En Cryptolog y

8/14/2019 En Cryptolog y

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Cryptology and Its Applications

Akshat Mathur


Presented By

AKSHAT MATHUR Roll # EC200118042

Under the guidance of

Dr. Parth S. Mallick


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Introduction

The science ofcryptology is the science of secure communications, formed from the Greek

words krypts, "hidden", and logos, "word".

Useful Terminology CIPHERTEXT

CODE

CRYPTANALYSIS

CRYPTOGRAPHY

CRYPTOSYSTEM

DECRYPTION

ENCRYPTION


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Cryptography

PRODUCT CIPHERS A D F G B X

A S U B J E C

D T A D F G H

F I K L M N O

G P Q R V W X

V Y Z 0 1 2 3

X 4 5 6 7 8 9

M E R C H A N T T A Y L O R S

FG AV GF AX DX DD FV DA DA DD VA FF FX GF AA


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Cryptography

Block Ciphers

It is a type of symmetric-key encryption algorithm that changesa fixed length of block text into same length of Cipher text.

Encryption works by means of key and Decryption is the reverse

of encryption process using the same key. Stream Ciphers

The encryption method is based on simple XOR of binary bits.It encrypts one bit at a time.

The key sequence is generated on highly complex mathematicalalgorithms. LFSR based on primitive polynomials andcombination of several LFSR using linear and nonlinear logic

provides a very high level of complexity.


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Cryptography

Public Key Cryptography

RSA Algorithm

In this system a user chooses a pair of prime numbers so large that

factorizing the product is beyond all computing capabilities.

Stages of sending the message by this method.

The receiver, M, distributes his public key pair.

The sender, F, composes a plain text message, m, and then uses Ms public key

to encrypt the message and from cipher text, c. c is the remainder left when m

is raised to the power ofe and divided by the modulus n.


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Cryptography c = me mod n (where e and n are Ms public key pair).

F sends the ciphertext, c, to M.

The receiver, M, decrypts the ciphertext and retrieves the

plaintext message, m. m is the remainder obtained when c is

raised to the power ofdand divided by n. m = cd mod n

As you can see, this process requires d, which only M knows.

Another person, I, who intercepts the message, can not decrypt

it.

Example:

Let p = 5, q = 11, n = pq = 55

The least common multiple of (p-1)(q-1) is 20 = 22 5.


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Cryptography Therefore, in this case, any key, e, not divisible by 2 or 5

will have a matching key, d(e must be relatively prime to

(p-1)(q-1) for it to be the key).

Let e = 7

(ed -1) mod (p-1)(q-1) = 0 \ d = 3 Let the plaintext message, m = b = 2

\ The ciphertext, c = me mod n = 27 mod 55 = 18

To decrypt this information it is necessary to know d.

m = cd mod n = 183 mod 55 = 2 \ The message has been

successfully decrypted.


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Cryptography in the "Real World"

Applications of Cryptography

military and diplomatic services

protecting confidential company information, telephone

calls

Internet Business

lottery tickets


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Cryptanalysis

A Triumph of Cryptanalysis Enigma

What Was Enigma?The Enigma machine consisted of a 26 letter keyboard for

input. The output was read off 26 lamps which each

corresponded to a letter. The encipherment was performed

by a device called a "scrambler" that was made of three

rotating wheels on a common spindle and a plug boardknown as a "Steckerboard" that added an additional level of

security.


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Cryptanalysis

What Made It Possible?

With the level of sophistication of the Enigma machines it

should have been unbreakable. However, the Germans had

a number of procedural flaws which allowed the British

and Polish to break the cipher.


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CONCLUSION

Military cryptography for encryption may still remain

mainly symmetric key based for obvious reasons.

Public key cryptography would develop more in near

future particularly in the context of key exchange anddigital signatures.

Simultaneously , the challenging area of the

cryptanalysis, being the other side of the development

exercise will gain the importance in the view of the

plethora of applications demanding assured security.


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THANK YOU !!!

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