Permutation of National Identification Number For A Better Security in Communication Channel
Permutation of National Identification Number For A Better Security in Communication Channel
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,
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).
[5]. Kashish G and Supriya K.(2013) Modified Ceaser [18]. Garba A. I, Zakari, Y. and Hassan, A. (2019), on the
Cipher for a Better Security Enhancement. fuzzy nature of constructed algebraic structure Gp.
International Journal of Computer Application.73:26- Bayero Journal of Pure and applied sciences,
31 12(1):146-150
[6]. Mishra A. (2013), Enhancing security of Ceaser cipher [19]. A. Hassan, A. Garko, S. Sani, U. Abdullahi and S.
using different methods. International Journal of Sahalu (2023) Combined Techniques of Hill Cipher
Research in Engineering and Technology. 2(09):327- and Transposition Cipher. Journal of Mathematics
332. Letters, 2023, 1, 822
[7]. Garba A. I and Ibrahim A. A. (2010), A new method www.scipublications.org/journal/index.php/jml DOI:
of constructing a Variety of Finite Group Based on 10.31586/jml.2023.822
some succession scheme. Internal Journal of Physical [20]. Rejewski, Marian (1980). "An application of the
Science. 2(3):23-26. theory of permutations in breaking the Enigma
[8]. Vukašin, G and Sandra, O (2024) Group Processes & cipher". Applicationes Mathematicae. 16 (4): 543–
Intergroup Relations Active rejection or passive 559. doi:10.4064/am-16-4-543-559. ISSN 1233-7234.
indifference? Mixed-methods evidence on national [21]. https://www.cbn.gov.ng/out/2017/ccd/circular%
(dis) identification, Group Processes & Intergroup 20and%20exposure% 20draft% 20on% 20the%
Relations.1–22 DOI: 0.1177/136 84302241229981 20framework% 20for%20bvn%
[9]. Rajendra K. B, Uzma B, Nupura V, Vidya K, Pramod 20operations%20and%20watchlist.pdf
R. C and Sushma G (2018) Proposing national
identification number on dental prostheses as
universal personal identification code – A revolution
in forensic odontology, Journal of Forensic Dental
Sciences . Vol 7 / Issue 2 pp:84-89
[10]. Osita, E (2023) Understanding the Mandatory use Of
National Identification Number in Nigeria.
https://www.Researchgate.net/publication/37596387
1
[11]. Maya B-W., Ella D., Einat, E. Noga, S and Peter F. T
(2024) Values and National Identification in Minority
and Majority Youth: Longitudinal Multi-Study
Findings. Journal of Youth and Adolescence
https://doi.org/10.1007/s10964-024-01965-0 pp:1-18
[12]. Audu M.S. (1986), Generating Sets for Transitive
Permutation groups of prime-power order. The
Journal of Mathematical Association of Nigeria
Abacus, 17(2), 22-26.
[13]. Ibrahim A. A. (2006), Correspondence between the
Length of some Class of Permutation patterns and
Primitive Elements of Automophism Group modulo n,
Abacus. The Journal of mathematical Association of
Nigeria, 33:143-154.
[14]. Alhassan, M. J; Hassan, A; Sani, S. and Alhassan, Y.
(2021). A Combined Technique of an Affine Cipher
and Transposition Cipher Quest Journals Journal of
Research in Applied Mathematics Volume 7. Issue 10
(2021) pp: 08-12
[15]. Hassan, A; Alhassan, M. J; Alhassan, Y. and Sani, S.
(2021). Cryptography as a Solution for a Better
Security International Journal of Advances in
Engineering and Management (IJAEM :3(12). pp:
849-853
[16]. Azzam A and Sumarsono (2017), A Modifying of Hill
Cipher Algorithm with 3 Substitution Ceaser Cipher.
Proceedings International Conference of Science and
Engineering, Indonesia.1: 157-163.
[17]. Garba A. I, Yusuf A and Hassan A. (2018), Some
Topological Properties of a Constructed Algebraic
Structure. Journal of the Nigerian Association of
Mathematical Physics, 45:21-26.