Archana, Ashish Vashist IJSRE Volume 05 Issue 07 July 2017 Page 6742 Volume||5||Issue||07||July-2017||Pages-6742-6747||ISSN(e):2321-7545 Website: http://ijsae.in Index Copernicus Value- 56.65 DOI: http://dx.doi.org/10.18535/ijsre/v5i07.08
Hill Cipher and Self Repetitive Matrix for Encryption and Decryption
Authors
Archana1, Ashish Vashist2
1
Student, Computer and Science, Kururkshetra Institute of Technology and Management, Kurukshetra
2
Assistant Professor, Kururkshetra Institute of Technology and Management Kurukshetra Email- [email protected]
ABSTRACT
The role of cryptography in today’s era is most significant. It not only secures information mathematically by mailing massage with a key but also provides confidentiality. Hill cipher is also one of the most famous symmetric cryptosystem that can be used to protect information from unauthorized access. This paper gives us dimensions of new technique in Hill cipher, here we are developing the complex procedure of key generation for the process of encryption of message to avoid any kind of data loss. Hill cipher is a matrix based poly graphic substitution which is an additional factor. The method of generating self-repetitive matrix for Hill Cipher algorithm has been proposed. In the self-repetitive matrix generation method, the matrix used for the encryption is itself self-invertible. So, at the time of decryption, we need not to find inverse of the matrix.
Key Words : Hill Cipher, Encryption, Decryption, Self-repetitive matrix, modified Hill Cipher
INTRODUCTION
Archana, Ashish Vashist IJSRE Volume 05 Issue 07 July 2017 Page 6743 HILL CIPHER
The core of Hill-cipher is matrix manipulations. It is a multi-letter ciphers ,developed by the mathematician Lester Hill in 1929. In encryption, algorithm takes m successive plaintext letters & instead of that substitutes m cipher letters. Futher said as Hill Cipher is an application of linear algebra, alphabets etc. in cryptography. The Hill Cipher algorithm take m successive plain text information & substitute m cipher info letter from them.
The substitute is determined by m linear equ. in which in which character is assigned a numerical value (a=0, b=1,….,z=25). Let m be a positive integer, the idea is of taking m linear combinations of the m alphabetic characters in one plaintext element generating m alphabetic characters in one cipher text elements.Then m*m matrix is used as a key of the system such that A is invertible module 26 but here we are considering much more values that changes the values to module 97 which include all letters and numeric values too. In Hill cipher each character is assigned a numerical value like:
A=0, B=1, .. .. .. Z=25.
The substitution of cipher text letters in place of plaintext generates m linear equations. For m=3, the systemcan be described as follows:
C1=(K11P1+K12P2+K13P3)MOD26 C1=(K21P1+K22P2+K23P3)MOD26
C1=(K31P1+K32P2+K33P3)MOD26. so on.
This can be expressed in terms ofcolumn vectors and matrices: C=KP
Where C is column vectors of length 3,P is representing the plaintext and the cipher text and K is a 3*3 matrix, which is the encrypted key. All operations are performed mod 26 here. Decryption have the inverse of matrix K. The the equation.K K-1= I where I is the Identity matrix.
NOTE: The self repetitive matrix help for information security and data confidentiality.
K-1 is applied to the cipher text, and then the plain text is recovered. In general terms we can write as follows:
When encryption: C=Ek(P)=Kp
When decryption: P=Dk(C) =K-1 C= K-1Kp=P Example: (For Modulo 97)
K = 0 0 78 0 0 0 0 0 24 0
Archana, Ashish Vashist IJSRE Volume 05 Issue 07 July 2017 Page 6744 Let m = 5, n = 97 and Seed number S =141
Then, K11 = 141 K22 = (K11*2) mod n ..
...
K55 = (K44*5) mod n Hence Key Matrix.
Consider the plaintext to be encrypted is “event” Letters of the plaintext are represented by their equivalent number vector (30 47 30 39 45) Then with the help of key matrix, encryption
matrix is generated. Encryption matrix we get as then Cipher text for the plain text is eg :[17 88 78 7 23]
Decryption can be done by doing inverse done by doing inverse method of above and the cipher text is converted to the original as “event”. Thus replacing the vector numbers (30 47 30 39 45) by their ASCII values we get the word “event”.Event is nothing just a name given to encrypted contents.
Self-invertible Matrix Generation Method
In Hill cipher, decryption requires invers of the matrix, we will be useing the self-invertible matrix generation method, also encryption in the Hill Cipher.In the self -invertible matrix generation,method, the matrix used for the encryption it itself self- invertible. So, at the time of decryption, we need not to find inverse of the matrix. A general method of generating self invertible matrix is substitute of its equivalent characters andwhich is the plaintext.
Novel Modification to the Algorithm
Archana, Ashish Vashist IJSRE Volume 05 Issue 07 July 2017 Page 6745 repetitive matrix. It should be non singular square matrix. This is also called as
itself repetitive matrix. .
Note: There are already many available methods, like self invertible matrix etc. but this method as suggested because it have both values easy to compute and simpler to implement.
In order to overcome this problem we suggest the use of self repetitive matrix.This matrix if multiplied with itself for a given mod value (i.e. mod value of the matrix is taken after every multiplication).
Generation of a self repetitive Matrix A for a Given N:
The generation is not that complex because we have to keep two things in our mind The initial conditions for the existence of a self of repetitive matrix are
1. The matrix should be square 2. It should be non-singular.
In trying to find out the value of N (the value where the matrix becomes identity matrix) through the method of brute force may not bethe best idea all time; because the matrix is of
dimension greater than 5*5 and with mod index(i.e.) greater than 91 then the brute force technique will be time consuming and also N value may be in the range of millions. A normal Pentium4 machine might hang if asked to do the calculations for 15*15 matrixes even more. Hence, it would be comfortable to know the value of N and then generate a random matrix
accordingThiscan be done as follow:
1. First a diagonal matrix A is selected , and Further values powers of each individual element when they reach unity is calculated and denoted as n1, n2, n3…. Now LCM of these values is taken to given the value of N
2. Now another step is generate a random square matrix whose value of N is same as 3. Take any random invertible square matrix B. The N calculated in the previous step.
GENERAL STEPS:
Steps At The Transmitter Side:
1. Take The Data In Blocks Of 5 As A Column Matrix Denoted By E 2. Multiply E The Matrix Generated Earlier With C(N-M) To
Generate The Encryption Code.(C Was Generated Earlier ) 3. M Is Some Random Number Selected And Known To Both The Ends. M<N.
4. Now Convert This Code Into Machine Code To Give Better Compression And Bit Saving.
(Note:The Algorithm For Conversion Into Machine Code Has Been Discussed Later.)
Steps At The Receiver Side:
1. Decompress The Hex Code Into Mod-97 Code 2. Then Multiply The Code Column Matrix With Cm. 3. The Corresponding Sustitutions Are Made And Text Recovered..
Note: Mathematical Background For The Above Technique Has Been Given In The Section For Hill-Cipher Previously.
Method For Compression Into Hex Code:
Archana, Ashish Vashist IJSRE Volume 05 Issue 07 July 2017 Page 6746 2. Now Divide The Polynomial By 16 To Generate A Remainder.
3. The Quotient Generated Forms The Next Dividend Polynomial And Divison Is Carried Out Once More And Remainder Collected. 4. This Process Is Carried On Untill Divisor Is Larger Than The Dividend.
5. All The Remainders Are Collected And The Array Is Inverted. This Is The Compressed Code
CONCLUSIONS
The HILL cipher technique using a novel method of self repetitive matrix was
successfully implemented. A transmitter-receiver pair was successfully modeled which used proper decompression techniques for effective communication. The numerical method suggested to find N value of a matrix was successfully tested and correlation between Eigen values and N value of a matrix. Here the algorithm is modified so it provide great security thus no one in between sender and receiver will hack the data.
Future Scope
The main achievement is the correctly functional tool of hill cipher. Unfortunately time constraints have meant that not all the originally mentioned objectives were accomplished. The various compression techniques may be applied for efficient utilization of bandwidth and storage. This system can be extended to work on the files containing Unicode characters as well leads too the formation of minor codes. This application can be extended to work with other file formats. By addition of transferring of data from one system to another, system can be enhanced.
Implementation of signatures for all higher levels :
Authorities with all means of confidentiality and authentication also it maintaines the rules and regulations regarding the various levels.The signature has been the foundation of business and government transactions for thousands of years. However, the tools of government and commerce are changing. Bits and bytes are replacing pen and parchment. Information is being created, transformed and transferred more often and more rapidly than ever before.The use of server certification for our Internet sites is another reasonable step for local government to take now. The move toward electronic service delivery and our ability to accept electronic payment depends on our ability to establish trust with those who use our systems. Accepting electronic payment of fees, fines and even utility bills has the potential for greatly reducing processing costs for city government
Real time security with distributed network system:
(1) Performing real-time encoding of the users who accessed the protected files and folders. (2) Limiting the user‟s capability to edit the protected documents
(3) Tracking transmitted files to the outside companies (4) Blocking the user‟s access to portable storage devices (5) Inserting security water marks on the printed outputs.
REFERENCES:
1. G.R. Blakley, Twenty years of cryptography in the open literature, Security and Privacy 1999,
Proceedings of the IEEE Symposium, 9-12 May 1999.
2. H. Imai, G. Hanaoka, J. Shikata, A. Otsuka, A.C. Nascimento, Cryptography with information theoretic security”, Information Theory Workshop, 2002, Proceedings of the IEEE, 20-25 Oct 2002. 3. A. J. Menezes, P.C. Van Oorschot, S.A. Van Stone, Handbook of applied cryptography
Archana, Ashish Vashist IJSRE Volume 05 Issue 07 July 2017 Page 6747 4. J. Overbey, W. Traves, J. Wojdylo, On the Keyspace of the Hill cipher. Cryptologia,
29(1), 2005, 59-72.
5. K. Petersen, Notes on number theory and cryptography,2000. Http://www.math.unc.edu/ Faculty/petersen/Coding/cr2.pdf.
6. Barr T.H., Invitation to cryptography (Prentice Hall, 2002)
7. W. Stallings, Cryptography and network security (4th edition, Prentice Hall, 2005)
8. Alam A., Sehat ullah, Itiaq W., Khalid S., (2011), International journal of advance computer science, Vol. 1, No. 3, pp. 113-117.
9. David S., (2008), “ The playfair cipher” Vinculum Vol. 45, No. 2, pp. 4-6.
10. Dhenakaran S. S., Llayaraja M., (2012)” Extansion of Playfair Cipher usinf 16×16 Matix”, International Journal of computer, Vol. 48, No . 7, pp. 37-41.
11. Hassan. H. A., Seab M., and Hameed H. D , (2005), “ The Pyramids of Block Cipher”, 12. International Journal of Network Security. Vol.1, No. 1, PP. 52-60.
13. Krishna A. V. N., Madhuravani K., (2012), “A Modified Hill cipher using Randamized Approach” I. J. Computer Network and Information Security, No. 5, 56-62.
14. Manas P. , Jyotsna K., (2012), “ A General Session Based a Bit Level Block Encoding Technique using Symmetric key Cryptography to enhance the security of Network Based Transmission”, International Journal of computer science, Engineering and Information Technolgy, Vol. 2, No. 3, pp. 31-42.
15. Michael A., (1995), The Metaphor is the key: Cryptography, the Clipper chip and the Constitution, University of Pennsylvania law Review, Vol. 143, No. 3.
16. Rushdi A., Farajallah M., (2009), “ A Design os a roust cryptosystem algorithm for Non- Invertable Matrices Based on Hill cipher”, International journal of computer science and Network Security, Vol. 9, pp. 11-16.
17. Sreenivasulu R., Murali S., (2012), International Journal of computer science and information technology, Vol. 2, No. 1, pp. 121-124.
18.Lalana, K., Tim, F., Anupam, J.: Developing secure agent systems using delegation based trust
