# Independent Zero-Knowledge Sets

@inproceedings{Gennaro2006IndependentZS, title={Independent Zero-Knowledge Sets}, author={Rosario Gennaro and Silvio Micali}, booktitle={ICALP}, 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…

## 35 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).

### A New Construction of Zero-Knowledge Sets Secure in Random Oracle Model

- Computer Science, MathematicsThe First International Symposium on Data, Privacy, and E-Commerce (ISDPE 2007)
- 2007

This paper proposes a new algebraic scheme that is completely different from all existing schemes and employs neither mercurial commitments nor tree frame as all previous schemes did.

### 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.

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

- Computer Science, MathematicsInternational 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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