=Paper=
{{Paper
|id=Vol-1755/177-180
|storemode=property
|title=Result Computation for University of Ibadan Statistics Department Using Anonymous Threshold Scheme
|pdfUrl=https://ceur-ws.org/Vol-1755/177-180.pdf
|volume=Vol-1755
|authors=Oluwaseun Otekunrin,Patience Emehinola
|dblpUrl=https://dblp.org/rec/conf/cori/OtekunrinE16
}}
==Result Computation for University of Ibadan Statistics Department Using Anonymous Threshold Scheme==
https://ceur-ws.org/Vol-1755/177-180.pdf
Result Computation for University of Ibadan Statistics
Department Using Anonymous Threshold Scheme
O. A. Otekunrin P. A. Emehinola
Department of Statistics Department of Statistics
University of Ibadan, Nigeria University of Ibadan, Nigeria
+234-803-835-7957 +234-706-635- 4730
oa.alawode@mail.ui.edu.ng emehinolapatience@gmail.com
include the works of [4], [5], [6], [7], [8], [9], [10] among others.
ABSTRACT Some applications of secret sharing schemes, which include
In this paper, we constructed (2, 7)-anonymous threshold scheme
private proximity testing and recursive information hiding, can be
from the (49, 56, 8, 7, 1) Resolvable Balanced Incomplete Block
found in [11] and [12].
Design (RBIBD) using MATLAB codes. The (2, 7)-anonymous
threshold scheme was then applied to Result Processing Scheme
in the Department of Statistics, University of Ibadan. The scheme 2.1 Perfect -Threshold Scheme
developed satisfied the security requirements of authenticity, A perfect threshold scheme is defined by [13] as follows:
integrity and verifiability thus making it better than the scheme Suppose that t and w are integers such that . A
currently being used in the Department. perfect -threshold scheme is a method of sharing a secret
value among a finite set { } of participants in
CCS Concepts such a way that any participants can compute the value of but
no group of (or fewer) participants can compute any
• Security and privacy ➝ Security privacy ➝ Access control information about the value of from the information they hold
collectively.
Keywords 2.2 Anonymous Threshold Schemes
Secret sharing; Resolvable Balanced Incomplete Block Designs; Anonymous threshold schemes were first investigated by [14]. In
Anonymous threshold scheme an anonymous threshold scheme, the secret can be reconstructed
without knowledge of which participants hold which shares. The
computation of the secret can be carried out by giving the shares
1. INTRODUCTION to a black box that does not know the identities of the participants
Keeping secrets is as old as man. In the early times, human beings holding those shares, [15]. According to [16], the scheme can be
kept secrets by inscribing special writings on rocks and walls, used to provide access to a secure area because security is
keeping of special articles in earthen wares and burying provided without any need for a separate identification protocol.
underground etcetera. This has changed drastically today where Ideal anonymous secret sharing schemes were investigated by
secrets are kept today using advanced forms of computer [17]. In this scheme, the size of the shares given to each
technology. Most of our personal information are now on the participant is equal to the size of the secret. They also proved that
databases of government, banks, healthcare institutions and other an ideal anonymous -threshold scheme can be realized if
organisations. When these secrets are properly managed, our and only if . The -threshold scheme was
lives, businesses, political activities and so on are ultimately characterized by [18] in terms of a regular difference family while
protected. Secure key management has been an active area of [19] constructed anonymous secret sharing schemes using
research since the independent works of [1] and [2]. combinatorial designs.
2. SECRET SHARING SCHEMES 2.2.1 Definition: [13]
Secret sharing is a method of dividing a secret among a set of A perfect (t, w)-threshold scheme is an anonymous threshold
{ } of n participants. Each of the participants is scheme if the following two properties are satisfied:
1. the w participants receive w distinct shares,
given a part (share) of the secret in such a way that only certain
2. the secret can be computed solely as a function of t shares,
specified (qualified) subsets of the n participants can reconstruct
without the knowledge of which participant holds which share.
the secret by combining their shares while certain set of
participants gets no information about the secret even when they
combine their shares[3].
Variants of secret sharing schemes abound in literature. These
CoRI’16, Sept 7–9, 2016, Ibadan, Nigeria.
177
3. BALANCED INCOMPLETE BLOCK these five members can therefore access the program and compute
results, once he/she gains access to the Office.
DESIGNS (BIBD)
3.1 Definition: [3] 5. CONSTRUCTION OF (2, W) -
Let be positive integers such that . A ANONYMOUS THRESHOLD SCHEME
BIBD is a pair such that:
FROM (v, b, r, w, 1)-RBIBD
is a set of elements called points
The following illustration, from [13] showed that -
is a collection of subsets of called block RBIBD can be used to construct anonymous (2, w)-threshold
Each block contains exactly points schemes.
Every pair of distinct points is contained in exactly Suppose that is a , then there are
blocks
parallel classes, , in the RBIBD. The Dealer
3.2 Resolvable Balanced Incomplete Block chooses a secret value from a specified set of secrets
Design (RBIBD) . This implies that there are possible secrets to
3.2.1 Definition: [13] choose from. The Dealer shares the secret value among the set
Suppose is a -BIBD. A parallel class in of participants with the assumption that
is a subset of disjoint blocks from whose union is . A partition . To share the secret K, gives some partial information,
of into parallel classes is called a resolution, and is said called a share, from a specified share set , to each of the
to be a resolvable BIBD if has at least one resolution. In an participants. The share set has cardinality . (X, A) and its
RBIBD, each point occurs exactly one block in each part of the resolution are known to all the participants.
partition (or parallel class) To share secret , , chooses a random block
and gives the points in to the participants, each of the
3.2.2 Necessary Conditions for the Existence of an RBIBD: [20] participants receiving one point.
Assume that any two participants with shares and want to
obtain the secret, recall that (X, A) is a BIBD with λ = 1, then there
An example of a resolvable BIBD is the is a unique block such that . Thus, the two shares can
displayed in Table 1. Each column is a parallel class. be used to find the parallel class that contains and the secret
Table 1: (9, 12, 4, 3, 1) RBIBD is revealed as .
{1, 2, 3} {1, 4, 7} {1, 5, 9} {1, 6, 8} The scheme is anonymous because the computation of the secret
depends on the shares and not on the identities of the
{4, 5, 6} {2, 5, 8} {2, 6, 7} {2, 4, 9}
shareholders. The security of the scheme is guaranteed because
{7, 8, 9} {3, 6, 9} {3, 4, 8} {3, 5, 7} any one share cannot lead to the determination of the secret key to
the program. Also, the authenticity, integrity and verifiability
requirements for the scheme are satisfied since any two
4. OVERVIEW OF RESULT participants must submit their shares to the machine in order to
have access to the program.
COMPUTATION PROCESS IN
STATISTICS DEPARTMENT, 6. THE RESULT PROCESSING SCHEME
UNIVERSITY OF IBADAN was selected from a list of RBIBDs in
[21] because of its suitability to the application area. An algorithm
Result computation issues are highly sensitive matters in any with five cell executions was written in MATLAB to generate the
University setting. In the Department of Statistics, University of parallel classes for . The steps taken in the
Ibadan, result computation issues are handled through the generation of the parallel classes are illustrated with the aid of the
collaborative efforts of eight out of the total population of staff workflow chart in Figure 1 while the parallel classes for the
members of the Department. They are the Head of Department RBIBD are displayed in Table 2.
(HOD), the Examination Officer, four Undergraduate Level Read Standard BIBD Table
Advisers and two System Analysts. The HOD is the overall
Coordinator of result computation matters in the Department. The Extract RBIBD Based on its Conditions
Level Advisers coordinate students’ registration while the
Examination Officer coordinates undergraduate students’
Create Parallel Classes
examinations and receives examination results from course
lecturers. The two System Analysts ensure that the students’
registration details and results are correctly stored on the system. Check for Uniqueness
The program used for computing the results was developed by a
trusted computer programmer who is not a member of the Send to Excel
University community. The HOD, Examination Officer, the final
Figure 1: Workflow chart for the construction of the Parallel
year level adviser and the two system analysts were all trained to
handle the program. Each of them is assumed to be trustworthy Classes for (49, 56, 8, 7, 1) RBIBD
and each has individual password that give them access to the
Table 2: Parallel Classes for (49, 56, 8, 7, 1) RBIBD
program. There is also a wireless intranet provision that allows
these five members to connect their personal laptops to the main 43 17 33 35 11 22 9 5 14 23 47 37 43 34
31 30 34 2 45 29 8 17 8 45 42 9 10 12
computer system and the result computation can only be done in 36 15 3 14 49 20 38 28 13 18 24 31 1 3
the office where the main computer system is located. Any of 42 13 7 47 28 23 16 22 27 49 4 30 35 39
24 37 44 10 19 1 6 25 20 2 21 6 15 16
178
48 18 5 21 46 40 41 36 41 29 44 38 32 33 Since any one member cannot access the program to compute the
25 27 26 39 32 4 12 26 46 48 40 19 11 7
students’ results, the scheme ensures that the security
46 44 29 30 12 3 33 36 44 40 11 39 10 22
requirements of authenticity, integrity and verifiability for the
35 8 1 41 36 25 47 26 14 37 24 30 20 47 scheme are satisfied. Thus, the scheme is preferable to the one
23 21 42 34 32 31 15 9 13 12 27 42 31 1 being used in the Department.
14 11 43 22 48 6 49 4 48 28 43 5 6 2
38 45 9 28 27 20 5 35 25 49 7 19 23 45
13 17 24 2 18 19 26
10 40 39 37 4 16 7
18 46 33 8 17 3 29
38 34 32 21 41 16 15
7. CONCLUSION
Secret sharing schemes are used for increasing the security of
important information. Different secret sharing schemes abound in
33 42 27 1 8 24 3 34 22 39 45 46 1 27
43 41 10 21 30 26 46 38 48 15 33 44 5 41 literature one of which is Anonymous threshold scheme. In this
31 22 47 34 32 7 35 9 42 4 16 25 19 13 paper, the (2,7) anonymous threshold scheme was constructed
9 19 17 39 28 25 6 29 14 17 23 7 20 40
44 5 18 11 37 23 14 12 47 8 32 31 37 43 from the (49, 56, 8, 7, 1) RBIBD. The (2, 7) anonymous threshold
40 15 48 12 29 2 36 11 2 6 26 36 49 24 scheme was then applied to Result Processing System in the
16 13 20 45 38 4 49 28 3 21 10 18 30 35
Department of Statistics, University of Ibadan. The scheme
developed satisfied the security requirements of authenticity,
11 2 45 35 39 31 24 13 28 6 29 35 26 22 integrity and verifiability since a single participant cannot have
23 22 5 8 32 44 27 42 44 14 11 16 36 23
21 18 49 20 33 30 3 9 15 4 27 49 18 12 access to the program used for computing the students’ result.
17 25 19 34 14 26 40 17 24 48 2 47 21 10 This makes the scheme better than the one currently being used in
38 1 6 46 43 29 47 32 20 37 31 19 41 30
16 36 10 48 13 37 9 5 34 33 46 38 1 40 the Department.
12 28 15 4 41 7 42 25 39 7 8 3 43 45
The RBIBD has point set X = {1, 2, 3,….., 49} 8. REFERENCES
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