENDER (A) side : K = (YB)X
A mod q
8. Calculation of Secret Key at RECEIVER (B) side : K = (YA)X mod q
[After calculation these K must be equal, then we say the key exchange happened successfully]

Example : q=11
1. q = 11 2 |10
2. α = ? 5
Steps to find primitive root :
n=11
F(n) = n-1 = 10
Find prime factors of 10 : 2 and 5
Take numbers from s = 2,3, 4….10 (n-1)
Calculate: [prime factor]s for each prime factors.
Take 2: first prime factor 22 mod 11 = 4
second prime factor 25 mod 11 = 10
As none of the answer is 1, 2 is a primitive root of 11
Select α = 2

Cont.
3. XA = 8
4. YA = 2 8 mod 11 = 3
5. XB = 4
6. YB = 2 4 mod 11 = 5
7. K at SENDER side = 5 8 mod 11 = 4
8. K at RECEIVER side = 3 4 mod 11 = 4

Elliptic Curve Arithmetic
• The principal attraction of ECC, compared to RSA, is that it appears to
offer equal security for a far smaller key size, thereby reducing
processing overhead.
• Disadvantage: Hardware Complexity

Cont.
• In ECC operation over elliptic curves called addition is used.
• Multiplication is defined by repeated addition
a*k=a+a+a+……+a (k times)
• A cryptanalyst finds it difficult to find this k even he knows a and ak.
• Xy=f(x): its an easy task
• But, x= f-1(y): it’s a difficult task.
• Finding x becomes easy if an additional value
is given, it is called trap door value.
• This is called as discrete logarithmic problem
for Elliptic curves.

Abelian group
• Abelian group G , sometimes denoted by {G,*} , is a set of elements
with a binary operation, denoted by * , that associates to each
ordered pair (a,b) of elements in G an element (a*b) in G, such that
the following axioms are obeyed:
(A1) Closure: If a and b belong to G , then a*b is also in G
(A2) Associative: a*(b * c) = (a * b) * c for all a ,b,c in G
(A3) Identity element: There is an element e in G such that
a*e = e*a =a for all in G
(A4) Inverse element: For each a in G there is an element a’ in G such
that a * a’ = a’*a = e
(A5) Commutative: a *b = b *a for all a,b in G

Elliptic Curve over Real Numbers
• Weierstrass equation: y2+axy+by=x3+cx2+dx+e
where a,b,c,d,e are real numbers.
• For our purpose, it is sufficient to limit ourselves to equations of the
form : y2 = x3+ax+b
• Curve is symmetric to x=0
• If we draw a line it will touch
3 points in the curve.

Elliptic Curve Cryptography
• Key Exchange using ECC
• ECC Encryption and Decryption

Key Exchange using ECC
• A key exchange between users A and B can be accomplished as
follows:

ECC Encryption
• Let the plain text be M.
• It is first converted into a point on Elliptic Curve.
• M Pm
• Choose a random positive integer number k.
• Cipher point = Cm=(KG,Pm+KPB) ; PB Public Key of B

ECC Decryption
• Multiply Cm’s first coordinate with receivers private Key.
KG , nB
• Subtract it from second point of curvature
Pm + KB – KG x nB
= Pm + KPB – KPB (Substitute: PB = nB x G)
= Pm

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