Information security using Z transforms and finite state machine

 

ABSTRACT:

Information security is the most burning topic in the field of computer science and engineering. Encoding is a very easy process but decoding is not so easy unless we know the apt key. Key management is very important in cryptology. Generating dynamic keys is most essential now a days and also the cipher text.

In mathematics the Z transforms converts discrete data sequence, which is real or complex in to complex domain. It is useful in many areas such as digital Signal processing, control theory, economics etc.

Automata theory is the study of abstract computing devices or machines. In computer science we find many examples of finite state system and the theory of finite state systems, as a useful design tool for these systems.

In the present paper an innovative technique for encrypting and hiding the data is proposed based on finite state machines and Z transformation. The efficacy of the proposed method is analysed, and the analysis shows an improved cryptographic protection in digital signals.

 

 

 

1. INTRODUCTION:

In the existing e world security problems plays very important role. Solution to the security problems are depends on many other security issues, which is again a problem to solve. It very difficult to overcome all security issues. Therefore dynamic key generation and management solves few security problems we discuss generate key and encrypt the message using the key in this paper.

 

We know that Cryptography is” the secret code for a given message”, but it is secret code till there is no attack on it. If we know the key the secrecy is no more. We must protect secrecy of key used in ciphering the text from decoding using the key. We must use mathematical procedures also so strong, so that no use the procedure to decode the cipher text. Therefore key and mathematical procedures are very important.

 

We develop key in many combinations so that no intruder will attack on the cipher text. Many researchers on the key generation, with strong mathematical procedures developed deferent algorithms.

 

Srlakshmi[8] in the paper used Laplace Transformation technique but security is very low, so in this paper we enhance security by using Z transformation to enhance the security of the algorithm.

 

1.1 Cryptography:

Cryptography refers to the art of protecting transmitted information from unauthorized interception or tampering. The other side of the coin, cryptanalysis, is the art of breaking such secret ciphers and reading the information, or perhaps replacing it with different information. It uses mathematical and logical principles to secure information. Encryption means the change of original information (plain text) into another form by some operations (algorithm) and decryption means the techniques of extracting the original information by some operation (algorithm) from the encrypted data (cipher text). In private key cryptography, the encryption and decryption on plaintext is done with the same key and key is known to the sender and receiver. Cryptography is well known and widely used in techniques that manipulate information in order to cipher or hide their existence.[1][2][3][4]

 

1.2 Finite state machine:

Automata theory is a key to software for verifying systems of all types that have a finite number of distinct states, such as communication protocols or protocol for secure exchange of information. In Moore Machine, every state of the finite state machine has a fixed output. [6][7] Mathematically Moore machine is a six- tuple machine and is defined as

M= ()

: A nonempty finite set of states in Moore machine

   : A nonempty finite set of inputs.

   : A nonempty finite set of outputs.

   : It is a transition function which takes two arguments one is input state and another is input symbol. The output of this function is a single state.

   : Is a mapping function which maps  x to, giving the output associated with each transition.

  : is the initial state of

 

Moore machine can also be represented by transition table, as well as transition diagram.[5][6][7]

Example

 

Figure 1 Moore machines which calculates residue of mod 4.

 

In this paper we use FSM in a different way [8].

 

1.3 Z Transformations:

Z transformation transforms discrete function to a continuous function. We define z transform of f(n) as

Provided infinite series exists. This is called one sided Z transformation. We can also use two sided z Transformation also which is defined as

 

Some basic formulas is in Z transformations are

 

Proposed Algorithm:

Forward process:

Step 1:

Let M={m₁,m₂,………..m_n} be the plain text.

 

Step 2:

Define Moor machine through public channel. Send secret key and private key to the receiver in binary form.

We allocate 0to A, 1 to B......25 to Z to convert the message in numeric form or give any values

 

Consider a function f(n) and its Maclaurin’s series expansion. We know that Z transform of f(n) exists iff f(n) is discrete. Messages in integers are converted into coefficient of infinite series expansion of f(n) of variable order. Apply Z transform in Maclaruin’s series expansion according to the power of n transformation on each block of messages and forward it to the Moore machine. Substitute the value of the out put in each state as z value and find the secret code. This is the cipher text. One block will process the information at a time n, z transform the substitution are kept secret.

 

Step 3:

Send the cipher text to the receiver.

 

Back ward process:

Step 1:

Let C be the cipher text in blocks.

Step 2:

Use Moore machine, secret key and private key to decrypt the message using the definition of the cipher text at q(i-1)th stage.

 

Performance of the proposed algorithm:

Mathematical work:

Algorithm proposed is based on ordinary multiplication using secret key and chosen finite state machine. The secrecy is maintained in secret key, private key and finite state machine. It is very difficult to break the cipher text without proper key and the chosen finite state machine. The number of element in the sequence S must be maximum to avoid the cipher attacks.

 

Security:

It is very difficult to extract the original information, due secret key, private key.

Brute force attack on key is also difficult due to the increase in key size.

 

Table 1 Security analysis

S.No	Name of the attack	Possibility of the attack	Remarks
1	Cipher text attack	Very difficult	Due to the secret key, private key and finite state machine.
2	Known plain text attack	Difficult	Due to the chosen finite state machine and secret key.
3	Chosen plain text attack	Difficult	Due to the chosen finite state machine and secret key.
4	Adaptive chosen plain text attack	Difficult	Due to the chosen finite state machine and secret key.
5	Chosen cipher text attack	Very difficult	Due to the secret key, private key and finite state machine.
6	Adaptive chosen cipher text attack	Very difficult	Due to the secret key, private key and finite state machine.

 

CONCLUSIONS:

Algorithm proposed, is based on finite state machine and Z Transformation. Secrecy is maintained at three levels, the secret key, the chosen finite state machine, and theZ Transformations. The obtained cipher text becomes quite difficult to break or to extract the original information even if the algorithm is known.

 

REFERENCES:

1.       A. Menezed, P. Van Oorschot and S. Vanstone Hand book of Applied Cryptography e-Book.

2.       Ciphers: http://en.wikipedia.org/wiki/Cipher.

3.       W. Stallings; “Cryptography and Network Security” 2nd Edition, Prentice Hall, 1999.

4.       Bruce Schneier: Applied Piper, “Encryption”. Security and Detection, Ecos 97. European Conference;

5.       Adesh K. Pandey. Reprint 2009, “An introduction to automata theory and formal languages ‘S.K. Kararia and sons. New Delhi.

6.       John E. Hopcroft, Rajeev Motwain, Jeffrey D.Ulman. “Introduction to automata theory, language, and computation” Vanstone3^rd imp.

7.       B. Krishna Gandhi, A. Chandra Sekhar, S. Srilakshmi “Cryptographic scheme for digital signals using finite state machine” international journal of computer applications (September 2011)

8.       S. Srilakshmi “New encryption schemes using Laplace transformation and Finite state machine ”IJIRSETVol3 Issue 13 July 2017.

 

 

 

 

Accepted on 08.12.2017      ©A&V Publications All right reserved