# Independent Zero-Knowledge Sets

@inproceedings{Gennaro2006IndependentZS, title={Independent Zero-Knowledge Sets}, author={Rosario Gennaro and Silvio Micali}, booktitle={International Colloquium on Automata, Languages and Programming}, year={2006} }

We define and construct Independent Zero-Knowledge Sets (ZKS) protocols. In a ZKS protocols, a Prover commits to a set S, and for any x, proves non-interactively to a Verifier if x ∈S or x ∉S without revealing any other information about S. In the independent ZKS protocols we introduce, the adversary is prevented from successfully correlate her set to the one of a honest prover. Our notion of independence in particular implies that the resulting ZKS protocol is non-malleable
On the way to…

## 36 Citations

### Universally composable zero-knowledge sets

- Computer Science, MathematicsInt. J. Grid Util. Comput.
- 2012

The negative result shows that the random oracle has both compression and extraction, which is a pair of paradoxical properties, to the first time this kind of property has been considered.

### Zero-Knowledge Sets With Short Proofs

- Mathematics, Computer ScienceIEEE Transactions on Information Theory
- 2011

The notion of trapdoor q -mercurial commitments (\ssr qTMCs), a notion of mercurial commitment that allows the sender to commit to an ordered sequence of exactly q messages, rather than to a single one is introduced.

### A New Efficient Construction for Non-Malleable Zero-Knowledge Sets

- Mathematics, Computer ScienceWISA
- 2010

This paper defines the independence property for ZKS in a more flexible way than the definition of Gennaro's and proves that for Z KS, the authors' independence implies non-malleability and vice versa.

### Statistically Hiding Sets

- Computer Science, MathematicsCT-RSA
- 2009

A new primitive called Statistically Hiding Sets (SHS), similar to zero-knowledge sets, but providing an information theoretic hiding guarantee, rather than one based on efficient simulation, is presented, and a new knowledge-of-exponent assumption is proved in the generic group model.

### Concise Mercurial Vector Commitments and Independent Zero-Knowledge Sets with Short Proofs

- Computer Science, MathematicsTCC
- 2010

This paper describes a new qTMC scheme where hard and short position-wise openings, both, have constant size and shows how this scheme is amenable to constructing independent zero-knowledge sets (i.e., ZKS’s that prevent adversaries from correlating their set to the sets of honest provers, as defined by Gennaro and Micali).

### Secure Database Commitments and Universal Arguments of Quasi Knowledge

- Computer Science, MathematicsIACR Cryptol. ePrint Arch.
- 2012

This work focuses on a simple database commitment functionality where besides the standard security properties, one would like to hide the size of the input of the sender, and achieves the first result where input-size hiding secure computation is achieved for an interesting functionality.

### Algebraic Construction for Zero-Knowledge Sets

- Computer Science, MathematicsJournal of Computer Science and Technology
- 2008

A new algebraic scheme that is completely different from all the existing ZKS schemes is proposed, which is computationally secure under the standard strong RSA assumption and commits the desired set without any trapdoor information.

### Concise ID-based mercurial functional commitments and applications to zero-knowledge sets

- Computer ScienceInternational Journal of Information Security
- 2019

The first ID-based mercurial functional commitment is presented which provides more efficient ZKS than Chen et al.

### Mercurial Commitments with Applications to Zero-Knowledge Sets

- Computer Science, MathematicsJournal of Cryptology
- 2012

It is demonstrated that a particular instantiation of mercurial commitments has been implicitly used by Micali, Rabin and Kilian to construct zero-knowledge sets.

### Polynomial Commitments

- Computer Science, Mathematics
- 2010

The polynomial commitment schemes are useful tools to reduce the communication cost in cryptographic protocols and apply to four problems in cryptography: verifiable secret sharing, zero-knowledge sets, credentials and content extraction signatures.

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