A new Algorithm for Encrypt Arabic Text by using first Order Equation for Three Variables

In this days many data exchanged over the Internet, so finding the best solution that offer the necessary protection against the information hackers becomes the basic goals of many researches. Many researches focus on the Encryption algorithms that play a main role in information security systems. The goal of every encryption algorithm is to make it as hard as possible. If a good encryption algorithm is used, there is no technique considerably better than trying every possible key to break the cipher text. It is difficult to define the quality of an encryption algorithm. Sometimes algorithms look strong and complicated but turn out to be very easy to break.In this research, a new encryption method is proposed to encrypt Arabic text by using the standard of first order equation for three variables. The sender and the recipient will share a first order equation for three variables and two randomly constants represent the values of y, z which represent the keys of used in encryption\decryption process. The result of the equation xored with randomly shared value between both sides which is represent the third key for the proposed method to get final cipher text of the proposed method. By applying different cryptanalysis techniques such as berlekamp Massey cryptanalysis, linear feedback shift register (LFSR), autocorrelation attack, brute force attack , frequency attack, m-138 cipher text only attack and side – channel attack to test the inevitability of the proposed method, the results showed that the proposed method is hard to be broken by the crypt analytics and

very easy to break.In this research, a new encryption method is proposed to encrypt Arabic text by using the standard of first order equation for three variables.The sender and the recipient will share a first order equation for three variables and two randomly constants represent the values of y, z which represent the keys of used in encryption\decryption process.The result of the equation xored with randomly shared value between both sides which is represent the third key for the proposed method to get final cipher text of the proposed method.By applying different cryptanalysis techniques such as berlekamp Massey cryptanalysis, linear feedback shift register (LFSR), autocorrelation attack, brute force attack , frequency attack, m-138 cipher text only attack and sidechannel attack to test the inevitability of the proposed method, the results showed that the proposed method is hard to be broken by the crypt analytics and

Introduction
Cryptography is the art of hiding the meaning of data and transmitting information over a communication channel securely in which only the recipients are allowed to read/interpret it and others should not be able to read/interpret it even though they get access to it [6].
The word Cryptography is came from the Greek word, "kryptos" which means 'hidden' and "graphein" that means 'to write'.Therefore, cryptography is the art and the science of making any information unintelligible to all except the recipients [5].In the terminology of cryptography, the sending data is called "the plain-text", while the encrypted data is called the "cipher-text".On the other hand, the art and the science of breaking Cipher text is called cryptanalysts, and the branch of mathematics that study both cryptography and cryptanalysis is called "cryptology" [7].
The system that uses encryption and decryption methods is called cryptosystem [6].These cryptosystems are classified into two types: classical ciphers and modern ciphers.The classical ciphers are further divided into two types of ciphers: substitution and transposition ciphers.
Where, the modern ciphers are also further divided according to the key into two cipher types: symmetric and asymmetric ciphers.

Types of Ciphers
There are two basic types of ciphers according to encryption/decryption mechanisms : substitution and transposition ciphers [11].In the substitution cipher the mechanism of encryption depending on replaced each letter in the alphabet with a corresponding letter from the alphabet, Beaufort cipher , Caesar Cipher, Vigenère cipher, pigpen cipher are some examples on substitution cipher [11].Where, transposition cipher permutes letters in the same message [1].Rail fence cipher, route cipher, columnar cipher, myszkowski cipher are some examples on transposition cipher [10].Moreover, types of cryptography are divided into two types according to the key generation mechanisms: symmetric and asymmetric cryptography.

Symmetric Cryptography
The mechanism of sharing the same key for the encryption and decryption process between both parties is called symmetric cryptography.Symmetric keys are also called secret keys because they must be kept as a secret key.The security of the symmetric encryption method depending on key protection [11].In addition, the key size and it is complexity determine the complexity of the encryption/decryption process.However, it requires more efficient and save way to delivering the keys securely to the communicating parties [11].

Asymmetric Cryptography
In a symmetric key cryptography, the key used in the encryption process differ from the key that used in the decryption process, and there are two keys in this type of cryptography public and privet keys.Using two keys one for encryption and the other for decryption.The public and private keys cannot be derived from each other.There are many examples of asymmetric key algorithms such as: RSA, Elliptic Curve Cryptosystem (ECC), Diffie-Hellman, El Jamal, Digital Signature Standard (DSS) [11].

Cryptographic Attack Methods and cryptanalysis
Cryptanalysis is the art and the science to break a cipher text to get the security information that is contained in the original message (plain text).There are many types of cryptanalysis methods according to the cryptographic methods through employing some mathematical methods; such as frequency and brute force attack …etc.[2].Cryptographic attacks as part of the cryptanalysis attempts to decrypt the cipher text without knowing the any information about the key.The following is the most common five related types of cryptographic attacks: Known plain text, Chosen plain text, Cipher text only, Chosen cipher text, Adaptive chosen cipher text.

Problem statement
The use of Internet and network is growing rapidly.This growth showed the need of protect the Arabic text that is transmitted over the Internet.Therefore, many attempts start to appear to provide secure environment to protect the Arabic text transmitted over the internet, and since there is no enough algorithms to fill this gap in this field and this is in addition to the enormous development in the cryptanalysis methods, So it became necessary to find new ways to encrypt/decrypt the messages written in Arabic language to transmit it securely over the internet.

Research Objectives
The objective of this research is to find a new algorithm which is depend on the first order equation for three variables to add more security to the Arabic text when transmit over the internet.And add more complexity to guess the correct text when applying a cryptanalysis on Have expanded to the performance of the parameters that used in the encryption processes [3].Prakash Kuppuswamy, Saeed Q Y Al-Khalidi (2012) a new symmetric key algorithm using modular 37 and select any number and calculate inverse of the selected integer using modular 37 is proposed.The symmetric key distribution should be done in the secured manner [4].
Ayushi (2010) symmetric key algorithm using ASCII characters is presented.Message in plain text can be understood by anybody knowing the language as long as the message is not codified in any manner [8].
From literature above we observed that, all these research uses the one random number to generate the key and the key generating mechanism is clear and using one format for generating the key, but in our proposed algorithm we use two random numbers to generate the key and moreover, the mechanism of generating the key is not constant and doesn't use constant format for the equation to generate the key and encrypt the message, but we use different equations as in the methodology section.

Result and discussion
The results show the encryption and decryption time is faster comparing to the stream and block cipher and also show the performance of the proposed method is better comparing with the stream and block cipher.Moreover, through using berlekamp massey cryptanalysis against the proposed method, the results shows failing of this cryptanalysis method to break the Arabic cipher text for the proposed method and didn't success to guess the correct keys and correct equation used in encryption the message, also using linear feedback shift register (LFSR) cryptanalysis lead to same results as in berlekamp massey.Table (1   By using different types of cryptanalysis methods such as berlekamp Massey cryptanalysis, linear feedback shift register (LFSR), autocorrelation attack, brute force attack , frequency attack, m-138 cipher text only attack and sidechannel attack on the proposed algorithm, the results showed that this method investable against this types of cryptanalysis, and couldn't guess the correct equation and doesn't guess the correct keys, because of guessing the correct equation and three variables requires number of attempts up to n! times which requires many years to break the cipher text, from the result above we concluded the strength of proposed algorithm and strength of the key generation technique.Moreover, the key generation technique is easy to compute but hard to invert which means that this algorithm is a one way function which means that P≠NP, and this leads to the fact that this problem is NP-hard problem.In the future we can use the second order equation to encrypt and decrypt the Arabic text.

Vol: 13
No:1 , January 2017 DOI : http://dx.doi.org/10.24237/djps.1301.67AP-ISSN: 2222-8373 E-ISSN: 2518-9255 this text.Moreover, to evaluate the inevitability of the proposed encryption technique against berlekamp Massey and linear feedback shift register.Literature Review Because of the huge and great development of encryption and cryptanalysis systems, many research which was carried in this area to improve or develop the cryptographic methods to make the encrypted texts most secret.Ragheb Toemeh, Subbanagounder Arumugam (2008) the Cryptanalysis of polyalphabetic by applying Genetic algorithm is discussed, and the applicability of Genetic algorithms for key space searching of the encryption method has been studied.By applying Genetic Algorithm in Vigenere cipher, the key size guessing is done.The frequency analysis is applied as an extremely important factor in objective function [9].John Justin M, Manimurugan S (2012) the paper focuses basically on the different types of encryption techniques that are existing, and wording all these techniques together in a literature survey.The study aimed to experimental study of the implementations of various encryption techniques.Also the study focuses on the information encryption techniques, image encryption techniques, Chaos-based encryption techniques and double encryption techniques.This study

Figure 1 :
Figure 1: Synthetic Specific Value for Arabic Alphabet

Figure 4 :
Figure 4: frequency attack on the proposed method By applying the berlekamp Massey cryptanalysis to guess the correct equation used in the proposed method and then guess the correct keys to obtain the correct plain text for the proposed method, the results showed that the cryptanalysis technique couldn't guess the correct equation used in the proposed method, so it's very difficult to break the cipher text as it shown in the Figure (7) below:

Figure 5 :
Figure 5: berlekamp Massey cryptanalysis on the proposed method

Figure 6 :Figure 7 :
Figure 6: linear feedback shift register cryptanalysis on the proposed method also by using auto correlation attack in order to trying to break the cipher text of the proposed method, the results showed that the correlation between the characters is very poor so it means that, it's difficult to guess the correct characters of the cipher text as it shown below in the Figure (9):