Topic

# Verifiable secret sharing

About: Verifiable secret sharing is a research topic. Over the lifetime, 4241 publications have been published within this topic receiving 99569 citations.

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01 Dec 1979TL;DR: Certain cryptographic keys, such as a number which makes it possible to compute the secret decoding exponent in an RSA public key cryptosystem, 1 , 5 or the system master key and certain other keys in a DES cryptos system, 3 are so important that they present a dilemma.

Abstract: Certain cryptographic keys, such as a number which makes it possible to compute the secret decoding exponent in an RSA public key cryptosystem, 1 , 5 or the system master key and certain other keys in a DES cryptosystem, 3 are so important that they present a dilemma. If too many copies are distributed one might go astray. If too few copies are made they might all be destroyed.

3,184 citations

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TL;DR: This work shows how GHZ states can be used to split quantum information into two parts so that both parts are necessary to reconstruct the original qubit.

Abstract: Secret sharing is a procedure for splitting a message into several parts so that no subset of parts is sufficient to read the message, but the entire set is. We show how this procedure can be implemented using Greenberger-Horne-Zeilinger (GHZ) states. In the quantum case the presence of an eavesdropper will introduce errors so that his presence can be detected. We also show how GHZ states can be used to split quantum information into two parts so that both parts are necessary to reconstruct the original qubit.

2,789 citations

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11 Aug 1991TL;DR: It is shown how to distribute a secret to n persons such that each person can verify that he has received correct information about the secret without talking with other persons.

Abstract: It is shown how to distribute a secret to n persons such that each person can verify that he has received correct information about the secret without talking with other persons. Any k of these persons can later find the secret (1 ? k ? n), whereas fewer than k persons get no (Shannon) information about the secret. The information rate of the scheme is 1/2 and the distribution as well as the verification requires approximately 2k modular multiplications pr. bit of the secret. It is also shown how a number of persons can choose a secret "in the well" and distribute it veritably among themselves.

2,543 citations

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28 May 2006

TL;DR: In this paper, a distributed protocol for generating shares of random noise, secure against malicious participants, was proposed, where the purpose of the noise generation is to create a distributed implementation of the privacy-preserving statistical databases described in recent papers.

Abstract: In this work we provide efficient distributed protocols for generating shares of random noise, secure against malicious participants. The purpose of the noise generation is to create a distributed implementation of the privacy-preserving statistical databases described in recent papers [14,4,13]. In these databases, privacy is obtained by perturbing the true answer to a database query by the addition of a small amount of Gaussian or exponentially distributed random noise. The computational power of even a simple form of these databases, when the query is just of the form ∑if(di), that is, the sum over all rows i in the database of a function f applied to the data in row i, has been demonstrated in [4]. A distributed implementation eliminates the need for a trusted database administrator.
The results for noise generation are of independent interest. The generation of Gaussian noise introduces a technique for distributing shares of many unbiased coins with fewer executions of verifiable secret sharing than would be needed using previous approaches (reduced by a factor of n). The generation of exponentially distributed noise uses two shallow circuits: one for generating many arbitrarily but identically biased coins at an amortized cost of two unbiased random bits apiece, independent of the bias, and the other to combine bits of appropriate biases to obtain an exponential distribution.

1,567 citations

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TL;DR: As the first part of a study of problems involving common randomness at distance locations, information-theoretic models of secret sharing (generating a common random key at two terminals, without letting an eavesdropper obtain information about this key) are considered.

Abstract: As the first part of a study of problems involving common randomness at distance locations, information-theoretic models of secret sharing (generating a common random key at two terminals, without letting an eavesdropper obtain information about this key) are considered. The concept of key-capacity is defined. Single-letter formulas of key-capacity are obtained for several models, and bounds to key-capacity are derived for other models. >

1,471 citations