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Permutation of National Identification Number For A Better Security in Communication Channel

This study proposes a new method to enhance the security of transmitting national identification number via various communication channels like SMS, email, and Box office. It introduces a permutation technique utilizing the Gamma 1 Non-Deranged Permutation group, ensuring the confidentiality of the information.
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0% found this document useful (0 votes)
25 views4 pages

Permutation of National Identification Number For A Better Security in Communication Channel

This study proposes a new method to enhance the security of transmitting national identification number via various communication channels like SMS, email, and Box office. It introduces a permutation technique utilizing the Gamma 1 Non-Deranged Permutation group, ensuring the confidentiality of the information.
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Volume 9, Issue 5, May – 2024 International Journal of Innovative Science and Research Technology

ISSN No:-2456-2165 https://doi.org/10.38124/ijisrt/IJISRT24MAY1655

Permutation of National Identification Number for a


Better Security in Communication Channel
Umar, M1; Hassan, A2; Abdullahi, I3; Muhammad Shehu, Z4
1,3,4
Department of Mathematics, Sokoto State University, Sokoto, Nigeria
2
Department of Mathematics, Federal University Birnin Kebbi, Kebbi,

Abstract:- This study proposes a new method to enhance in some countries the use of Tax Identification Number is
the security of transmitting national identification necessary before any overseas payment procedure can be
number via various communication channels like SMS, consummated; unlike in US where parameters like date of
email, and Box office. It introduces a permutation birth could serve without demanding for other nations’ Tax
technique utilizing the Gamma 1 Non-Deranged Payer Identification Number. In countries where an
Permutation group, ensuring the confidentiality of the established nationwide number failed to exists, the need to
information. By employing 11 factorial (11!) create their own number for each individual arise and the risk
permutations, the national identification number is of mismatching people identity could be high.
transformed into a mixed format for unintended
recipients, yet remains easily decrypted by the intended In [6],[5],[4],[2] the study of cryptography was
recipient. This approach mitigates concerns regarding conducted, Cryptography was derived from two Greek words
data interception and unauthorized access, providing a “Kryptos” which means “Hidden or Secret” and “Graphein”
robust solution for secure information transmission “to write” which is the art and science of making
across diverse media channels. communication. Cryptography is a method or technique by
which a message can be altered so that it becomes
Keywords:- NIN, Permutation, Cryptography, Factorial, Non meaningless to anyone else but the intended recipient. This is
Deranged Permutation. done primarily in two basic ways, one is to change the
position of letters or words in a message known as
I. INTRODUCTION “Transposition” and the other is by substituting letters or
words by different ones, known as “substitution”
National Identity Management Commission (NIMC) as respectively. The science of encryption and decryption can be
a national body in Nigeria is responsible for allocating the traced back all the way to year 2000BC in Egypt. In 2010,
national identity number (NIN), an 11-digit number code using the concept of Catalan numbers the scheme for prime
(e.g.: 41134789082) designed and given to Nigerians and numbers (𝑝 ≥ 5) was developed. They defined the
legal residents by government irrespective of their ages. The generating function for 𝑮𝒑 = {𝑤𝑖 ⋮ 𝑖 ∈ 𝑝 − 1} such that
issuance of National identification Number, a National
𝑤𝑖 = ((1)(1 + 𝑖)𝑚𝑝 (1 + 2𝑖)𝑚𝑝 … (1 + (𝑝 − 1)𝑖)𝑚𝑝 )
Identity or National Insurance Number by Nigerian
government is in line with the global best practices in keeping where 𝑚𝑝 ≔ 𝑚𝑜𝑑𝑢𝑙𝑜𝑝 . Permutation of Gp was studied by
a good track record of its citizen and those who resides both [7],[12],[13],[14],[15]
in permanent and temporary basis serving government in a
variety of functions. The study of identification was In this research 𝑮𝒑 permutation group was employed to
extensively conducted by [8],[9],[10],[11]. secure NIN over the communication channel such as social
media, emails, box office, etc. Cryptography is divided into two,
The distribution and allocation of National Symmetric key cryptography and Asymmetric key
Identification Number may vary among countries but the cryptography. In Symmetric key cryptography single key is
issuance of identification number is mostly done to citizens used between the sender and receiver, while the Asymmetric
when they reach certain legal age or at the point of birth. key cryptography each user is assigned a pair of keys, a public
Unlike non-citizens whom will be given identification upon key and a private key, the public key is made known to all
entrance of a particular country or when a permanent or members, while the private key is hidden by the user (sender),
temporary resident permit is obtained. In some countries the the sender uses the public key to encrypt the message, while the
purpose of issuing such numbers may be singular but in the receiver uses his own hidden (private) key to decrypt the
long run the numbers may serve a National Identity. In United message. In this work, we consider Symmetric key
State of America, for example, the use of (SSN) i.e. Social cryptographic approach.
Security Number system had been introduced in order to
distribute and manage social security benefits. But over time
a significant expansion of the widespread use of the SSN is
recorded beyond its original purpose leading to the wide
range of activities such as opening bank accounts, getting
credit cards, driving permit to mention but a few. However,

IJISRT24MAY1655 www.ijisrt.com 3096


Volume 9, Issue 5, May – 2024 International Journal of Innovative Science and Research Technology
ISSN No:-2456-2165 https://doi.org/10.38124/ijisrt/IJISRT24MAY1655

II. PRELIMINARIES  Plaintext: - Is an unencrypted information pending input


into cryptographic algorithms.
Let 𝑮𝒑 = {𝑤𝑖 ⋮ 𝑖 ∈ 𝑝 − 1} be a structure such that each  KEY: - A string of characters used within an encryption
𝑤𝑖 is generated from the arbitrary set for any prime 𝑝 ≥ 5, algorithm for altering data so that it appears random.
using the scheme  TRANSPOSITION: The process of changing objects
from one position to another.
𝑤𝑖 = ((1)(1 + 𝑖)𝑚𝑝 (1 + 2𝑖)𝑚𝑝 … (1 + (𝑝 − 1)𝑖)𝑚𝑝 )  TRANSPOSITION CIPHER: - Is an encryption
technique that rearranges the position of characters
without altering the characters themselves.
Then each 𝑤𝑖 is called a cycle and the elements in each 𝑤𝑖
are distinct and called successors.  Example of transposition cipher is as follows.
 Plaintext: GOVERNMENT
 Example
Using the above setting, if 𝑝 = 11, then we have 𝑮𝟏𝟏 Table 1: Plaintext
as 𝑮𝟏𝟏 = {𝑤1 , 𝑤2 , … , 𝑤10 } where Since 0 and 5 in 1 2 3 4 5 6 7 8 9 10
𝑚𝑜𝑑𝑢𝑙𝑜5 are equivalent, thus instead of using 0 in 𝑚𝑜𝑑𝑢𝑙𝑜𝑝 G O V E R N M E N T
we will be using p.
Table 2: Transposition
 Cipher: - Is a method of transforming a message to 1 3 5 7 9 10 2 4 6 8
conceal its meaning. G V R M N T O E N E
 Encryption: - Is the process of encoding an information.
 Decryption: - Is the process of converting a data into its The resulting transposition will be “GVRMNTOENE”.
original form. The cipher process is given by the figure below:

Fig 1: Cipher Algorithm

The above diagram represents Encryption and III. ILLUSTRATION


Decryption process of a Symmetric key cryptography.
Let:
 Experimental Result 𝑃𝑇: 35789426315

 Let PT be a plaintext Where 𝑃𝑇 is a plaintext containing the NIN in which the


 Let C be the ciphertext encryption algorithm is to be applied.
 Let i be the key
 Encryption Stage
 The Encryption Procedure to Take the Following Stages. Applying encryption function of 𝐺𝑝 on 𝑤1 (𝑝 = 11,
number of characters and p is always a prime,)
 Applying encrypted function of 𝐺𝑝 on 𝑃𝑇 will yield 𝐶,
where the 𝐶 is the ciphertext to be sent to the receiver. 𝐺11 = {𝑤1 , 𝑤2 , 𝑤3 , … , 𝑤10 }
 The encrypted function obtained is given by Where
𝑤1 = (1 2 3 4 5 6 7 8 9 10 11)
𝐶: 𝑤1 → 𝑤1+𝑖 , 𝑖 < 𝑝 − 1 𝑤2 = (1 3 5 7 9 11 2 4 6 8 10)
𝑤3 = (1 4 7 10 2 5 8 11 3 6 9)
 The Decryption Procedure to Take the Following Stages. 𝑤4 = (1 5 9 2 6 10 3 7 11 4 8)
𝑤5 = (1 6 11 5 10 4 9 3 8 2 7)
 Reverse the encrypted function of 𝐺𝑝 on 𝐶 to obtain 𝑤6 = (1 7 2 8 3 9 4 10 5 11 6)
stacked ciphertext 𝑃𝑇. 𝑤7 = (1 8 4 11 7 3 10 6 2 9 5)
𝑤8 = (1 9 6 3 11 8 5 2 10 7 4)
 The reversed function obtained is given by
𝑤9 = (1 10 8 6 4 2 11 9 7 5 3)
𝑤10 = (1 11 10 9 8 7 6 5 4 3 2)
𝑃𝑇: 𝑤1+𝑖 → 𝑤1
𝐶: 𝑤1 → 𝑤1+𝑖 , 𝑖 < 𝑝 − 1, 𝑖 = 4.
By producing the 𝑃𝑇 the receiver can then use the
national identification number used. 𝐶: 𝑤1 → 𝑤5
Where 𝑤1 is the 𝑃𝑇

IJISRT24MAY1655 www.ijisrt.com 3097


Volume 9, Issue 5, May – 2024 International Journal of Innovative Science and Research Technology
ISSN No:-2456-2165 https://doi.org/10.38124/ijisrt/IJISRT24MAY1655

Table 3: The Table Below Shows the Permutation Values of 𝑤1


1 2 3 4 5 6 7 8 9 10 11
3 5 7 8 9 4 2 6 3 1 5

Table 4: The Table Below Shows the Permutation Values of 𝑤5


1 6 11 5 10 4 9 3 8 2 7
3 4 5 9 1 8 3 7 6 5 2

The ciphertext to be sent to the receiver is  Decryption Stage


345918376524, where the subscript 4 is to be used as a key for Reverse the encryption of Gp on the 𝐶 to get 𝑃𝑇
the decryption process.
𝑃𝑇: 𝑤1+𝑖 → 𝑤1

Table 5: The Table Below Shows the Permutation Values of 𝑤5


1 6 11 5 10 4 9 3 8 2 7
3 4 5 9 1 8 3 7 6 5 2

The table above is the table of permutation of NIN digits  The Decryption Takes Place in Two Forms.
in which the sender is assumed to receive then use the
decryption method and decode the coding process to use the  Identifying the key
original NIN numbers which was intended for concealing.  Using the key to decode the message
From (i) above, the message is 345918376524 and the
subscript is 4 which is the key used in the encoding process,
and then we move to item (ii).

 𝑃𝑇: 𝑤1+𝑖 → 𝑤1 , where (𝑖 = 4)


 𝑃𝑇: 𝑤1+4 → 𝑤1 ⋮ 𝑤4−1 → 𝑤1
 And 𝑤1 is the final arrangement of the letters.

Table 6: Transposed NIN


1 6 11 5 10 4 9 3 8 2 7
3 4 5 9 1 8 3 7 6 5 2

Table 7: Decoded NIN


1 2 3 4 5 6 7 8 9 10 11
3 5 7 8 9 4 2 6 3 1 5

The above tables indicate the arrangements of the encoded REFERENCES


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