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Register a new userSecret sharing with a class of minimal linear codes
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Added by
Yun Song
Publication date
2012
fields
Informatics Engineering
and research's language is
English
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There are several methods for constructing secret sharing schemes, one of which is based on coding theory. Theoretically, every linear code can be used to construct secret sharing schemes. However, in general, determining the access structures of the schemes based on linear codes is very hard. This paper proposed the concept of minimal linear code, which makes the determination of the access structures of the schemes based on the duals of minimal linear codes easier. It is proved that the shortening codes of minimal linear codes are also minimal ones. Then the conditions whether several types of irreducible cyclic codes are minimal linear codes are presented. Furthermore, the access structures of secret sharing schemes based on the duals of minimal linear codes are studied, and these access structures in specific examples are obtained through programming.
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A secret can be an encrypted message or a private key to decrypt the ciphertext. One of the main issues in cryptography is keeping this secret safe. Entrusting secret to one person or saving it in a computer can conclude betrayal of the person or destruction of that device. For solving this issue, secret sharing can be used between some individuals which a coalition of a specific number of them can only get access to the secret. In practical issues, some of the members have more power and by a coalition of fewer of them, they should know about the secret. In a bank, for example, president and deputy can have a union with two members by each other. In this paper, by using Polar codes secret sharing has been studied and a secret sharing scheme based on Polar codes has been introduced. Information needed for any member would be sent by the channel which Polar codes are constructed by it.
In the $left( {t,n} right)$ threshold quantum secret sharing scheme, it is difficult to ensure that internal participants are honest. In this paper, a verifiable $left( {t,n} right)$ threshold quantum secret sharing scheme is designed combined with classical secret sharing scheme. First of all, the distributor uses the asymmetric binary polynomials to generate the shares and sends them to each participant. Secondly, the distributor sends the initial quantum state with the secret to the first participant, and each participant performs unitary operation that using the mutually unbiased bases on the obtained $d$ dimension single bit quantum state ($d$ is a large odd prime number). In this process, distributor can randomly check the participants, and find out the internal fraudsters by unitary inverse operation gradually upward. Then the secret is reconstructed after all other participants simultaneously public transmission. Security analysis show that this scheme can resist both external and internal attacks.
How to construct an ideal multi-secret sharing scheme for general access structures is difficult. In this paper, we solve an open problem proposed by Spiez et al.recently [Finite Fields and Their Application, 2011(17) 329-342], namely to design an algorithm of privileged coalitions of any length if such coalitions exist. Furthermore, in terms of privileged coalitions, we show that most of the existing multi-secret sharing schemes based on Shamir threshold secret sharing are not perfect by analyzing Yang et al.s scheme and Pang et al.s scheme. Finally, based on the algorithm mentioned above, we devise an ideal multi-secret sharing scheme for families of access structures, which possesses more vivid authorized sets than that of the threshold scheme.
In this work we present hbAVSS, the Honey Badger of Asynchronous Verifiable Secret Sharing (AVSS) protocols - an AVSS protocol that guarantees linear amortized communication overhead even in the worst case. The best prior work can achieve linear overhead only at a suboptimal resilience level (t < n/4) or by relying on optimism (falling back to quadratic overhead in case of network asynchrony or Byzantine faults). Our protocol therefore closes this gap, showing that linear communication overhead is possible without these compromises. The main idea behind our protocol is what we call the encrypt-and-disperse paradigm: by first applying ordinary public key encryption to the secret shares, we can make use of highly efficient (but not confidentiality preserving) information dispersal primitives. We prove our protocol is secure under a static computationally bounded Byzantine adversary model.
To detect frauds from some internal participants or external attackers, some verifiable threshold quantum secret sharing schemes have been proposed. In this paper, we present a new verifiable threshold structure based on a single qubit using bivariate polynomial. First, Alice chooses an asymmetric bivariate polynomial and sends a pair of values from this polynomial to each participant. Then Alice and participants implement in sequence unitary transformation on the $d$-dimensional quantum state based on unbiased bases, where those unitary transformations are contacted by this polynomial. Finally, security analysis shows that the proposed scheme can detect the fraud from external and internal attacks compared with the exiting schemes and is comparable to the recent schemes.
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