# FAREY FRACTION BASED VECTOR PROCESSING FOR SECURE DATA TRANSMISSION

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1 FAREY FRACTION BASED VECTOR PROCESSING FOR SECURE DATA TRANSMISSION INTRODUCTION GANESH ESWAR KUMAR. P Dr. M.G.R University, Maduravoyal, Chennai. Every day, millions of people use telephones, fax machines, and computer networks for interactions. Sensitive data is transmitted over insecure channels leading to eavesdropping. The accelerating introduction of electronic communication will increase the importance of information security, i.e. all the questions concerning privacy, authenticity, authority etc. Some of the examples of business deals happening over public channel are insurance companies deals, doctors and medical centers carry on electronic exchanges about patient treatment, money transfers across the glob to various bank accounts, there is a need for means to provide for the integrity of information. A very important part of the solutions on the information integrity is cryptographic in nature. OBJECTIVE OF THE WORK Signature: Verify the identity of origination. Integrity: Ensure that the message or transaction received is same as that sent, without accidental Non Repudiation: Prove to a third party that transaction actually took place. This having engaged in transaction. Privacy (Secrecy): Keep communications private. Physical protection mechanisms have evolved to ensure the privacy of transactions. CRYPTOLOGY: It is the science of cryptography and cryptography is the art of designing process of encryption and decryption. Cryptology provides the logic, the technique of producing the cryptograms (the method of encryption).present day public encryption service is based on large prime number occupying around 1024 bits.our main aim in the present paper is the extension of encryption process using product of prime numbers we are trying to generate a group of integers from the product of prime numbers. With the help of this prime number we will develop a cryptology process to generate secure codes for the encryption of the sensitive data. These codes are generated in such a way to conceal the sensitive data so that it could be prevented from hacking. METHODS OF DOING ENCRYPTION Introduction: - ACS-International Journal on Computational Intelligence, Vol-1, Issue-1 Aug

2 GANESH ESWAR KUMAR. P Industrial espionage among highly competitive businesses often requires that extensive security measures be put into place. And, those who wish to exercise their personnel freedom, outside of the oppressive nature of governments, may also wish to encrypt certain information to avoid suffering the penalties of going the wishes of those who attempt to control. Still the method of data encryption is relatively straightforward. METHODS OF ENCRYPTING DATA: Traditionally, several methods can be used to encrypt data stream, all of which can easily be implemented through software, but not so easily decrypted when either the original or its encrypted data stream are unavailable (when both source and encrypted data are available, code-breaking becomes much simpler, though it is not necessarily easy). The best encrypting methods have little effect on system performance The encryption method consists of two methods: i) Conventional method ii) Public key method CHARACTER-LEVEL ENCRYPTION: In this method, encryption is done at the character level. Character level encryption consists of two methods: i) Substitutional ii) Transpositional BIT LEVEL ENCRYPTION: of bits then altered by encoding / decoding, Permutation, Substitution, Exclusive OR, Rotation Data Encryption Standards (DES): One example of bit level Encryption is the data encryption standards (DES). DES was designed by 22 ACS-International Journal on Computational Intelligence, Vol-1, Issue-1 Aug 2010

3 Farey Fraction Based Vector Processing for Secure Data Transmission military use. The algorithm encrypts a 64-bit plain text using a 56-bit key. The text is put through 19-bit cipher text. PUBLIC KEY METHOD: In Public key Encryption, every user has the same encryption algorithm and key. The decryption algorithm and key however are kept secret. Anyone can encrypt information, but only an authorized receiver can decrypt it. The decryption algorithms designed in such a way that it is not the inverse of the encryption algorithms use completely different functions, and knowing one does not enable a user to know the other. In addition the keys are different. ACS-International Journal on Computational Intelligence, Vol-1, Issue-1 Aug

4 GANESH ESWAR KUMAR. P The encryption algorithm and key are publicly announced. Every customer can use them. The decryption algorithm and key are kept secret and used only by the bank. Encryption Algorithm: The Encryption algorithm follows these steps in RSA encryption. Encode the data to be encrypted as a member to create the plain text P. Calculate the Cipher text C as C= P Kp modulo N (modulo means divide P Kp by N and keep only the remainder). Send C as the cipher text. In RSA scheme, the system uses a private and a public key. To start two large prime numbers are selected and then multiplied together; n=p*q. If we let f(n)=(p-1)(q-1),and e>1,such that GCD (e, f(n))=1. be a part of encryption key. If we solve the linear equation; Ed congruent 1(mod f (n)), for d. The pair of integers (e, n) are the public key & (d, n) form the private key. Encryption of M can be accomplished by the following expression; Farey Fractions: Me = q n + c where 0 < c < n. Farey sequences are named after the British geologist John Farey Sr. Farey conjectured that each term in a Farey sequence is the median of its neighbour. The Farey fraction sequence is proved by Cauchy. 24 ACS-International Journal on Computational Intelligence, Vol-1, Issue-1 Aug 2010

5 Farey Fraction Based Vector Processing for Secure Data Transmission - ing size. Each Farey sequence starts with the value 0, denoted by the fraction 0/1 and ends with the value 1, denoted by fraction1/1. 0<a<b<=n & (a, b) == 1 arranged in increasing order. F1 = {0/1, 1/1} F2 = {0/1, 1/2, 1/1} F3 = {0/1, 1/3, 1/2, 2/3, 1/1} F4 = {0/1, 1/4, 1/3, 1/2, 2/3, 3/4, 1/1} The Farey sequence is a well known concept in no. theory. Several interesting solutions exist for this problem. Farey Sequence: The sequence of all reduced with denominator not exceeding n, listed in order of their size is called STEP 1: STEP 2: ACS-International Journal on Computational Intelligence, Vol-1, Issue-1 Aug

6 GANESH ESWAR KUMAR. P Then N = n-y STEP 3: Divide N into block of integers and assigning each letter to each block through one to one mapping. STEP 4: STEP 5: The corresponding inverse alphabet is considered. STEP 6: Then considering the Block Number to which the inverse integers and inverse alphabets belong. Example of Encryption Process: P1=7, P2=7 & P3=11.The important fact we keep in mind is that it is not necessary to restrict our self to just the two prime numbers. 26 ACS-International Journal on Computational Intelligence, Vol-1, Issue-1 Aug 2010

7 Step 1: Compute n & N. We compute N=7*7*11=539, note that n is composite (not a prime) number. Now we have communicative group N which is a set of all integers from 1 to 539 excluding the integers 7 & 11 and their multiples. N={1,2,3,4,5,6,8,9,10,12,13,15,16,17,18,19,20, } Farey Fraction Based Vector Processing for Secure Data Transmission totally 119 integers that do not belong to N. Hence N has totally 539-( ) =420 integers which have their inverse element in N under modulo n. Step 2: dividing N into blocks of integers. We now divide the set of all integers N to number of blocks.for simplicity we make the following assumption. Leaving 1 & 538 as there inverse are themselves, we are left with 418 integers. Blocks are of size 26 integers (to increase the complexity we can choose the blocks of different sizes).one to one onto mapping of integers in each block with each English alphabet with integers can be made randomly for further increase in the complexity. Then we have total of 17 blocks, 16 of them are of size 26 integers each and last block is of size 2 integers, constituting total of 418 integers. ACS-International Journal on Computational Intelligence, Vol-1, Issue-1 Aug

8 GANESH ESWAR KUMAR. P Step 3: Association of Alphabets with Blocks Associate each alphabet of the plain text JEERY with different blocks in random way as J B1 E B3 E B7 R B9 Y B16 * NOTE- only one letter is chosen for each block. The table below gives the complete picture about the encryption process of the plain text into cipher text. We do select the blocks and associate the integers with alphabets randomly so that the hacker task Encryption test result: Natural number: 539 No of invertible elements: 418 Plain text per block: Plain text ACS-International Journal on Computational Intelligence, Vol-1, Issue-1 Aug 2010

9 engineering college. The topic of my project is implementation of encryption scheme on internet and intranet security. The basic concept of my project is using modulo inverse technique Cipher text GGVKFHQLHHDTRSGEJDUHJK/IERJR%%HGHUFYWDHYFHDDUIAFJBGAFIFGLHGI GOIRHPOPEVKIEHWFGQEWTFEIGYGENBLKJPRJBNBIIBNBJNRJHRHNBRHJRHNHRJ HLKHRHJRHJRHJHJHJIOW. Number of Keys used = 04 Nature of plain text = Alphabets Nature of Cipher text = Alphabets Frequency Analysis: Number of character matching 0% Security level = High Number of levels of Security = 04 Nature of the primary key = Fractions Nature of the secondary keys = Fractions. RESULT ANALYSIS: Farey Fraction Based Vector Processing for Secure Data Transmission The Proposed method maintains the cryptosystem which is simple, highly secured with the following advantages. I. The transmitted key does not give any room for the hackers to guess when it is interrupted / inter cepted. The very reason for the same is that, the key may be numerals or name of a person whose date of birth can be used as a key. II. The primary Key is not used for the encryption/ Decryption, but series of secondary keys are generated and the same is used in sequence for encryption. Similarly at the receiving end the series of Inverse keys are generated using the primary key and the same is used in sequence for the decryp tion process. III. Farey fractions are used to generate the primary key, which makes more confusion for the hackers to break or interpret the code. impossible to break the code using the frequency analysis. CONCLUSION Identifying the number of blocks which are arbitrarily different sizes. It will be a very cumbersome ACS-International Journal on Computational Intelligence, Vol-1, Issue-1 Aug

10 GANESH ESWAR KUMAR. P the integers in each block. This is purely a random process. Blocks with integers fewer than 26 will not have all alphabets from English language associated. However this can be advantage as it confuses the chosen for a better understanding and of increasing the complexity of decryption for a hacker. The crucial thing for encryption is the omission 1 and 538 from the set of blocks. The omission are the simplest of give-always while the hacker tries in decrypting the message: the 1 hint the hacker get straight away is: own reverse. The same motive makes us to remove the number 538 from all consideration. We have 181 prime numbers of size less than 4 digits between 1 and 1000.we can obtain the larger number, but at this stage, it becomes less important that to design methods of using these already accessible primes to construct security system. The principle is to design newer methods based on the already known primes. LIST OF REFERENCES [2] Ronald L. Riverst, A. Shamir, and L. Adlernan. A method for obtaining digital signatures and public-key cryptosystems, Communications of the ACM, volume 21, Feb. 1978, pp [5] H. Chandrashekhar, Algebraic coding theory based on Farey Fractions, Thesis Submitted to the Bangalore University for the award of the Ph. D. Degree. 1997, Feb. 1978, pp [7] Concepts of Programming Languages Eighth Edition by Robert W. Sebesta. [8] Database Management Systems Third Edition by Rama Krishnan and Gehrke. IJCI-2K ACS-International Journal on Computational Intelligence, Vol-1, Issue-1 Aug 2010

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