A Model on Dynamic Threshold Multi-Secret Sharing Scheme using Pell's Equation with Jacobi Symbol

Rao, Michaël; Sarma, K V S S R S S; Avadhani, P. S.

doi:10.1109/itng.2013.140

Cited by 3 publications

(2 citation statements)

References 11 publications

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“…The efficiency of its implementation using GMP library [Gt12] is analyzed in [RAL15]. Also a Dynamic Threshold Multi Secret Sharing scheme [RSAB13] and a Signature scheme [Mis14] have been recently published. Other RSA type cryptosystems based on elliptic curves exist, such as [Koy95], [KMOV92], and [Dem94].…”

Section: The Use Of Conic Equations In Cryptographymentioning

confidence: 99%

An efficient and secure RSA-like cryptosystem exploiting Rédei rational functions over conics

Bellini¹,

Murru²

2016

Finite Fields and Their Applications

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We define an isomorphism between the group of points of a conic and the set of integers modulo a prime equipped with a non-standard product. This product can be efficiently evaluated through the use of Rédei rational functions. We then exploit the isomorphism to construct a novel RSA-like scheme. We compare our scheme with classic RSA and with RSA-like schemes based on the cubic or conic equation. The decryption operation of the proposed scheme turns to be two times faster than RSA, and involves the lowest number of modular inversions with respect to other RSA-like schemes based on curves. Our solution offers the same security as RSA in a one-to-one communication and more security in broadcast applications.

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Section: The Use Of Conic Equations In Cryptographymentioning

confidence: 99%

An efficient and secure RSA-like cryptosystem exploiting Rédei rational functions over conics

Bellini¹,

Murru²

2016

Finite Fields and Their Applications

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show abstract

“…The main example is provided by elliptic curves over finite fields, whose use in cryptography was introduced, independently, by Koblitz [12] and Miller [17]. Moreover, curves with a group's structure, usually cubics or conics, can be exploited for constructing RSA-like schemes (see, e.g., [4,8,13,19,20,22,23,24]), for improving the performances in the decryption procedures, and having also more security than RSA in some contexts, like broadcast scenarios. Many of these cryptosystems were studied exploiting the properties of the Pell's hyperbola that is the set of solutions in a field F of the famous Pell's equation x 2 −Dy 2 = 1, with D ∈ F * , like in [5], where the authors exhibited an RSA-like cryptosystem over the Pell's hyperbola exploiting multi-factor moduli.…”

Section: Introductionmentioning

confidence: 99%

Group law on affine conics and applications to cryptography

Bellini

Murru

Scala

et al. 2021

Applied Mathematics and Computation

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Novel Threshold Changeable Secret Sharing Schemes Based on Polynomial Interpolation

Yuan

Guo

et al. 2016

PLoS ONE

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After any distribution of secret sharing shadows in a threshold changeable secret sharing scheme, the threshold may need to be adjusted to deal with changes in the security policy and adversary structure. For example, when employees leave the organization, it is not realistic to expect departing employees to ensure the security of their secret shadows. Therefore, in 2012, Zhang et al. proposed (t → t′, n) and ({t1, t2,⋯, tN}, n) threshold changeable secret sharing schemes. However, their schemes suffer from a number of limitations such as strict limit on the threshold values, large storage space requirement for secret shadows, and significant computation for constructing and recovering polynomials. To address these limitations, we propose two improved dealer-free threshold changeable secret sharing schemes. In our schemes, we construct polynomials to update secret shadows, and use two-variable one-way function to resist collusion attacks and secure the information stored by the combiner. We then demonstrate our schemes can adjust the threshold safely.

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A Model on Dynamic Threshold Multi-Secret Sharing Scheme using Pell's Equation with Jacobi Symbol

Cited by 3 publications

References 11 publications

An efficient and secure RSA-like cryptosystem exploiting Rédei rational functions over conics

An efficient and secure RSA-like cryptosystem exploiting Rédei rational functions over conics

Group law on affine conics and applications to cryptography

Novel Threshold Changeable Secret Sharing Schemes Based on Polynomial Interpolation

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