A new weighted secret splitting method 2-3-4-5-6-7-8-9-10-11-12-13-14-15-16-17-18

International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –

6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 6, September – October (2013), © IAEME

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A NEW WEIGHTED SECRET SPLITTING METHOD

1Dr. Abdulameer Khalaf Hussain,

2Dr. Mohammad Alnabhan,

3Prof. Faris M.AL-Athari

1Computer Science, Faculty of Information Technology, Jerash University, Jordan

2Computer Science, Faculty of Information Technology, Jerash University, Jordan

3Department of Mathematics, Faculty of Information Technology, Zarqa University, Jordan

ABSTRACT

This paper presents a new method for splitting a secret information method according to the

importance role of each party in a group of users. The splitting procedure takes the secret

information with a suitable length computed in terms of the number of users and their corresponding

weights. Therefore, this method grants an amount of information with respect to each user’s weight.

All previous methods of secret splitting methods did not take into account the user’s priority so the

secret splitting may the same as the length of that secret. This paper also presents a solution for the

problem of the user’s absence and the lost secret part which is considered a major problem in most of

secret splitting methods.

KEYWORDS: Threshold Cryptography, Secret Splitting, Secret Sharing, Weighted Authentication.

I. INTRODUCTION

A secret sharing scheme is any method that can be used to distribute shares of a secret value

among a set of participants. The recovering of the secret value can be done only by qualified subsets

of participants from their shares. Such a scheme is called a perfect scheme if the unqualified subsets

do not obtain any information about the secret value. The qualified subsets form the access structure

of the scheme, which is a monotone increasing family of subsets of participants.

The first secret sharing was introduced independently by Shamir [1] and Blakley [2] in 1979.

They proposed two different methods for constructing secret sharing schemes used for threshold

access structures. In these two schemes, the qualified subsets are those with at least some given

number of participants. Such schemes are ideal. i.e., the length of every share is the same as the

length of the secret, which is the best possible condition [3].

A secret sharing scheme can be used as a fundamental method in secure multiparty

computations which is found in [1,2], where a secret is divided into different shares for distribution

among participants (private data), and a subset of participants then cooperate in order to recover the

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secret. Shamir proposed the (t, n)-threshold secret sharing scheme .In this scheme, the secret is

divided into n shares to be distribution among certain players. The shares can be constructed such

that any t participants can combine their shares to recover the secret, but any set of t -1 participants

have no knowledge about the secret.

Since the concept of the early secret sharing which was proposed by Shamir in 1979 [1]

(Blakley also did the similar work at that time [2]), there have been many papers extending Shamir’s

scheme and investigating new secret sharing schemes [4], [5], [6], [7], [8], [9],[10], [11], [12], [13],

[14], [15], [16], [17].

Secret sharing schemes can be classified into various categories according to different

criteria. There are two classes (in terms of numbers of secrets to be shared): single secret and

multiple secrets.

When we consider the shares’ capabilities, there are two classes: same-weight shares and

weighted shares. In weighted shares schemes, different shares have different capabilities to recover

the secret(s)–a more weighted share needs fewer other shares and a less weighted share needs more

other shares to recover the secret(s). Also secret sharing can be classified depending on the

underlying techniques used: polynomial based schemes and Chinese Remainder Theorem (CRT)

based schemes. Shamir’s scheme [1] is considered a well –known example polynomial based scheme

and Mignotte’s scheme [12] is a representative among the CRT based secret sharing schemes.

II. RELATED WORKS

In [18] a proposal deals with weighted threshold schemes. This method concentrates mainly

about the properties related to the information rate. The paper presents the complete characterization

of the access structures of weighted threshold schemes when all the minimal authorized subsets have

at most two elements. Finally this paper gave the lower bounds for the optimal rate of these access

structures.

In [19] a construction of a new threshold secret sharing scheme is made by using the concept

of share vector. In this scheme, the number of shareholders can be adjusted by randomly changing

the weights of them. This proposed system was more suitable in the case that the number of

shareholders needs to be changed randomly during the scheme is carrying out.

Z. Yanshuo and L. Zhuojun proposed a secret sharing scheme of shared participants. In this

scheme, based on identity, the secret sharing scheme among weighted participants was analyzed and

a dynamic scheme about secret sharing among weighted participants was presented [20].

Another scheme was proposed to combine the weighted threshold secret sharing schemes

based on the Chinese remainder theorem with the RSA scheme. The aim of this scheme was to

obtain a novelty, weighted threshold decryption or weighted threshold digital signature

generation.[21]

In [22] a secret sharing scheme constructed on adversary structure was proposed based on

Chinese remainder theorem .This scheme is considered a prefect secret sharing scheme and it poses a

reconstruction property and confidentiality property which leads efficiently for prevention of

attacking from external attackers and cheating among participants. Another important property of

this scheme is that allowing participants to be added or deleted dynamically.

A scheme among different weights based on Shamir's secret sharing and Chinese remainder

theorem was proposed. Because of introducing a public –key cryptosystem in elliptic curve in this

scheme, this method did not suffer from any cheating and also a secret channel is not needed to build

between the participants and distributors. [23]

In [24] the authors used the theory of Jordan matrix factorization and combine with the

formulary of Lagrange putting forward an algorithm of (r, n) threshold secret sharing with short



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share and high efficiency. In this scheme, the length of secret share that each participator needs to

conserve has no relation with the length of the secret information. So this scheme has a very high

space, computation and communication efficiency.

III. PRPOPSED SYSTEM

The proposed system of secret splitting in this paper presents a new and a variable

decomposition of secret information. The length of the secret information(S) is chosen depending on

the number of users and their corresponding weights and represented in binary string. This binary

string is divided into amounts depending on the weight (w) of each user in such a way that the

larger amount of the binary string is dedicated to the user of the higher weight. This piece of the

secret binary information must be discarded from the original binary string and apply the same

splitting procedure to the next lower weight.

To perform this task, this paper suggests a set of users and two sets of corresponding weights,

one for the highest weights and the other for the lower weights. These two sets can be used to

provide a partial solution to the problem of the absence of one or more users of lower priorities by

giving certain privileges to the users of the high weights. This task needs a trusted manager to

distribute the shares of other users to those of higher weights. For this reason, the manager must

agree with the latter users with public and private keys to encrypt the distributed shares of lower

weights in the location of users with high weights. The latter users can be able to extract these shares

in the case of absence or the lost of the lower weights shares.

The proposed system assumes a secret splitting system with a new parameter that is (t,n,m) ,

where t is the total number of users , n the number of users that can reconstruct the secret information

and m is the percentage of secret splitting depending on the weight of each user .

THE ALGORITHM

Let S be the binary secret information

Let L be the length of S

Let G={U1,U2,…….Un) be the set of group users

Let WH={wh1,wh2,…..,whm} be the set of high weights

Let WL ={wl1,wl2,…..,wlk} be the set of low weights

Let WT=WhUWL such that:

Wh1>wh2…>whm>whl1>wh2…>whk

Let t be the total of users

Let n be the selected users responsible for recovering the secret S

Let m be the percentage dedicated for each weight

Calculate the length of S :

L= t*n*m

Divide S into variable divisions s1 ,s2 ,…..sn

For i=1 to n

Si=S *wi(m) // The first share is calculated by multiplying S with the percentage of each user //

S= (S-Si) // The new S is calculated by subtracting S from the fist share and we now deal with

the remaining of S to take a percentage of the next user //

Next i

To perform this system it is necessary to construct two tables. The first table (table1) contains the

users of high weights and their corresponding weights and the second table (table 2) is dedicated for

users of low weights and their weights.



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Table 1: Users of high weights

User Weight

Uh1 Wh1

Uh2 Wh2

. .

. .

. .

Uhn Whn

Table 2 : Users of low weights

User Weight

Ul1 Wl1

Ul2 Wl2

. .

. .

. .

Uln Wnn

IV. RESULTS

We take an example of some authenticated users with high weights and the corresponding

users of low weights in order to reconstruct the secret information in the case of the absence of users

of low weights .In this example we have 5 users of low weights. Table 3 represents a sample of a

secure repository used for this purpose.

Table 3: Repository Sample

User Weight Corresponding users of low weights

Uh1 Wh1 WL1={Ul1,Ul2,Ul3}

Uh2 Wh2 WL2={ Ul4,Ul5 }

Where WL1 and WL2 represent the sets of users of low weights.

So the user (Uh1) of the first high weight can reconstruct the total secret information by using

information pieces dedicated to Ul1,Ul2 and Ul3 of low weights in cooperation with user (Uh2) who

can extract information pieces of users Ul4 and Ul5 .

V. ANALYSIS

Splitting secrets according to the weights or priories of some users in a variable splitting

shared secrets leads to a more strong authentication mechanism , because the large pieces of secret

information is dedicated to those users who are more trusted than other users who have less amount

of secret information . Also, this proposed system lets the users of higher weights to recover the total

secret information in the case of the absence of the users of lower priorities. In this case we

overcome the major problem found in most splitting methods which is the absence of these users

sharing the secret information by using a secure repository.



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VI. CONCLUSION

This proposed system splits the secret information depending on the priority and importance

of users sharing the secret. Weighted splitting of the secret is considered a new method that enhances

the authentication of parties by granting the most trusted users the more secret information. Another

important point in this system is that it takes into account the most common problem in the

traditional methods which is the absence of the other users that pose the low weights of information

secret. This problem is solved by designing a protected repository containing the corresponding set

of low weight pieces for each user of high weight secret pieces of information. Finally, this method

uses a new parameter which is (w) to the original secret splitting method.

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A new weighted secret splitting method 2-3-4-5-6-7-8-9-10-11-12-13-14-15-16-17-18

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