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… 

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References

SHOWING 1-10 OF 24 REFERENCES

Non-interactive and reusable non-malleable commitment schemes

TLDR
It is shown how to construct non-interactive NM commitments that remain non-malleable even if the adversary has access to an arbitrary number of commitments from honest players - rather than one, as in several previous schemes.

Universally Composable Commitments

We propose a new security measure for commitment protocols, called Universally Composable (UC) Commitment. The measure guarantees that commitment protocols behave like an "ideal commitment service,"

Zero-knowledge sets

  • S. MicaliM. RabinJ. Kilian
  • Computer Science, Mathematics
    44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings.
  • 2003
We show how a polynomial-time prover can commit to an arbitrary finite set S of strings so that, later on, he can, for any string x, reveal with a proof whether x /spl isin/ S or x /spl notin/ S,

Multi-trapdoor Commitments and Their Applications to Proofs of Knowledge Secure Under Concurrent Man-in-the-Middle Attacks

TLDR
The notion of multi-trapdoor commitments is introduced which is a stronger form of trapdoor commitment schemes and the construction of a compiler is constructed that takes any proof of knowledge and transforms it into one which is secure against a concurrent man-in-the-middle attack.

Magic functions

TLDR
It is shown that three apparently unrelated problems are in fact very closely related, and the Fiat-Shamir Methodology is cryptographic, and addresses a methodology suggested by Fiat and Shamir to construct a (non-interactive) signature scheme from any 3-round (not necessarily zero-knowledge) public-coin identification scheme.

Efficient and Non-interactive Non-malleable Commitment

TLDR
New constructions of non-malleable commitment schemes, in the public parameter model, based on the discrete logarithm or RSA assumptions, achieve near-optimal communication for arbitrarily-large messages and are noninteractive.

A discrete logarithm implementation of perfect zero-knowledge blobs

TLDR
The notion of a product blob is introduced, whose favorable properties depend only on at least one of these assumptions holding, and which has the advantage that it leads to proof systems which are perfect zeroknowledge, rather than only almost perfect zero-knowledge.

On Simulation-Sound Trapdoor Commitments

TLDR
A new, simpler definition for an SSTC scheme is presented that admits more efficient constructions and can be used in a larger set of applications, and how to construct S STC schemes from any one-way functions and based on specific number-theoretic assumptions is shown.

New Generation of Secure and Practical RSA-Based Signatures

TLDR
Under an appropriate assumption about RSA, the scheme is proven to be not existentially forgeable under adaptively chosen message attacks and presented a digital signature that offers both proven security and practical value.

Nonmalleable Cryptography

TLDR
The cryptosystem is the first proven to be secure against a strong type of chosen ciphertext attack proposed by Rackoff and Simon, in which the attacker knows the ciphertext she wishes to break and can query the decryption oracle on any ciphertext other than the target.