On existence of nonassociative LA-ring

Rehman, Inayatur; Shah, Muhammad

doi:10.2478/auom-2013-0054

Cited by 2 publications

(1 citation statement)

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“…The set of all units in an LA-ring forms a multiplicative LA-group [32]. An LA-Ąeld is an LA-ring whose non-zero elements form a multiplicative LA-group [33]. The existence of a non-associative LA-ring is proved in [33] and examples of some Ąnite LA-rings and LA-Ąelds are also provided.…”

Section: La-ringsmentioning

confidence: 99%

An RGB Image Encryption Scheme based on Amalgamation of 3D-Dynamical Systems and a Left Almost ring

Haider,

Sanam

2023

Preprint

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Digital images are widely used in the areas of medicine, defense, and space technology but their safeguarding and secure transmission is becoming a prevalent issue for researchers and engineers. Image encryption techniques usually make use of commutative and associative algebraic structures like finite Galois fields and unitary commutative rings. In this paper, first, a non-associative LA-ring of order 256 is obtained using computational techniques, and then this LA-ring and the three-dimensional non-linear chaotic Rucklidge system are combined to generate three chaotic-algebraic sequences which are used to cause confusion in encryption. For the sake of diffusion, the three dimensional non-linear chaotic Genesio-Tesi system is utilized. The motivation behind using an LA ring is to boast the robustness and increase the key space due to this algebraic structure's non-associative and non-commutative properties. Furthermore, the number of control parameters has increased because of two, three dimensional chaotic systems which aid in expanding the key space and increase encryption efficiency thus providing better security. Performance metrics are carried out for encrypted images and a comparison with some of the existing chaos dependent schemes is made, proving that the suggested technique approaches the standard prime level and is good enough for encryption processes and real-time communication.

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Section: La-ringsmentioning

confidence: 99%