Enhancing Security using Cryptography with Matrices
P.Sai Tejesh
12bce0359
VIT University
Ph. No: 7502935512
Abstract :
Cryptography is the study of encoding and decoding secret messages. In the information age, cryptography has become one of the major methods for protection in all applications like cloud computing, mobile security. It allows people to do business electronically without worries of deceit and deception. When people started doing business online and needed to transfer funds electronically, the applications of cryptography for integrity began to surpass its use for secrecy .The constant increase of information transmitted electronically has lead to an increased reliance on cryptography and authentication. An obvious application of cryptography is the transformation of information to prevent other from observing its meaning. Secure communication is the most straightforward use of cryptography. Two people may communicate securely by encrypting the messages sent between them. The paper presents modifications of the Hill cipher generating dynamic encryption key matrix

Index Terms—Hill cipher, Matrix encryption, Permutation matrix

NOMENCLATURE :

Introduction:
INTRODUCTION
The Hill cipher (HC) algorithm [1] is one of the famous and known symmetric algorithms in the field of cryptography. HC is computationally attractive as using multiplication of a key matrix. HC has several advantages such as masquerading letter frequencies of the plaintext and high throughput [2, 3]. . Despite the ease and speed of the HC, the original HC is no longer used due to the vulnerability against known plaintext-cipher text attack [3]. Recent research and development efforts have been done to improve the security of HC. HC modification [4], HCM-PT, uses a dynamic key matrix obtained by random permutations of rows and columns from the master key matrix and transfers an HC-encrypted permutation to the receiving side. Thus, in HCM-PT, each plaintext vector...

...HILLCIPHER
TERM-PAPER
3/31/2013
LPU
vidit
Name: Vidit kumar Singh.
Reg no: 11009010
Roll no: B38.
Cap : 323.
Sub : Information Security and privacy.
INDEX
Introduction
Workings
Decryption
Matrix Inverse
Hillciphers that encipher larger blocks
Ciphertext Attack
Known plaintext attack
Security
Key size
Diffusion and Confusion
Conclusion
ReferencesHillCipher
Introduction
Invented by Lester S. Hill in 1929, the Hillcipher is a polygraphic substitution cipher based on linear algebra. Hill used matrices and matrix multiplication to mix up the plaintext.
To counter charges that his system was too complicated for day to day use, Hill constructed a cipher machine for his system using a series of geared wheels and chains. However, the machine never really sold. [1]
Hill's major contribution was the use of mathematics to design and analyse cryptosystems. It is important to note that the analysis of this algorithm requires a branch of mathematics known as number theory .Many elementary number theory text books deal with the theory behind the Hillcipher, with several talking about the cipher in detail (e.g. Elementary Number Theory and its applications, Rosen, 2000). It is...

...October 22, 2007
Strings and Ciphers
Based on a handout by Eric Roberts.
Cryptography, derived from the Greek word κρυπτοσ meaning hidden, is the science of creating and decoding secret messages whose meaning cannot be understood by others who might intercept the message. In the language of cryptography, the message you are trying to send is called the plaintext; the message that you actually send is called the ciphertext. Unless your adversaries know the secret of the encoding system, which is usually embodied in some privileged piece of information called a key, intercepting the ciphertext should not enable them to discover the original plaintext version of the message. On the other hand, the intended recipient, who is in possession of the key, can easily translate the ciphertext back into its plaintext counterpart. Caesar ciphers One of the earliest documented uses of ciphers is by Julius Caesar. In his De Vita Caesarum, the Roman historian Suetonius describes Caesar’s encryption system like this:
If he had anything confidential to say, he wrote it in cipher, that is, by so changing the order of the letters of the alphabet, that not a word could be made out. If anyone wishes to decipher these, and get at their meaning, he must substitute the fourth letter of the alphabet, namely D, for A, and so with the others.
Even today, the technique of encoding a message by shifting letters a certain distance in the...

...Brittany Lewis Cryptology and Cipher Codes Math Fair Report
In a world where identity theft is on the rise, hackers are hard at work trying to get people’s credit card numbers, and where companies are getting your information to sell you unwanted things, tight security has become a large factor of keeping the personal and confidential information of our society safe. Cryptology and Cipher codes are commonly used ways to keep confidential information protected by preventing people not in on the secret from understanding what is being transmitted. Cryptology is the science of secure communication which is also the encoding and decoding of data. Cipher codes are more complicated because it is a method used to transform a message into an obscure form. The use of these secured messages has been dated back to the first societies of the world where they were used for many of the same reasons they are today. The first use of written cryptology was believed to take place at about 1900 B.C when an Egyptian scribe first used a non-standard form of hieroglyphics in his writing. Then in 1500 B.C in Mesopotamia (common day Iraq), an enciphered message in cuneiform was used to conceal a formula to make glazes for pottery. In the years 500 through 600 B.C, Hebrew scribes used a reverse alphabet simple substitution cipher to write the book of Jeremiah which was known as ATBASH. The Greeks used a device...

...Jordan University of Science and Technology
Computer Engineering Department
Cryptography & Network Security
CPE (541)
HW#5
Contemporary Symmetric Ciphers
(Double-DES, Triple-DES & Blowfish)
Supervised by:
Dr Loái Tawalbeh
Eng. Sulaiman Al-Basheer
Simsam R.Hijjawi
20022171043
Review Problems:
6.1 What is the triple encryption?
It is a three-stages encryption with three different keys, to avoid costly requirements arises from using three different keys with total length of 3x56 = 186 bits a triple encryption with two keys maybe used.
6.2 What is the meet in the middle attack?
It's that attack doesn't depend on any particular property of the DES, instead, it will work against any type of block ciphers.
For the double-DES cipher & a given (P,C) pair, this attack works as follow:
1. Encrypt the plaintext P with all possibilities of K1, store the results in a table, & sort that table by the value of X.
2. Decrypt C with all possible values of K2, check each resulted value with the entries in the table, in case of match, check these two keys against another known pair (P1,C1), if match, accept them as the correct keys.
6.4 Why is the middle portion of 3DES is a decryption rather than an encryption ?
1. It's a decryption process in order to change the traditional nature of the DES, if it's an encryption, it'll stay a DES but...

...e-Business Security
CAESER CIPHER – THE SHIFT CIPHER
1. Introduction
2. History & Development
3. How It Works
4. C++ Source Code [Encryption]
5. C++ Source Code [Decryption]
6. Step By Step Explanation [Decryption]
7. Step By Step Explanation [Decryption]
8. Pros & Cons
9. Conclusion
10. Reference
INTRODUCTION
In cryptography, a Caesar cipher, also known as Caesar's cipher, the shift cipher, Caesar's code or Caesar shift, is one of the simplest and most widely known encryption techniques. It is a type of substitution cipher in which each letter in the plaintext is replaced by a letter some fixed number of positions down the alphabet. For example, with a left shift of 3, D would be replaced by A, E would become B, and so on. The method is named after Julius Caesar, who used it in his private correspondence.
The encryption step performed by a Caesar cipher is often incorporated as part of more complex schemes, such as the Vigenère cipher, and still has modern application in the ROT13 system. As with all single alphabet substitution ciphers, the Caesar cipher is easily broken and in modern practice offers essentially no communication security.
HISTORY & DEVELOPMENT
The cipher was named after Julius Caesar. It was used during 50BC by notable Romans...

...Substitution and transposition ciphers are two categories of ciphers used in classical cryptography. Substitution and transposition differ in how chunks of the message are handled by the encryption process. Substitution ciphers encrypt plaintext by changing the plaintext one piece at a time. Transposition ciphers encrypt plaintext by moving small pieces of the message around. A transposition cipher doesn't change the characters in the plaintext when it generates the cipher text, it just re-arranges them. It applies some kind of permutation function to the text to produce a re-arrangement, which can be reversed by knowing the secret to the permutation. In this report, I have chosen columnar transposition cipher.
In a columnar transposition cipher, the message is written out row by row into the matrix. The matrix is based on the length of the keyword. If there is any blank space in the matrix, replace it with nulls. This method is for a regular columnar transposition cipher. For an irregular columnar transposition cipher, the spaces are left blank. Then read out the message column by column, and the columns are chosen in some scrambled order based on the keyword. For example, the word CODEC is of length 5, so the rows are of length 5, and the permutation is defined by the alphabetical order of the letters in the keyword. In this case,...

...In Hemingway’s “Hills Like White Elephants,” Jig undergoes a transformation enabling her to realize and declare her own feelings. At the story’s beginning Jig is passive, unaware of her own feelings, and in the habit of looking to the American direction. She soon comes to realize her own desires and struggles to assert herself for the first time.
The story is structured around the two sides of the valley, the division symbolizing the opposition between the American’s values and Jig’s. “The two sides of the valley of the Ebro represent two ways of life, one a sterile perpetuation of the aimless hedonism the couple have been pursuing, the other a participation in life in its full natural sense” (Renner, 32). On one side are the values associated with abortion, and on the other are the values associated with having the child. “In this setting, then, Hemingway works out the story’s conflict, which revolves around the development of his female character” (28).
The dialogue between Jig and the American about hills and drinks “is in actuality an articulated but decisive struggle over whether they continue to live the sterile, self-indulgent, decadent life preferred by [the American] or elect to have the child that Jig is carrying and settle down to a conventional but, in Jig’s view, rewarding, fruitful, and peaceful life” (Holladay, 1). The American argues adamantly for the abortion while Jig, being accustomed to doing what he wants, “has not yet...

...Olga Serzhantova
English 1A
Sean Kim
13 September 2010
Essay 1
Hills Like White Elephants
Everyday people make decisions that might have a big influence on their future lives. One can never say if this or that decision is right simply because there is no right or wrong. The choices that people make or believe in depend on their individual qualities and personal preferences. Therefore, what is right for one person might be totally wrong for the other. The only thing we shouldn’t forget is that once the decision is made there is no way back, once the action is done there is no way to change it.
Ernest Hemingway, one of the most influential writers of the first half of the twentieth century, in his realistic story “Hills Like White Elephants” tried to depict and understand contradicting human nature while making a life choice. The story takes in the Ebro River valley of Spain, where an American man and his female companion Jig are waiting for a train and having drinks discussing "doing it." Obviously, by "doing it," they're referring to whether or not they should have an abortion. In order the readers to understand the core of the problem the author uses such powerful literary elements as setting and symbolism. The story takes place in a very short period of time and presents a dialogue between two main characters. It is very laconic, but yet tells a tale that is much bigger than itself.
From the very first paragraph the author...