On three cryptographic identities in left universal Osborn loops

Jaiyeola, Temitope Gbolahan

doi:10.1080/09720529.2011.10698322

Cited by 6 publications

(4 citation statements)

References 18 publications

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“…(A-A1-A2-A3-A4-B Cryptographic Algorithm with Single Key) A cipher algorithm based on the assumption that (G, + 1 ) obeys the left involutory law. LIL1 is a cryptographic identity (see [24,25,Def. 2.2]) of order 6.…”

Section: Is An Involutory Quandle If and Only If Rdli And Rili Are Satisfied; (3) (G + I ) Is A Right-latin Quandle If And Only If Rdli Amentioning

confidence: 99%

“…2.2]) of order 6. In [24,25], 'many receivers' cipher algorithm was discussed in detail and it applies here. That is, information from A (Isere) to B (Jaiyeola) through some other trusted parties (4) who the information is not meant for, but mindful of possible intruders.…”

Section: Is An Involutory Quandle If and Only If Rdli And Rili Are Satisfied; (3) (G + I ) Is A Right-latin Quandle If And Only If Rdli Amentioning

confidence: 99%

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Latin quandles and applications to cryptography

Jaiyeola¹,

Adeniran²,

Isere³

2021

Math. Appl.

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This work investigated some properties of Latin quandles that are applicable in cryptography. Four distinct cores of an Osborn loop (non-diassociative and non-power associative) were introduced and investigated. The necessary and sufficient conditions for these cores to be (i) (left) quandles (ii) involutory quandles (iii) quasi-Latin quandles and (iv) involutory quasi-Latin quandles were established. These conditions were judiciously used to build cipher algorithms for cryptography in some peculiar circumstances.

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Section: Is An Involutory Quandle If and Only If Rdli And Rili Are Satisfied; (3) (G + I ) Is A Right-latin Quandle If And Only If Rdli Amentioning

confidence: 99%

Section: Is An Involutory Quandle If and Only If Rdli And Rili Are Satisfied; (3) (G + I ) Is A Right-latin Quandle If And Only If Rdli Amentioning

confidence: 99%

Latin quandles and applications to cryptography

Jaiyeola¹,

Adeniran²,

Isere³

2021

Math. Appl.

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“…lá and Adéníran [15] and Jaiyéo . lá [11,13]. Shcherbacov [27] has a chapter dedicated to the application of quasigroups in cryptology.…”

Section: Introductionmentioning

confidence: 99%

On the universality and isotopy-isomorphy of (r,s,t)-inverse quasigroups and loops with applications to cryptography

Ilemobade,

George,

Gbolahan

2023

QRS

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This paper introduced a condition called $\mathcal{R}$-condition under which $(r,s,t)$-inverse quasigroups are universal. Middle isotopic $(r,s,t)$-inverse loops, satisfying the $\mathcal{R}$-condition and possessing a trivial set of $r$-weak inverse permutations were shown to be isomorphic; isotopy-isomorphy for $(r,s,t)$-inverse loops. Isotopy-isomorphy for $(r,s,t)$-inverse loops was generally characterized. With the $\mathcal{R}$-condition, it was shown that for positive integers $r$, $s$ and $t$, if there is a $(r,s,t)$-inverse quasigroup of order $3k$ with an inverse-cycle of length $gcd(k,r+s+t)>1$, then there exists an $(r,s,t)$-inverse quasigroup of order $3k$ with an inverse-cycle of length $gcd\big(k(r+s+t), (r+s+t)^2\big)$. The procedure of application of such $(r,s,t)$-inverse quasigroups to cryptography was described and explained, while the feasibility of such $(r,s,t)$-inverse quasigroups was illustrated with sample values of $k,r,s$ and $t$.

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“…The application of some identities in universal Osborn loops to cryptography were reported in Jaiyéo . lá [19,21], Jaiyéo . lá and Adéníran [27].…”

Section: Introductionmentioning

confidence: 99%

Classification of Osborn loops of order 4n

Isere

Adeniran

Jaiyeola

2019

Proyecciones (Antofagasta)

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The smallest non-associative Osborn loop is of order 16. Attempts in the past to construct higher orders have been very difficult. In this paper, some examples of finite Osborn loops of order 4n, n = 4, 6, 8, 9, 12, 16 and 18 were presented. The orders of certain elements of the examples were considered. The nuclei of two of the examples were also obtained and these were used to establish the classification of these Osborn loops up to isomorphism. Moreover, the central properties of these examples were examined and were all found to be having a trivial center and no non-trivial normal subloop. Therefore, these examples of Osborn loops are simple Osborn loops.

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On three cryptographic identities in left universal Osborn loops

Cited by 6 publications

References 18 publications

Latin quandles and applications to cryptography

Latin quandles and applications to cryptography

On the universality and isotopy-isomorphy of (r,s,t)-inverse quasigroups and loops with applications to cryptography

Classification of Osborn loops of order 4n

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