Threshold cryptography based on Asmuth–Bloom secret sharing

Kaya, Kamer; Selçuk, Ali Aydın

doi:10.1016/j.ins.2007.04.008

Cited by 62 publications

(13 citation statements)

References 27 publications

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“…1. the variant in [7] considers extended Asmuth-Bloom (t + 1, n)-threshold sequences of co-primes instead of Asmuth-Bloom (t + 1, n)-threshold sequences of co-primes, which are simply defined by replacing the Asmuth-Bloom constraint by the following one:…”

Section: The Asmuth-bloom Secret Sharing Scheme and Variationsmentioning

confidence: 99%

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On the asymptotic idealness of the Asmuth-Bloom threshold secret sharing scheme

Drăgan

Ţiplea

2018

Information Sciences

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Section: The Asmuth-bloom Secret Sharing Scheme and Variationsmentioning

confidence: 99%

“…Moreover, [4] studies the security of the Asmuth-Bloom threshold scheme [1] and also proposes some asymptotically perfect and ideal variants of it. Another variant of the Asmuth-Bloom threshold scheme was proposed in [7] which provides better security than the original Asmuth-Bloom threshold scheme.…”

Section: Introductionmentioning

confidence: 99%

On the asymptotic idealness of the Asmuth-Bloom threshold secret sharing scheme

Drăgan

Ţiplea

2018

Information Sciences

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“…This property shows that the probability of computing s ℓ by means of ( 10) is exactly the probability of computing s ℓ by means of (9). Plugging this into the definition of loss of entropy, we obtain that the loss of entropy associated to A in the CRT-DMAS scheme when recovering s ℓ is exactly the loss of entropy associated to A in the Asmuth-Bloom scheme with public shares for the level ℓ.…”

Section: Theorem 2 the Crt-dmas Secret Sharing Scheme Is Asymptotically Ideal With Respect To The Uniform Distribution On The Secret Spacmentioning

confidence: 82%

“…There is one more important property that we need, namely: distinct solutions to (9) leads to the same number of solutions to (10). Let α be the number of solutions to (10) obtained from a solution to (9), Sol(n) be the number of solutions to the system (n) of equations, and Solðn; x ℓ Þ ¼ s ℓ Þ be the number of solutions with x ℓ = s ℓ to the system (n) of equations, where n = 9, 10. Then,…”

Section: Theorem 2 the Crt-dmas Secret Sharing Scheme Is Asymptotically Ideal With Respect To The Uniform Distribution On The Secret Spacmentioning

confidence: 99%

Asymptotically ideal Chinese remainder theorem ‐based secret sharing schemes for multilevel and compartmented access structures

Ţiplea

Drăgan

2021

IET Information Security

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Multilevel and compartmented access structures are two important classes of access structures where participants are grouped into levels/compartments with different degrees of trust and privileges. The construction of secret sharing schemes for such access structures has been the attention of researchers for a long time. Two main approaches have been taken so far, one of them is based on polynomial interpolation and the other one is based on the Chinese Remainder Theorem (CRT). In this article the first asymptotically ideal CRT‐based secret sharing schemes for (disjunctive, conjunctive) multilevel and compartmented access structures are proposed. Our approach is compositional and it is based on a variant of the Asmuth‐Bloom secret sharing scheme where some participants may have public shares. Based on this, the proposed secret sharing schemes for multilevel and compartmented access structures are asymptotically ideal if and only if they are based on 1‐compact sequences of co‐primes. Possible applications for secret image and multi‐secret sharing are pointed‐out.

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“…A method based on Blakley's concept is proposed in [13]. In the secret sharing scheme presented in [14], Asmuth-Bloom scheme has been used.…”

Section: B Blakley Secret Sharing Schemementioning

confidence: 99%

Random sequence based secret sharing of an encrypted color image

Kandar

Dhara

2012

2012 1st International Conference on Recent Advances in Information Technology (RAIT)

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Secret sharing was first proposed by Shamir and Blakley individually. It refers to a method of distributing secret information amongst a group of individuals say n, each of whom is allocated a share of the secret information. The secret can only be reconstructed when a sufficient number of individuals' shares say k are combined together. The existing Secret sharing schemes are complex and depend on intensive mathematical calculation. Secret sharing technique has lack of security as from a sufficient number of shares secret information can easily be retrieved. In this current work we have taken a color image as a secret and have proposed a new technique called random sequence which needs very less computation for k-n secret sharing. For security purpose the image is encrypted by bit sieving with another image used as a key.

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Threshold cryptography based on Asmuth–Bloom secret sharing

Cited by 62 publications

References 27 publications

On the asymptotic idealness of the Asmuth-Bloom threshold secret sharing scheme

On the asymptotic idealness of the Asmuth-Bloom threshold secret sharing scheme

Asymptotically ideal Chinese remainder theorem ‐based secret sharing schemes for multilevel and compartmented access structures

Random sequence based secret sharing of an encrypted color image

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