Enhanced 3-D PLAYFAIR Cipher

Transcription

1 Enhanced 3-D PLAYFAIR Cipher Anju Bala Research Scholar, DCSA, M.D.U. Rohtak, Haryana (India) Publishing Date: June 10, 2017 Abstract Cryptography is where security engineering meets mathematics. It provides us with the tools that underlie most modern security protocols. The Playfair cipher or Playfair square is a manual symmetric encryption technique. 3D- Playfair cipher is the multiple letter encryption cipher, which encrypts a trigraph of plaintext into corresponding cipher text trigraph. This dissertation proposed a 3d play fair cipher technique. The proposed uses the 5x5x4 matrix. The capacity of the proposed technique is 100 symbols while the existing technique can only store 64 symbols. The proposed algorithm is capable of the differentiating between the lower and upper case letter. Some special symbols are also added in proposed technique as compared to existing technique. The proposed technique double encrypts the plain text. It increases the security. The proposed technique is implemented using the MATLAB. The comparison of the proposed technique is done with the existing technique using the execution time, throughput and the avalanche effect. The increase in the throughput shows the better performance of the proposed algorithm as compared to the existing algorithm. The avalanche effect confirms the higher security of proposed algorithm as compared to existing algorithm. Keywords: Playfair Cipher, 3D-Playfair, Encryption, Decryption. 1. Introduction The Playfair cipher or Playfair square is a manual symmetric encryption technique and was the first literal digraph substitution cipher [1]. The technique encrypts pairs of letters (digraphs). The cryptanalysis of the Playfair cipher is also aided by the fact that a diagram and its reverse will encrypt in a similar fashion. That is, if AB encrypts to XY, then BA will encrypt to YX. So by looking for words that begin and end in reversed diagrams, one can try to compare them with plaintext words that are similar. To eliminate this loophole this proposed cipher does work on trigraph rather than digraphs. With the assumption, the characters of the plaintext belong to the set of ASCII characters, 64 characters among ASCII character set is considered for the cipher. For choosing 64 characters among 128, it selected 26 alphabets, 10 numerals and 28 most commonly used special characters of ASCII charter set. 3D-Playfair cipher is a case insensitive cipher, so it requires only 26 alphabets (only upper case) rather than 52 alphabets (including lower and upper case both). Here, our interest is to eliminate the security loopholes and provide a cipher which is not vulnerable to any cryptanalytic attack [1]. 2. The 3D- PLAYFAIR Cipher 3D- Playfair cipher is the multiple letter encryption cipher, which encrypts a trigraph of plaintext into corresponding cipher text trigraph. For that purpose it requires a 4 X 4 X 4 matrix to store 26 alphabets, 10 numerals and 28 special symbols. These letters are arranged in 4 X 4 X 4 matrix based on secret key. By assuming a null key the 4 X 4 X 4 matrix will be arrange as following (Sequence of 64 characters) [1]. 3D-Playfair cipher has mainly 3 algorithms, Key- Matrix Generation, Encryption and Decryption. These are described below- 2.1 Key-Matrix Generation 3D-Playfair Cipher makes use of 4 X 4 X 4 matrix (table), which is used to store a keyword that becomes the key for encryption and decryption. Storing keyword into 4 X 4 X 4 matrix is based on some simple rules, [2] as below. i. Enter the secret (password) which may contain numerals, alphabets and special symbols like: aman2012nitj@gmail.com, ravindra_1987_singh@nitj.ac.in, cipher, etc. 37

2 ii. Find out the keyword by dropping the duplicate letters of key. Ex: cipher, for above keys. from the trigraph (Dropping any extra X and Z that don't make sense in the final message when finished) to find out the actual text (plaintext) [3]. iii. iv. Arrange the keyword in 4 X 4 X 4 matrix floor by floor, row-wise: left to right and then top-to-bottom. Fill the remaining spaces in the matrix with the rest of numerals (0-9), alphabets (A-Z), special symbols that were not the part of our keyword. For the secret FRIENDS4EVER@NITJ_2012.CSE, keyword will be FRIENDS4V@TJ_201.C and Key- Matrix will be [3]: 2.2 Encryption Code To encrypt a message, one would break the message into trigraph (groups of 3 letters). If any two letters are the same or only one letter is left, add two filler letter X and Z after the first letter in the trigraph. And if any two letter is left, add a filler x after the second letter. So that BALLOON would be treated as {BAL}, {LOX}, {ONX}, and HELLOWORLDS would be treated as {HEL}, {LOW}, {ORL}, {DSX} and would be treated as {MAS}, {TI_}, {M.T}, {ECH}, {@NI}, {TJ.}, {201}, {2XZ}. A letter in the trigraph will be replaced by the letter that will lay on the same row of the letter and the column of the next letter and at the floor of next-tonext letter in circular fashion. [4] Circular fashion means if we consider 1st letter for encryption then 2nd letter will be the next letter and 3rd letter will be the next-to-next letter and if we consider 2nd letter for encryption then 3rd letter will be the next letter and 1st letter will be the next-tonext letter and if we consider 3rd letter for encryption then 1st letter will be the next letter and 2nd letter will be the next-to-next letter [2]. 2.3 Decryption A letter in the trigraph will be replaced by the letter that will lay on the same row of the letter and at the floor of the next letter and the column of next-to-next letter in circular fashion. Remove the filler letter 3. Proposed Work 3D-Playfair cipher is the multiple letter encryption cipher, which encrypts a trigraph of plain text into corresponding cipher text trigraph. The size of the matrix increases to increase the capacity of the playfair. But it can increase the execution time. The proposed work has the matrix of size 5X 5 X 4. So the total capacity of the matrix is 100 symbols. It includes 26 lower case alphabet, 26 upper case alphabets, 10 digits, 38 special symbols. These key matrix are used for encryption by using the following algorithm [5]. 3.1 Proposed Algorithm 1. Input secret Key say K. 2. Remove duplicate characters from K. 3. Arrange the keyword in 5X 5 X 4 matrix floor by floor, row-wise: left to right and then top-to-bottom. 4. Fill the remaining spaces symbols that were not the part of our keyword. 5. Input plain Text say P. 6. Break the message into trigraph (groups of 3 letters) 7. If any two letters are the same or only one letter is left then fill the remaining places by using NULL. 8. Encrypt the P using table Newcipher= 10. For each character in secret key say Si 11. Pi=Find position of Si 12. If i==1 13. Result= binary(pi) 14. Else 15. Result=xor(result,binary(pi)) 16. End if 17. End 18. For each character in cipher text say Ci 19. Pos=find Ci position 20. New Pos= xor(result,pos) 21. newcipher =append(newcipher,charat(newpos)) 22. end 23. new cipher is the encrypted text 38

3 3.2 Decryption Algorithm 1. Input secret Key say K. 2. Remove duplicate characters from K. 3. Arrange the keyword in 5X 5 X 4 matrix floor by floor, row-wise: left to right and then top-to-bottom. 4. Fill the remaining spaces symbols that were not the part of our keyword. 5. Input Cipher Text say C. 6. Newcipher= 7. For each character in secret key say Si 8. Pi=Find position of Si 9. If i==1 10. Result= binary(pi) 11. Else 12. Result=xor(result,binary(pi)) 13. End if 14. End 15. For each character in cipher text say Ci 16. Pos=find Ci position 17. New Pos= xor(result,pos) 18. newcipher =append(newcipher,charat(newpos)) 19. end 20. Break the newcipher into trigraph (groups of 3 letters) 21. If any two letters are the same or only one letter is left then fill the remaining places by using NULL. 22. Plain=Decrypt the newcipher using table Plain is the decrypted text Table 1: Floor Based On Secret Key Table 2: Floor 2 Based On Secret Key Table 3: Floor 3 Based On Secret Key The above algorithms can be easily explained by the following Example. The secret key is PankajAttri@murthal.ac.in, drop the duplicate letters. It will result PankjAtri@muhl.c Arrange the keyword in 5X 5 X 4 matrix floor by floor, row-wise: left to right and then top-to-bottom. Fill the remaining spaces symbols that were not the part of our keyword. The 3-d keymatrix generated on the basis of the secret key is shown below: 39

4 Table 4: Floor 4 Based on Secret Key Table 6: Relative Value of Letters Then Break the message into trigraph (groups of 3 letters) and fill blank places by using the NULL. The encryption process carried out n the basis of table 5. Table 5: Encryption Process Then the relative position of the character generated in cipher text and key can be found by using the table 6. The key relative position is shown in table 7. Table 7: Secret Key Relative Position Similarly the relative position of the cipher text can be generated and the xor to get the new position. The new position character are the resultant encrypted text. The decryption process goes in reverse manner. The only difference is the decryption process shown in table 8. 40

5 Table 8: Decryption Process Table 9: Analysis of Proposed Algorithm 4. Performance Parameter Table 10: Analysis of Existing Algorithm For an algorithm it is important to be efficient and secure. Efficiency of an algorithm is computed on the bases of time complexity and space complexity. Execution Time Throughput Avalanche Effect The execution time is considered the time that an encryption algorithm takes to produce a cipher text from a plaintext. Execution time is used to calculate the throughput of an encryption scheme. It indicates the speed of encryption. The throughput of the encryption scheme is calculated as the total plaintext in bytes encrypted divided by the execution time. Throughput = (Total plaintext in bytes encrypted) / (Total Execution Time) * 100 Avalanche effect is important characteristic for encryption algorithm. This property can be seen when changing one bit in plaintext and then watching the change in the outcome of at least half of the bits in the cipher text Avalanche Effect: Number of bits flipped in cipher text/number of bits in cipher text *100 % Hear we will evaluate proposed encryption model with existing encryption model on above mention parameter and results are shown in table 9 and table

6 E x e c u t i o n T i m e Proposed Existing Table 11: Effect of Avalanche So the avalanche effect is % in proposed that varies from 0 to % in existing. On average the existing technique has avalanche effect while the % in proposed. T h r o u g h p u Figure 1: Comparison of Execution Time t Figure 2: Comparison of Throughput Proposed Existing In cryptography, the different types of cryptanalytic attacks are: (1) Cipher text only (Brute force) attack, (2) Known plaintext attack and (3) Chosen plaintext/cipher text attack. In the example illustrated in above table, the length of the cipher text in is 6*7=42 binary bits and the length of the plaintext is also 42 bits. Thus, in order to arrive at the cipher text, the size of the plaintext space which is to be searched is The time required for this is enormously large. Hence, this sort of cipher text only attack is ruled out. The plaintext is known at the beginning whereas the cipher text at the end and in the between we have the procedure which not only includes substitution but also randomization. Therefore the correlation between plaintext and cipher text is not possible. Thus, breaking the cipher in the case of the known plaintext attack also is impossible. 5. Conclusion The proposed uses the 5x5x4 matrix. The capacity of the proposed technique is 100 symbols while the existing technique can only store 64 symbols. The proposed algorithm is capable of the differentiating between the lower and upper case letter. Some special symbols are also added in proposed technique as compared to existing technique. The proposed technique double encrypts the plain text. It increases 42

7 the security. The proposed technique is implemented using the MATLAB. The comparison of the proposed technique is done with the existing technique using the execution time, throughput and the avalanche effect. The increase in the throughput shows the better performance of the proposed algorithm as compared to the existing algorithm. The avalanche effect confirms the higher security of proposed algorithm as compared to existing algorithm. References [1] Kaur, A., Verma, H. K., & Singh, R. K. (2012). 3D (4 X 4 X 4)-Playfair Cipher. International Journal of Computer Applications, 51(2), [2] Kaur, A., Verma, H. K., & Singh, R. K. (2013, August). 3D Playfair cipher using LFSR based unique random number generator. In Contemporary Computing (IC3), 2013 Sixth International Conference on (pp ). IEEE. [3] Kumar, V., kr Upadhyay, S., Mishra, S. K., & Singh, D. Modified Version of Playfair Cipher Using Linear Feedback Shift Register and Transpose Matrix Concept. [4] Bhattacharyya, S., Chand, N., & Chakraborty, S. (April, 2013) A Modified Encryption Technique using Playfair Cipher 10 by 9 Matrix with Six Iteration Steps. International Journal Of Engineering And Computer Science ISSN: Volume 2 Issue 4 Page No [5] Vidiksha, (2013) Data Encryption and Decryption using Deterministic Random Key for Transmission: A Review, International Journal of Advanced Research in Computer Science and Software Engineering, Volume 3, Issue 8, August 2013 ISSN: X.. 43