Classification of Osborn loops of order 4n

Isere, A. O.; Adeniran, John Olushola; Jaiyeola, Temitope Gbolahan

doi:10.4067/s0716-09172019000100031

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Theorem 224 a Loop (G •) Is An Osborn Loop If And Only If For All X Y Z ∈ G It Satisfies Any Of The Identities Below1

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2021

2023

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“…The smallest Osborn loop is of order 16 [39]. Osborn loops of order 4n were constructed in [17][18][19][20]. For more works on Osborn loops see [14, 21, 22, 24-26, 29-32, 46].…”

Section: Theorem 224 a Loop (G •) Is An Osborn Loop If And Only If For All X Y Z ∈ G It Satisfies Any Of The Identities Belowmentioning

confidence: 99%

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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“…The smallest Osborn loop is of order 16 [39]. Osborn loops of order 4n were constructed in [17][18][19][20]. For more works on Osborn loops see [14, 21, 22, 24-26, 29-32, 46].…”

Section: Theorem 224 a Loop (G •) Is An Osborn Loop If And Only If For All X Y Z ∈ G It Satisfies Any Of The Identities Belowmentioning

confidence: 99%