This document presents a new method for splitting a secret among a group of users according to each user's importance or weight. The secret is divided into shares of varying lengths based on each user's weight, with higher weighted users receiving more of the secret. It also addresses the problem of shares being lost if lower weighted users are absent. The method uses two tables, one listing higher weighted users and one for lower weighted users. It includes a secure repository allowing higher weighted users to reconstruct the full secret using shares from corresponding lower weighted users if needed. The method introduces a new parameter for secret splitting schemes called (t,n,m) accounting for total users, reconstructing users, and the percentage of secret split based on each user's

1. 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
1
A NEW WEIGHTED SECRET SPLITTING METHOD
1
Dr. Abdulameer Khalaf Hussain, 2
Dr. Mohammad Alnabhan, 3
Prof. Faris M.AL-Athari
1
Computer Science, Faculty of Information Technology, Jerash University, Jordan
2
Computer Science, Faculty of Information Technology, Jerash University, Jordan
3
Department 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

3. 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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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.

4. 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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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.

5. 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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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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