An Approach towards Development of Efficient Encryption Techniques

Abstract

In this thesis, six encryption techniques have been proposed. All techniques

are of the nature of bit-level implementation, which means that the stream of bits

under consideration is fed to the process of proposed encryption techniques. Each of

the proposed techniques is a block cipher as the stream of bits is subdivided into a

finite number of blocks of bits. The techniques are secret-key techniques as the same

key is to be used for both encryption and decryption. The proposed techniques have

been termed to as follows:

1. Recursive Positional Substitution Based on Prime-Nonprime of

Cluster (RPSP)

2. Triangular Encryption Technique (TE)

3. Recursive Paired Parity Operation (RPPO)

4. Recursive Positional Modulo-2 Substitution Technique

(RPMS)

5. Recursive Substitutions of Bits Through Prime-Nonprime

Detection of Sub-stream (RSBP)

6. Recursive Substitutions of Bits Through Modulo-2 Detection of

Sub-stream (RSBM)

Among these proposed techniques, the basic operation used in the TE

technique and the RPPO technique is the Boolean operation, whereas in the

remaining proposed techniques, non-Boolean operations have been used as basic

operations. Except the technique of RSBP, for each of the remaining techniques,

there is no storage overhead. In the RPSP technique, there exists the possibility of

the size alteration in both directions. The principle of transposition is followed in the

RPSP technique, whereas in the remaining techniques the principle of substitution

is followed. For each of the techniques of RPSP and RPPO, a cycle is generated,

through which the source block is regenerated after a finite number of iterations,

and any of the intermediate blocks is to be considered as the corresponding

encrypted block.

For each proposed technique, a key structure has been proposed. All keys

have been constructed with reasonably long key space. It is seen that using

cryptanalysis or even the brute-force attack, it is computationally infeasible to break

the keys.

All techniques have been implemented onto a real type of file streams of

various categories. Several factors have been considered to evaluate the proposed

techniques. These include the followings:

• Frequency Distribution Test

• Goodness-of-fit Chi Square Test

• Analysis of the Key Space

• Computation of the Encryption/Decryption Time

• Comparison of Performance with the RSA System

The first two factors are considered to asses the degree of security of the

proposed techniques against the cryptanalytic attack. Through the frequency

distribution tests performed on the original as well as the encrypted files, the

frequencies of all 256 characters in two files are shown graphically. Through the chi

square tests performed on the original and the encrypted files, the non-homogeneity

of the two files is tested.

The third factor plays an important role in attempting to tackle the Brute-

force attack successfully. The key space of each technique has been attempted to

enlarge reasonably to make the techniques computationally secure.

The forth factor plays an important role in assessing the efficiencies of the

algorithms from the execution point of view. Here it has been attempted to establish

a relationship between the size of the file being encrypted and the

encryption/decryption time.

Now, the time consumed in encrypting and decrypting files is related to the

code written for that purpose and the architecture of the machine where the code is

being executed. All the results in this regard are taken after compiling and executing

C codes.

The last factor attempts to evaluate the proposed techniques with respect to

the existing field of cryptography. The most popular public key system, the RSA

technique, has been considered here as the model and the comparative analysis is

done on the basis of frequency distribution and chi square distribution for the

purpose of evaluation.

It is seen that the encryption/decryption time almost linearly varies with the

source size. Since all techniques are of the nature of the bit-level implementation,

the encryption/decryption does not depend on the type of the file.

Results of the frequency distribution tests establish a clear indication that the

characters in encrypted files are well distributed. These results have been taken

graphically.

The values obtained through Pearsonian Chi Square tests strongly establish

the fact that the encrypted files are highly non-homogeneous with the respective

source files.

The comparative analysis with the results for the RSA technique establishes

the fact that these techniques are well compatible with the RSA technique, and there

also exist a number of instances in which performances of different proposed

techniques are observed to be better in terms of Pearsonian Chi Square values.

To implement proposed techniques, it is suggested to choose blocks to be of

varying lengths, so that longer key spaces may be generated to enhance the security.

Different proposed techniques also have been implemented in a cascaded

manner. In this approach, after the source file is encrypted using a technique, the

resultant encrypted file again is encrypted using another technique, and this process

goes on for all six proposed techniques. This approach of cascading ensures security

of highly satisfactory level due to the complicatedness of the approach and the

requirement of a reasonably long and informative key.

A model cascaded implementation also has been suggested using the different

proposed techniques in a highly flexible manner. This approach offers an arbitrary

sequence of implementations of different independent techniques. For each level of

implementations different block sizes may be adopted.

On the basis of the entire activity of development and simple implementation

of different proposed encryption policies, and comparison of these implementations

with the well-accepted RSA system of encryption, it may be accepted that if each of

the proposed encryption techniques is implemented independently following the

protocol of the model implementation; or if the proposed techniques are

implemented in the cascaded manner following the protocol of the model

implementation, perfect, computationally secure cipher stream may be generated;

and on the basis of all possible kinds of factors normally used for evaluation, this

may be proved to be well-compatible with the existing encryption systems.

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(J. K. MANDAL) (SAURABH DUTTA)

Supervisor Candidate