Cryptography Prateek Sharma

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Zimmermann Telegram By aurther Zimmermann, Foreign Secretary of the German Empire, 1917

Prateek Sharma

Cryptography Cryptography The art/ science of devising ciphers.

Cryptanalysis The art/ science of breaking the ciphers.

Cryptology Both cryptography & cryptanalysis are collectively known as cryptology.

Encryption The sender transforms the original information to another form & sends the resulting unintelligible message out over the network.

Decryption Reverses the encryption process in order to transform the message back to its original form.

Annotation:  The study & practice of encryption is called the science of Cryptography (US)/ Cryptology (Netherland).  Both encryption & decryption are processes.  Cryptology ( cryptography & cryptanalysis) is an art/ science.

The Encryption Model Passive intruder just listens

Plaintext, P

Encryption method/ algorithm

Active intruder can alter msg.

Intruder

Cipher text

Decryption method/ algorithm

C = EK(P) Encryption Key

Decryption Key

Plaintext, P

Notational relation b/w plaintext, cipher text & keys

DK {EK (P)}=P Where, P = plaintext C = cipher text obtained by encrypting plain text, C = EK(P) EK (P) = Encryption of plaintext P using key K. DK (P) = Decryption of the cipher text.

Conventional

Public Key

Methods

Methods

Encryption/ Decryption Methods

(1) Conventional Methods

Character Level Encryption Mono- alphabetic Encryption Algorithm Poly- alphabetic Encryption Algorithm

Character Level Encryption

Transpositional Encryption

Bit Level Encryption Encoding/

Decoding

(2)

Public Key Methods

Permutation

Substitution

DES

Product

Bit Level Encryption

X-OR

Rotation

RSA Encryption

Mono- alphabetic Encryption Algorithm Sender

Receiver

KE = 3 DEAR

Plaintext

Add KE Encryption Algorithm

KD = 3 GHDU

Cipher text

Subtract KD Decryption Algorithm

DEAR

Plaintext

Poly- alphabetic Encryption Algorithm Sender

Receiver

KE = Position DEAR

Plaintext

Add KE Encryption Algorithm

KD = Position EGDV

Cipher text

Subtract KD Decryption Algorithm

DEAR

Plaintext

Transpositional Encryption KE = KD Encryption

1 2 3 4 5 6 6 4 2 3 1 5

Decryption

1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

A T F R I

U T N I

A F R

R U E E N D

Plaintext Sender

Transpose Encryption Algorithm

R E A E R D F

Cipher text

Transpose Decryption Algorithm

T R U E I E N D

Plaintext Receiver

Encoding / Decoding Input 00 01 10 11

   

Output

Input

0001 0010 0100 1000

0001 0010 0100 1000

2 X 4 Decoder

Output    

00 01 10 11

4 X 2 Encoder

 An Decoder changes an I/P of n bits into an O/P of 2^n bits.  An Encoder has 2^n bits I/P & n bits O/P.

Permutation (P- Boxes) Input 1 0 1 0

1

1 0 0

Input 1 1 0 0 0 1 1

0

1

1

0 1

1

Straight Permutation

Compressed Permutation

Number of bits in I/P & O/P are preserved; only positions are interchanged.

Number of bits is reduced

P- Boxes: Permutation units which can easily be made as

Input 1 0 1 1

0

1 1 1

Expanded Permutation Number of bits is increased (some bits are repeated).

H/w circuits with internal wiring.

Substitution (S- Boxes) 2 X 4 Decoder Substitution of n bits by another n bits can be achieved using a combination of P-Boxes, encoders, & decoders.

Input 00 01 10 11

P- box

Output    

01 00 11 10

S- box 4 X 2 Encoder

Product P- boxes

A product is a combination of P- boxes & S- boxes

S- boxes

P- boxes

S- boxes

Exclusive OR Sender

Receiver

0 1 1 0 0 1 1 1 1 1 0 1 1 0 0 1 1 0 1 1 1 1 1 0

8– bit plaintext

1 0 1 1 1 1 1 0 1 1 0 1 1 0 0 1 0 1 1 0 0 1 1 1

8– bit cipher text

Key 8– bit cipher text

Key 8– bit plaintext

Rotation Ptext

Ctext

0

1

1

0

0

0

1

1

Before

1

0

1

1

0

0

0

1

After one rotation

1

1

0

1

1

0

0

0

After two rotation

0

1

1

0

1

1

0

0

After three rotation

Data Encryption Standards (DES) Key (56 bits)

Sub key Generator K1

K2

Sub Keys

K16

3

Transposition

2

Swapping

1

...

Complex

Complex

64 bits

Complex

Plain Text

Transposition

(Each 48 bits)

17

18

19

 The algorithm encrypts 64 bit plaintext using 56 bit key.  Steps 2 & 17 are very complex. Each step is a combination of transposition, substitution , swapping, X- OR, & rotation.

Cipher Text 64 bits

Public Key Encryption (RSA- Rivest, Shamir, Aldeman) Customer 1 Public Key Private Key

Customer 2 Public Key

Customer n

.. .. Public Key

Bank

 Each user has same encryption algo. & key.  The decryption algo. & key are kept secret.

Limitations of Conventional Methods Sender

KE = 3

DEAR Plaintext

Add KE

Encryption Algorithm

Receiver

KD = 3 GHDU Cipher text

Subtract KD

DEAR Plaintext

Decryption Algorithm

 Both algorithms (encr. & decr) uses the same key.  Anyone who knows the encryption algorithm & key can deduct the decryption algorithm, e.g. reasoning questions in various examinations.

 If we consider the case of bank accounts for remote customers, millions of algorithms are required for individual customers.  The decryption algorithm is just the inverse of the encryption algorithm.

Advantages of Public Key Methods  The decryption algorithm is not the inverse of encryption algorithm.  Every user have the same encryption algorithm & key.  The decryption algorithm & key are kept secret.  Anyone can encrypt information, but only an authorized receiver can decrypt it.

Applications of Cryptography  Defense.  Diplomatic corps.  Diarists.

 Lovers.  Security of ATM cards.  Computer passwords.

 Electronic commerce.  Framing reasoning questions.

Enjoy the scenic beauty at Joox Islands…

Joox Islands…

If ABCDEFGHIJKLMNOPQRSTUVWXYZ Is ZYXWVUTSRQPONMLKJIHGFEDCBA

Then, X I B K G LT I Z K S B leads to

Fortifying Network Securities

Thank You