Codes Over a Subset of Octonion Integers

Flaut, Cristina

doi:10.1007/s00025-015-0442-6

Cited by 2 publications

(4 citation statements)

References 13 publications

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“…We have successfully extended some of the results of Hamiltonian quaternion integers [40], which are applicable for the above discussed associative and commutative ring ∨ where ∨ ⊂ O (Octavian integers) [34].…”

Section: Conjugate and Norm Of Octonionsmentioning

confidence: 85%

“…In this manuscript, we proposed a robust way for constructing S-boxes using Gravesian octonion integers. In general, octonions are non-commutative and non-associative [34], but under certain conditions, they are commutative; we discussed that study throughout this paper. The presented work is developed so that for every valid input, it yields two S-Boxes with strong cryptographic properties, while in [24][25][26][27], there is no guarantee of establishing S-boxes on both coordinates.…”

Section: B Our Contributionmentioning

confidence: 99%

“…. + e 7 ) : h 0 , h 1 ∈ Z} which is a subring of Octavian integers [34], the commutativity property of multiplications holds over O(K).…”

Section: B the Product Of Octonionsmentioning

confidence: 99%

“…this shows that the octonionic norm is multiplicative. In this work, we focus on Gravesian octonion integers O(Z), the octonions with all coordinates in Z [34].…”

Section: Conjugate and Norm Of Octonionsmentioning

confidence: 99%

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Design of Nonlinear Component of Block Cipher Using Gravesian Octonion Integers

et al. 2023

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Being the only nonlinear component in many cryptosystems, an S-box is an integral part of modern symmetric ciphering techniques that creates randomness and increases confidentiality at the substitution stage of the encryption. The ability to construct a cryptographically strong S-box solely depends on its construction scheme. The primary purpose of an S-box in encryption standards is to establish confusion between the m-bit input into the n-bit output (both m, n >= 2). This article proposed a robust way to construct S-boxes based on the Gravesian octonion integers. We chunk the paper into threefold: firstly, a comprehensive technique for constructing S-box using affine mapping is described. The presented work is developed in such a way that for every valid input, it generates two S-boxes. Secondly, the strength of the newly generated S-box is evaluated by passing through a rigorous security analysis. Finally, a thorough comparison of the newly developed method with some well-known existing schemes is conducted. We mainly targeted some elliptic curve-based S-boxes in comparison by taking the same parameters in our scheme. The computational results and performance analysis reveal that the propose algorithm can construct a large number of distinct S-boxes that are cryptographically secured and create high resistance against various cryptanalysis attacks.

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Section: Conjugate and Norm Of Octonionsmentioning

confidence: 85%

Section: B Our Contributionmentioning

confidence: 99%

“…. + e 7 ) : h 0 , h 1 ∈ Z} which is a subring of Octavian integers [34], the commutativity property of multiplications holds over O(K).…”

Section: B the Product Of Octonionsmentioning

confidence: 99%

“…this shows that the octonionic norm is multiplicative. In this work, we focus on Gravesian octonion integers O(Z), the octonions with all coordinates in Z [34].…”

Section: Conjugate and Norm Of Octonionsmentioning

confidence: 99%

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