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International Journal of Advancements in Technology (IJoAT) http://ijict.org/ ISSN 0976-4860

Vol 1, No 1 (June 2010) ©IJoAT

Role of Statistical tests in Estimation of the Security of a New Encryption

Algorithm

A.V.N. Krishna,

Professor, Computer Science Department, Indur Institute of Engineering & Technology, Siddipet,

Andhra Pradesh, India.

Email: hari_avn@Rediffmail.com

A.Vinaya Babu,

Director, Admissions, J.N.T.U, Hyderabad.

Abstract

Encryption study basically deals with three levels of algorithms. The first algorithm deals with

encryption mechanism, second deals with decryption Mechanism and the third discusses about the

generation of keys and sub keys used in the encryption study. In the given study, a new algorithm is

discussed which generates a random sequence which is used as sub key for encryption process. The

algorithm executes a series of steps and generates a sequence. This sequence is being used as sub key

to be mapped to plain text to generate cipher text. The strength of the encryption & Decryption process

depends on the strength of sequence generated against crypto analysis. In this part of work some

statistical tests like Uniformity tests, Universal tests & Repetition tests are tried on the sequence

generated to test the strength of it.

Keywords: Encryption & Decryption Mechanism, Key & Sub key Generation, Statistical tests,

Strength of the algorithm.

1. Introduction

A crypto system [1-5] is an algorithm, plus all possible plain texts, cipher texts and keys.

There are two general types of key based algorithms: symmetric and public key. With symmetric-key

encryption, the encryption key can be calculated from the decryption key and vice versa. With most

symmetric algorithms, the same key is used for both encryption and decryption.

Implementations of symmetric-key encryption can be highly efficient, so that users do not

experience any significant time delay as a result of the encryption and decryption. Symmetric-key

encryption also provides a degree of authentication, since information encrypted with one symmetric

key cannot be decrypted with any other symmetric key. Thus, as long as the symmetric key is kept

secret by the two parties using it to encrypt communications, each party can be sure that it is

communicating with the other as long as the decrypted messages continue to make sense.

Symmetric-key encryption is effective only if the symmetric key is kept secret by the two

parties involved. If anyone else discovers the key, it affects both confidentiality and authentication. A

person with an unauthorized symmetric key not only can decrypt messages sent with that key, but can

encrypt new messages and send them as if they came from one of the two parties who were originally

using the key.

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International Journal of Advancements in Technology (IJoAT) http://ijict.org/ ISSN 0976-4860

Vol 1, No 1 (June 2010) ©IJoAT

2. Algorithm [6-11]

The new algorithm has the following features

1. A set of poly alphabetic substitution rule is used.

2. A new block cipher is developed.

3. A Random matrix is being used as key.

4. Generated sequence being used as sub key.

5. Coding method.

The steps that are involved in the proposed algorithm.

1. A sequence of n values say n=0-26 is considered.

2. This sequence is represented in ternary format.

3. Let this be

“

”.

4. 1 is subtracted from all the values of ternary vector.

5. A random matrix is used as a key. Let it be A.

6. The modified ternary vector is multiplied with the matrix key.

7. A sign function is applied on the product of ternary vector & matrix key.

8. 1 is added to all values of step 7.

9. A sequence is generated which is used as sub key

10. Equality of values of the sequence generated by step 9 are considered to develop a random

sequence.

Example

Step1:

Consider the sequence for n= 0 to 26 values.

Step2:

Convert the sequence to ternary form of a 3 digit number

i.e. 0 ------- 000

1-------- 001

2-------- 002

26-------- 222

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International Journal of Advancements in Technology (IJoAT) http://ijict.org/ ISSN 0976-4860

Vol 1, No 1 (June 2010) ©IJoAT

Step3:

Represent above ternary form in 27x3 matrix















2 2 2

2 2 2 1

2 2 0

2 1 1 2

2 1 1 1

2 1 1 0

2 0 2

2 0 0 1

2 0 0

1 2 2 2

1 2 2 1

1 2 2 0

1 1 1 2

1 1 1

1 1 1 0

1 0 0 2

1 0 0 1

1 0 0 0

0 2 2

0 2 2 1

0 2 0

0 1 1 2

0 1 1 1

0 1 1 0

0 0 2

0 0 0 1

0 0 0

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International Journal of Advancements in Technology (IJoAT) http://ijict.org/ ISSN 0976-4860

Vol 1, No 1 (June 2010) ©IJoAT

Step 4:

Subtract 1 from each element of the above matrix and the resulting matrix R is

































Step5:

Consider a random matrix

















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International Journal of Advancements in Technology (IJoAT) http://ijict.org/ ISSN 0976-4860

Vol 1, No 1 (June 2010) ©IJoAT

Step6:

R= R X A





















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International Journal of Advancements in Technology (IJoAT) http://ijict.org/ ISSN 0976-4860

Vol 1, No 1 (June 2010) ©IJoAT

Step7:

Convert all positive values to 1, negative values to -1 and zero to 0 of the resulting matrix of

step 6.





















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International Journal of Advancements in Technology (IJoAT) http://ijict.org/ ISSN 0976-4860

Vol 1, No 1 (June 2010) ©IJoAT

Step8: Add 1 to each element of the matrix R















2 2 0

2 2 2

0 2 2 2

2 2 2

2 1 1 2

0 2 2 2

2 0 2

0 2 2 0

2 2 0

2 0 2

0 2 2 0

1 1 1

2 0 2

0 2 2 0

0 0 0 2

2 0 2

0 2 2 0

2 0 0

0 1 1 0

0 0 0 0

2 0 0

0 0 0 0

0 0 0 2

Step9:

Convert each row of the matrix R to decimal form to generate sequence.

ie 0 0 2 will form 0*3

+0*3

+2*3

= 2

The sequence formed is = 2 0 0 18 0 3 18 18 6 20 2 6 20 13 6 20 24 6 20 8

8 23 26 8 26 26 24.

Generating Sub keys from sequence generated:

1. n [27]=

0 1 2 3 4 5……………………………………………...26

2. r [27] = 2 0 0 18 0 3 18 18 6 20 2 6 20 13 6 20 24 6 20 8 8 23 26

8 26 26 24.

3. Read n[0]=0. Store the values of n[0],r[0] in a basin. ie b(0)=(0,2).

4.1. n[0] ie. „0‟ is compared with r[27] values. There is a match at r[1],r[2] & r[4]. Neglect already

visited elements. Thus b(0)=[0,1,2,4).

International Journal of Advancements in Technology (IJoAT) http://ijict.org/ ISSN 0976-4860

4.2 Step 4.1 is repeated with other elements of basin ie. 1, 2 & 4 values. For elements 1& 4, there is no

match of values in r[27]. For element 2, there is a match at r[10]. Thus the basin b(0) is

updated to (0, 2, 1, 4 &10).

5. The procedure is repeated for the next element of the sequence of step 1 which is not visited earlier.

The random sequence formed is

(0,2,1,4,10,3,18,5,6,7,8,11,14,17,19,20,23,9,12,15,21,13,24,26,16,22,25)

This can be used as sub keys in encryption decryption process.

4. Case Studies:

Different cases using different keys have been tried to test the strength of algorithm against crypto

analysis.

Case 1:

Considering the key A of size (3*3)

A = key



Sequence generated from the proposed model

r=2 0 0 18 0 3 18 18 6 20 2 6 20 13 6 20 24 6 20

r= 8 8 23 26 8 26 26 24.

Considering the equality of values, the random sequence that can be formed using this sequences are

(0,2,1,4,10,3,18,5,6,7,8,11,14,17,19,20,23,9,12,15,21,13,24,26,16,22,25)

Case 2: By increasing the values of key by 1 at each row

A = key =



Sequence generated

r= 1 0 0 18 0 0 18 18 3 20 2 6 20 13 6 20 24 6 23 8 8 26 26 8 26 26 25.

International Journal of Advancements in Technology (IJoAT) http://ijict.org/ ISSN 0976-4860

The random sequence generated from this sequence is

0,1,2,4,5,10,3,18,8,6,7,19,20,23,11,14,17,9,12,15,13,24,6,16,21,22,25.

Case 3:

By decreasing the key values by 1 at each row.

A = key =



Sequence generated by the model.

r= 11,1,3,20,0,6,18,18,6,20,2,6,20,13,6,20,24,6,20,8,8,20,26,6,23,25,15.

The random sequence generated from this sequence is

0,11,4,1,2,3,10,6,18,5,8,14,17,23,7,19,20,24,9,12,15,21,16,26,22,13,25

Case 4:

By increasing the key size to [4*4], we can increase the number of values of the sequence, which

increases the strength of the algorithm.

A = key =

3 3

6 1



Sequence generated for n=0 to 80 values represented to the base 3.

r=0,33,60,0,0,6,0,9,20,54,57,60,0,0,40,0,19,20,54,54,60,54,54,74,9,20,20,33,60,60,0,6,26,9,20,26,57,6

0,61,0,40,80,19,20,23,54,60,71,54,74,80,20,20,47,60,60,71,6,26,26,20,26,26,60,61,80,40,80,80,20,23,

26,60,71,80,74,80,80,20,47,80.

The random sequence formed by considering similar values,

0,3,4,6,12,13,15,30,39,5,31,57,10,36,9,54,7,24,33,18,19,21,22,45,48,1,27,16,42,20,60,8,17,25,26,34,4

3,51,52,69,78,2,11,28,29,37,46,54,55,63,72,32,35,

58,59,61,62,71,9,18,19,21,22,45,48,38,64,47,56,73,7,24,33,16,42,53,79,1,27,23,74,44,70,49,75,40,14,

66,80,41,50,65,67,68,76,77.

International Journal of Advancements in Technology (IJoAT) http://ijict.org/ ISSN 0976-4860

Case 5:

A = key =

3 3

6 1



Sequence generated n=0 to 80 values represented to the base 3.

r=0,6,33,0,0,6,0,0,20,54,54,60,0,0,0,0,9.20,54,54,57,54,54,65,0,20,20,33,60,60,0,6,26,9,20,26,57,60,6

1,0,40,80,19,20,23,24,60,71,54,74,80,20,20,47,60,60,80,15,26,26,23,26,26,60,71,80,80,80,80,20,26,26

,26,16,80,80,74,80,80,47,74,80.

The random sequence formed from the generated sequence

0,3,4,6,7,12,13,14,15,24,30,39,1,5,31,57,45,20,36,8,17,25,26,34,43,44,51,52,69,32,35,58,59,61,62,70,

71,38,47,64,53,78,9,54,16,33,10,18,19,21,27,48,72,2,42,23,65,60,11,28,29,37,46,54,

55,63,9,10,18,19,21,22,48,16,33,42,72,2,27,40.

Case 6:

A = key =

3 3

6 1



Sequence generated for n=0 to 80 values being represented to the base 3.

r=0,3,6,0,0,3,0,0,10,54,54,60,0,0,0,0,0,20,54,54,54,54,54,55,0,10,20,33,60,60,0,6,26,9,20,26,57,60,61,

0,40,80,19,20,23,54,60,71,74,54,80,20,20,47,60,70,80,25,26,26,26,26,26,60,80,80,80,80,80,20,26,70,8

0,80,77,80,80,74,77,80.

The random sequence formed from the generated sequence is

0,3,4,6,7,12,13,14,15,16,22,28,37,79,80,1,5,2,29,39,48,54,62,63,64,65,66,67,71,72,74,75,78,9,10,18,

9,20,43,47,45,46,76,31,8,23,40,17,24,32,41,49,50,68,51,42,38,25,33,55,21,26,60,30,56,57,58,59,69,11

,27,35,44,52,61,34,36,70,53,77,73.

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