Fr. C.

Rodrigues Institute of Technology, Vashi, Navi-Mumbai

Department of Computer Engineering

Cryptography and System Security (CSS)

CSC602

By
Mrs. Smita Rukhande

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 Chapter 1- Introduction to Number Theory & cryptography

 Classical Encryption techniques –

 substitutiontechniques: mono-alphabetic (Caesar) and poly-
alphabetic (Vigenère cipher, Playfair cipher)
 transposition techniques : keyed and keyless transposition ciphers

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 Classical Encryption techniques
(Symmetric encryption or conventional encryption or single key
encryption was only type of encryption in use prior to the
development of public key encryption in the 1970s.)

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 What is Cryptography?

Cryptography derived its name from a Greek word called

“Kryptos” which means “Secrets writing”.
 Cryptography is the practice and study of hiding information.
 It is the Art or Science of converting a plain intelligible data into
an unintelligible data and again retransforming that message into
its original form.

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How cryptography works?

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 Some Basic Terminology
• plaintext - original message
• ciphertext - coded message

• cipher - algorithm for transforming plaintextto ciphertext

• key - info used in cipher known only to sender/receiver
• enciphering or encryption – process of converting plaintext tociphertext

• deciphering or decryption - recovering plaintext from ciphertext

• cryptography - study of encryption principles/methods

• cryptanalysis (codebreaking) - study of principles/ methods of deciphering ciphertext

without knowing key (breaking the code).
• cryptology - field of both cryptography andcryptanalysis
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 Symmetric Cipher Model
Plaintext - original message that will be fed to the encryption algorithm as an input.
Encryption algorithm - performs various substitutions and transformations on the
plaintext.
Secret key - a value independent of the plaintext and of the algorithm.

The exact substitutions and transformations performed by the algorithm depend on the
key.

Fig- Simplified Model of Symmetric Encryption

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 Encryption Requirements

a strong encryption algorithm

a secret key known only to sender / receiver

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Model of Symmetric Encryption

Figure - Model of Symmetric Cryptosystem

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 Cryptography
Dimension used to describe cryptographic system :
 type of operations used for transforming plaintext to ciphertext
(classical techniques)
 Substitution
 Transposition
 number of keys used
 Symmetric, single-key, secret-key, or conventional encryption.
 Asymmetric, two-key, or public-key encryption.
 way in which plaintext is processed
 Block cipher
 Stream cipher
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X X X X X X 12
 Classical Encryption Techniques

• or conventional / private-key / single-key.

• sender and recipient share a common key.
• all classical encryption algorithms are private-key.
• was only type prior to invention of public-key in 1970’s.
• The only security service (Classical Encryption Techniques)
these systems provide is confidentiality of information.
• Unlike modern systems which are digital and treat data as binary
numbers, these systems worked on alphabets as basic element.

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 Classical Encryption Techniques

(letters are (letters are

replaced by arranged in a
other letters) different order)

Substitution ciphers are Transposition ciphers are

• Monoalphabetic cipher • keyless
• Polyalphabetic cipher • keyed

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 Groups of substitution cipher are

 Monoalphabetic cipher is a substitution cipher in which a character (or a symbol) in the

plaintext is always replaced by the same character (or symbol) in the ciphertext irrespective
of its position in the text.
• For example, if ‘A’ is encrypted as ‘D’, for any number of occurrence in that plaintext,
‘A’ will always get encrypted to ‘D’.
• Monoalphabetic cipher include additive (or shift cipher or Caesar cipher ),
multiplicative, affine cipher
• Relation between letters in the PT & CT is one to one.

 Polyalphabetic Cipher is a substitution cipher in which the cipher alphabet for the
plaintext alphabet may be different at different places during the encryption process.

• The relationship of a character in the PT & CT is one-to many.

• Playfair, Vigenère and Hill Cipher are polyalphabetic ciphers.
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 Mono Alphabetic Ciphers
Example

The following shows a plaintext and its corresponding ciphertext. The cipher is
monoalphabetic because both l’s are encrypted as O’s.

Example
The following shows a plaintext and its corresponding ciphertext. The cipher is not
monoalphabetic because each l is encrypted by a different character.

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Substitution technique: 1. Shift Cipher or Additive cipher or Caesar cipher

 The plaintext and ciphertext consist of uppercase letters (A to Z) only.

 In this cipher, the encryption algorithm is “shift key characters down”, with key equal
to some number.
 The decryption algorithm is “shift key characters up”.
 For example, if the key is 5, the encryption algorithm is "shift 5 characters down"
(toward the end of the alphabet).
 The decryption algorithm is "shift 5 characters up" (toward the beginning of the
alphabet).
 If we reach the end or beginning of the alphabet, wrap around.
 Julius Caesar used the shift cipher to communicate with his officers. For this reason, the
shift cipher is sometimes referred to as the Caesar cipher.
 Caesar used a key of 3 for his communications.
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 Shift Cipher

 Example - Use the shift cipher with key= 15 to encrypt the message "HELLO”

Solution
• Encrypt one character at a time.
• Each character is shifted 15 characters down.
• Letter H is encrypted to W. Letter E is encrypted to T. The first L is encrypted
to A. The second L is also encrypted to A. And O is encrypted to D.
• The cipher text is WTAAD.
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 Shift Cipher

 Example- Use the shift cipher with key = 15 to decrypt the message “WTAAD.”

Solution
• Decrypt one character at a time.
• Each character is shifted 15 characters up.
• Letter W is decrypted to H. Letter T is decrypted to E. The first A is decrypted
to L. The second A is decrypted to L. And, finally , D is decrypted to O.
• The plaintext is HELLO.
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Substitution technique: Caesar Cipher/ Additive Cipher/ Shift Cipher

• This technique is proposed by Julius Caesar.

• This is substitution cipher technique in which each letter in the plaintext
is replaced by a letter standing three places further down the alphabet.

• It is also called monoalphabetic cipher / additive cipher.

• This cipher is sometimes called as Shift Cipher.
• This encryption algo adds the key to the PT character, the decryption
algorithm subtracts the key from the CT character.

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Caesar Cipher/ Additive Cipher/ Shift Cipher

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 Caesar Cipher

 Then the algorithm can be expressed as follows

C = E (p, 3) = (p + 3) mod 26

 Shift may be of any amount, then general Caesar cipher algorithm is

C = E (p, k) = (p + k) mod 26

 The decryption algorithm

p = D (C, k) = (C - k) mod 26

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 Caesar Cipher

 replaces each letter by 3rd letter on or shifting of letters is based on key value ie 3.
 Assign a number to each letter

 can define transformation as:

 example: (key=3)
PT - meet me after the toga party
CT- PHHW PH DIWHU WKH WRJD SDUWB
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 Example:
Use the additive cipher or Caesar Cipher with key=15 to encrypt the message
“hello”
Solution
Encrypt one character at a time. Each character is shifted 15 characters down. Letter H is
encrypted to W. Letter E is encrypted to T. The first L is encrypted to A. The second L is also
encrypted to A. And O is encrypted to D.
The cipher text is WTAAD
C = E (p, k) = (p + k) mod 26

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Example- Use the shift cipher with key = 15 to decrypt the message “WTAAD.”

Decryption
Note-: the operation is in modulo 26 which means that a –ve result
needs to be added to Z (26)
(eg-: -15 becomes 11)
p = D (C, k) = (C - k) mod 26

(00-15)mod 26 = -15 +26=11

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 Qu- Why we called additive cipher as shift cipher or Caesar cipher?
 Caesar cipher-: Julius Caesar used an additive cipher to communicate
with the officers. For this reason additive ciphers are sometimes referred
to as Caesar cipher. Caesar used a key of 3 for his communication.

 Shift cipher-: the reason is that the encryption algorithm can be

interpreted as “shift key characters down” and decryption algorithm can
be interpreted as “shift key characters up” .

Example-: Eve has intercepted the CT “UVACLYFZLJBYL” what is

the plain text?

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 Security Value of Caesar Cipher
Disadvantages-
• Caesar Cipher is not a secure cryptosystem because if it is known
that a given ciphertext is a Caesar cipher, then a brute-force
cryptanalysis is easily performed. simply try all the 25 possible keys.
• With only 25 keys , this method is not secure.

Three important characteristics of this problem enabled us to use a brute

force cryptanalysis:

1. The encryption and decryption algorithms are known.

2. There are only 25 keys to try.
3. The language of the plaintext is known and easily recognizable.
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 Example-
Eve has intercepted the ciphertext “UVACLYFZLJBYL”. Show how
she can use a brute-force attack to break the cipher.
Solution
Eve tries keys from 1 to 7. With a key of 7, the plaintext is “not very
secure”, which makes sense.

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Multiplicative cipher

In a Multiplicative cipher the Encryption algo specifies multiplication of PT

by the key & Decryption algorithm specifies division of the CT by the key.

P =(C

Decryption here means multiplying by the multiplicative inverse of the key.

So encryption & decryption are inverse of each other.
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Encryption
Example
Use a multiplicative cipher to encrypt the message “hello” with a key of 7.
The ciphertext is “XCZZU”.

Example
PT = Saturday
Key = 5 CT =?
(Ans-MARWHPAQ)
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Decryption
Example
Use a multiplicative cipher to decrypt the ciphertext “XCZZU” with a key
of 7.

the multiplication inverse of the key (where the multiplication inverse of 7 is 15 )

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To find inverse modulo
Example – to find 𝟕−𝟏 mod 26
Step 1-
1= x * 7 – y *26 first find out x and y values
for that write table of 7 and 26 so value of x is 15
in table of 7 and y is 4 in table of 26.

So 1= 15* 7 – 4 *26
1= 105 -104

So 𝟕−𝟏 mod 26 is 15 (ie. x=15 in above equation)

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 Affine cipher
• combine additive & multiplicative ciphers to get affine cipher.
• A combination of both ciphers with pair of keys.
• For Encryption- The first key is used with the multiplicative cipher the second key is
used with the additive cipher.

The additive cipher is a

special case of an affine
cipher in which k1 = 1.

The multiplicative cipher

is a special case of affine
cipher in which k2 = 0.

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 Use an affine cipher to encrypt the message “hello” with the key pair (7, 2).
Example Modular arithmetic properties:
1. [(a mod n) + (b mod n)] mod n = (a + b) mod n
2. [(a mod n) - (b mod n)] mod n = (a - b) mod n
3. [(a mod n) * (b mod n)] mod n = (a * b) mod n

The additive cipher is a special case of an affine cipher in which

k1 = 1. The multiplicative cipher is a special case of affine cipher in
which k2 = 0.
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 Example
Use the affine cipher to decrypt the message “ZEBBW” with the key pair (7, 2) in modulus 26.
Modular arithmetic properties:
1. [(a mod n) + (b mod n)] mod n = (a + b) mod n
Solution 2. [(a mod n) - (b mod n)] mod n = (a - b) mod n
3. [(a mod n) * (b mod n)] mod n = (a * b) mod n

The additive cipher is a special case of an affine cipher in which

k1 = 1. The multiplicative cipher is a special case of affine cipher in which k2 = 0.
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