**Cryptography**

History

Modern Cryptography

Algorithms

Classical Cryptography

Permutations

Caesar Substitution

T O B E O R N O T T O B E

A C U L C V U C M A C U L

Computer Era

Symmetric-Key Cryptography

Public Key Cryptography

Perfect Cryptography: The One-Time Pad

Advantages of One-Time pad

Encryption using Matrices

Represent the Message in a 2*n matrix

Choose a 2*2 non-singular matrix as the Public Key. Multiply the above matrix by this 2*2 matrix from the left

Find modulus 26 for each element in the new matrix and write down the corresponding alphabets for each element

What is it?

Encoding

Decoding

Messages encrypted with keys based on randomness have the advantage that there is theoretically no way to "break the code" by analyzing a succession of messages. Each encryption is unique and bears no relation to the next encryption so that some pattern can be detected.

Algorithms

Simple Replacements

Shifting Replacements

RSA Algorithm

Every character is mapped to a different character.

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Q W E R T Y U I O P A S D F G H J K L Z X C V B N M

How are you?

Igv qkt ngx?

Cryptanalysis of the new mechanical devices proved to be both difficult and laborious. In the United Kingdom, cryptanalytic efforts at Bletchley Park during WWII spurred the development of more efficient means for carrying out repetitious tasks. This culminated in the development of the Colossus, the world's first fully electronic, digital, programmable computer, which assisted in the decryption of ciphers generated by the German Army's Lorenz SZ40/42 machine.

In this algorithm, we again replace every character with another, but not directly. The character which another character is replaced with, depends on the relative position of the character in the line.

RSA is a cryptosystem, which is known as one of the first practicable public-key cryptosystems and is widely used for secure data transmission.

• Around 400 BC Spartan employed a device known as the scytale.

• The device, used for communication between military commanders, consisted of a tapered baton around which was wrapped a spiral strip of parchment or leather containing the message.

• Words were written lengthwise along the baton, one letter on each revolution of the strip. When unwrapped, the letters of the message appeared scrambled and the parchment was sent on its way.

• The receiver wrapped the parchment around another baton of the same shape and the original message reappeared.

Permutations

SSL 128-bit encryption

• Julius Caesar used a simple letter substitution method. Each letter of Caesar's message was replaced by the letter that followed it alphabetically by three places.

• The letter A was replaced by D, the letter B by E, and so on. For example, the English word COLD after the Caesar substitution appears as FROG. This method is still called the Caesar cipher, regardless the size of the shift used for the substitution.

• Simple substitution ciphers are easy to break. For example, the Caesar cipher with 25 letters admits any shift between 1 and 25, so it has 25 possible substitutions (or 26 if you allow the zero shift).

• One can easily try them all, one by one. The most general form of one-to-one substitution, not restricted to the shifts, can generate possible substitutions.

26! or 403,291,461,126,605, 635,584,000,000 And yet, ciphers based on one-to-one substitutions, also known as mono alphabetic ciphers, can be easily broken by frequency analysis.

As the development of digital computers and electronics helped in cryptanalysis, it made possible much more complex ciphers. Furthermore, computers allowed for the encryption of any kind of data representable in any binary format, unlike classical ciphers which only encrypted written language texts; this was new and significant.

Cryptography has become a widely used tool in communications, computer networks, and computer security generally. Some modern cryptographic techniques can only keep their keys secret if certain mathematical problems are intractable, such as the integer factorization or the discrete logarithm problems, so there are deep connections with abstract mathematics.

It now makes extensive use of mathematics, including

statistics, abstract algebra, number theory, etc.

to understand this algorithm lets take an example

lets assume that our message is a single word CAGE from a set of alphabets A B C D E F G H I each alphabet is associated with a number starting from 1

A B C D E F G H I

1 2 3 4 5 6 7 8 9

Therefore the numerical representation of CAGE is 3175 the following slides shows the steps involved in coding this –

step 1: Choose any two primes .lets take 5 and 7

step 2: Multiply 2 numbers to get the module in this case it is 35

step 3: Calculate the p =(5-1)(7-1)=24

step 4: Choose a number x such that 1<x<p which is prime i.e. any 1 of(7,11,13,17,19,.....,) in this case 7 be the is the public key

step 5: Raise all the associated numbers to the power of public key 3^7 1^7 7^7 5^7

step 6: Divide each number in step 5 by the module in step 2 and note the remainders

Decrypting CAGE-3175

for decryption we need a private-key or decoder.

Step 1: Lets take the private key as 11

step 2: Repeat steps 5 and 6 and you will get the original numbers

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The art of protecting information by transforming it (encrypting it) into an unreadable format, called cipher text. Only those who possess a secret key can decipher (or decrypt) the message into plain text. Encrypted messages can sometimes be broken by cryptanalysis, also called codebreaking, although modern cryptography techniques are virtually unbreakable.

As the Internet and other forms of electronic communication become more prevalent, electronic security is becoming increasingly important. Cryptography is used to protect e-mail messages, credit card information, and corporate data. One of the most popular cryptography systems used on the Internet is Pretty Good Privacy because it's effective and free.

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