Inside adversary combinatorial attacks in secret sharing scheme via linear system of equations when n = 5

Reddy, L. Sreenivasulu; Kumar, Indrajeet

doi:10.47974/JDMSC-1866

Open Access Research Article

Inside adversary combinatorial attacks in secret sharing scheme via linear system of equations when n = 5

^*L. Sreenivasulu ReddyCorresponding authorsreenivasulureddy.svu@gmail.comDepartment of MathematicsKalasalingam Academy of Research and EducationKrishnankoil, Tamil Nadu, 626126, IndiaView full profile → , Indrajeet Kumarindrajeet.stats@gmail.comDepartment of StatisticsCentral University of South BiharGaya, Bihar, 824236, IndiaView full profile →

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pp. 715–732Vol. 28Issue 3April 2025DOI: 10.47974/JDMSC-1866 Crossmark XML

Received:: 17 May 2023
Published Online:: 18 Dec 2024
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-1866
Pages:: 715–732

Abstract

When an insider possesses greater than or equal to the threshold number of secret shares, he can retrieve an entire secret without any difficulty. This kind of task doesn’t have any big problems. In this work, even if the inside adversary only knows a smaller number of secret shares than the threshold amount, we give the different computational approaches to retrieve the whole secret share. We limit five secret shares in this investigation to be used only for calculation. The assaults in this work are classified into four categories utilising probabilistic and algebraic systems of linear congruence relations, based on the number of secret shares of the adversary and the order of an algebraic field where the secret shares are formed by the distributor. Together with these assaults, this study offers a worst-case and best-case outcome for the inside adversary to retrieve the entire secret. The relationship between the threshold value t and the quantity of secret shares n is the basis of these scenarios. Lastly, we displayed the graphical analysis about the quantity of shares in the secret sharing system as well as the order of an algebraic field in which the distributor creates the secret shares.

Keywords

Secret-sharing scheme Threshold secret sharing scheme Synchronously Asynchronously Hybrid Perfect secret sharing scheme

Subject Classifications

94A0594A60

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