Encryption/Decryption Algorithm for Devanagri Script(Affine Cipher)
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The document discusses the design and implementation of an encryption/decryption scheme for Devanagari script using the affine cipher, a mathematical function that maps letters to numeric values. It outlines the encryption and decryption processes, key calculation methods, and provides algorithms for implementation along with time and space complexity analysis. The conclusion emphasizes the uniqueness of the affine cipher's key determination based on character unicodes.
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- 1. ENCRYPTION-DECRYPTION of Devanagri Script Using Affine Cipher Team : Astha Goel Harshit Bhatia Mohit Singhal Prachi Gupta Swati Nagpal Deen Dayal Upadhaya College
- 2. Objective To design and implement an Encryption/Decryption scheme based on affine cipher for plain text in Devanagri(Unicode) communicating message in Hindi. Also, to develop a solver which solves the crypt when the encryption parameters(key) are not known.
- 3. Introduction CRYPTOGRAPHY Cryptography, derived from Greek words krptos- secret and graphy- writing. It is the science of using mathematics to hide information. With the help of Cryptography we can store sensitive information, or transmit it over insecure networks (such as the internet) so that it can only be read by the intended recipient.
- 4. Encryption Encryption is the process of converting readable data (called the plaintext) into a form which hides its content, called the ciphertext. Decryption Decryption is the reverse process, with a ciphertext converted back into the corresponding plaintext.
- 5. NOTE: Cryptography should not be confused with encryption. The name encryption itself defines the basic difference. EN-CRYPT: “en” means to make and “crypt or crypto” means hidden or secret. Hence, Encryption is a fundamental tool for protection of information while Cryptography is the method of transforming the representation of information for secured transmission of information.
- 6. Ciphers A cipher is a mathematical function used in the encryption and decryption processes. Most ciphers use a secret key when encrypting, and different keys will typically encrypt a given plaintext into different ciphertexts. The key is usually only known by the person who encrypts the data, and the intended recipient.The secrecy of the key ensures that even if an eavesdropper were to intercept the transmitted data, they would be unable to decrypt it.
- 7. In general the security of encrypted data is dependent on two factors: 1. The strength of the cipher. 2.The secrecy of the key.
- 8. Classes Of Cipher Affine Cipher
- 9. Affine Cipher The affine cipher is a type of monoalphabetic substitution cipher, wherein each letter in an alphabet is mapped to its numeric equivalent, encrypted using a simple mathematical function, and converted back to a letter. Each letter is enciphered with the function , E(x)=(ax+b) (mod m) where modulus m is the size of the alphabet and a and b are the key of the cipher. The value a must be chosen such that a and m are coprime. Also, 0 ≤ a < m, and 0 ≤ b < m
- 10. The decryption function is: D(x) = a-1(x-b) mod{m} Where a-1 is the modular multiplicative inverse of a modulo m, i.e. it satisfies the equation: 1=aa-1 mod{m} Special Cases: The Caesar Cipher is the Affine cipher when since the encrypting function simply reduces to a linear shift ie. when a=1. The Decimation Cipher is the Affine cipher when the encryption function reduces to (ax)MOD m as the value of b=0.
- 11. Algorithms Encryption : The value of the appropriate key (ie. Fulfilling the condition of the affine cipher), and the plaintext in devanagri is asked from the user. The characters from plaintext are mapped according to the encryption function.The mapped characters are then printed in the encrypted file using FileUtils class (provided by Apache). Decryption : The values of a & b for the decryption function, and the encrypted file are asked from the user. The pre-image of the characters is hence found and printed in the decrypted file using FileUtils class( as done in Encryption).
- 12. Algorithms Key Calculation : Take any two random characters (x1,x2) from plaintext and the corresponding mapped characters(y1,y2) from ciphertext. CASE- 1: SOLVING THE SYSTEM OF LINEAR EQUATIONS (x1, x2 has both odd and even unicodes ) I. Form the equations in terms of a & b by substituting the values of x & y in the encryption function. II. We have 2 variables and 2 equations. Solving the equations, we get the values of a & b.
- 13. CASE - 2 BRUTE FORCE (when both x1 and x2 have even OR odd unicodes only) I. For all possible values of a( ie. All the co-primes of m less than the value of m), we check for all the values of b, satisfying the encryption function. II. Then this encryption function is checked for the rest of the file text. If it matches with the rest of the file, the values for a & b are returned. III. Otherwise the value of a & b are discarded and the steps I and II are repeated again and again till the time a consistent value of key(that matches the key of the rest of the file) is not found. Note: In this case, more than 1 unique solution is possible.
- 14. Time-Complexity Encryption: O(n) Decryption: O(n) Key Calculation: * Best Case: O(n)/O(1)cz it is not not dependent on the file size now *Worst Case: O(m2n) where m = 128, n = no. of characters in original file
- 15. Space-Complexity Encryption: O(1) Decryption: O(1) Key Calculation: O(n) where n = no. of characters in original file
- 16. SystemRequirements SOFTWARE REQUIREMENTS Java Development Kit 1.6 (jdk 1.6) or more Java Runtime Environment Platform (IDE) (for running source code): NetBeans IDE 7.0.1 MEMORY REQUIREMENTS Software: 500 KB Implementation Software and Platform: 1 GB
- 17. Conclusion The key of the affine cipher can be uniquely found with just 2 characters from the plaintext and the corresponding mapped characters from the ciphertext provided the characters have odd and even unicodes. But if unicodes of both the characters are even or odd(which is somewhat a rare case), we need to compare the different combinations of key with the rest of the text to obtain single unique key for the entire text.
- 18. References Websites: http://en.wikipedia.org/wiki/Affine_cipher http://www.johndcook.com/blog/2008/12/10/solving -linear-congruences/ http://www.math.sunysb.edu/~scott/Book331/Affine _enciphering.html http://www.engineersgarage.com/articles/what-is- cryptography-encryption?page=1 http://www.javaranch.com http://cryptointro.wordpress.com