# Statistical Zero-Knowledge Proofs with Efficient Provers: Lattice Problems and More

@inproceedings{Micciancio2003StatisticalZP, title={Statistical Zero-Knowledge Proofs with Efficient Provers: Lattice Problems and More}, author={Daniele Micciancio and Salil P. Vadhan}, booktitle={CRYPTO}, year={2003} }

We construct several new statistical zero-knowledge proofs with efficient provers, i.e. ones where the prover strategy runs in probabilistic polynomial time given an NP witness for the input string.

## 149 Citations

### Zero knowledge with efficient provers

- Mathematics, Computer ScienceSTOC '06
- 2006

We prove that every problem in NP that has a zero-knowledge proof also has a zero-knowledge proof where the prover can be implemented in probabilistic polynomial time given an NP witness. Moreover,…

### The Complexity of Zero Knowledge

- Mathematics, Computer ScienceFSTTCS
- 2007

We give an informal introduction to zero-knowledge proofs, and survey their role both in the interface between complexity theory and cryptography and as objects of complexity-theoretic study in their…

### Zero-Knowledge Interactive Proof Systems for New Lattice Problems

- Mathematics, Computer ScienceIMACC
- 2015

In this work we introduce a new hard problem in lattices called Isometric Lattice ProblemILP and reduce Linear Code Equivalence over prime fields and Graph Isomorphism to this problem. We also show…

### Zero-Knowledge Proofs and String Commitments Withstanding Quantum Attacks

- Computer ScienceCRYPTO
- 2004

The concept of zero-knowledge (ZK) has become of fundamental importance in cryptography. However, in a setting where entities are modeled by quantum computers, classical arguments for proving ZK fail…

### Efficient Lattice-Based Zero-Knowledge Arguments with Standard Soundness: Construction and Applications

- Mathematics, Computer ScienceIACR Cryptol. ePrint Arch.
- 2019

We provide new zero-knowledge argument of knowledge systems that work directly for a wide class of language, namely, ones involving the satisfiability of matrix-vector relations and integer relations…

### On NC1 Boolean Circuit Composition of Non-interactive Perfect Zero-Knowledge

- Computer Science, MathematicsMFCS
- 2004

NIPZK and PZK are the class of languages having a Perfect Zero-Knowledge proof system in the non-interactive and interactive model, respectively.

### Batch Verification for Statistical Zero Knowledge Proofs

- Computer Science, MathematicsIACR Cryptol. ePrint Arch.
- 2020

It is shown that, for every problem Π, there exists an honest-verifier SZK protocol for batch verification of k instances, with communication complexity poly(n)+k ·poly(log n, log k), where poly refers to a fixed polynomial that depends only on Π (and not on k).

### Noninteractive Statistical Zero-Knowledge Proofs for Lattice Problems

- Mathematics, Computer ScienceCRYPTO
- 2008

These systems are the first known NISZK proofs for any cryptographically useful problems that are not related to integer factorization and generally admit efficient prover algorithms (given appropriate auxiliary input).

### Precise Zero Knowledge

- Computer Science, Mathematics
- 2011

The notion of Precise Zero Knowledge is put forward and its rst implementations in a variety of settings under standard complexity assumptions are provided.

### A study of perfect zero-knowledge proofs

- Mathematics, Computer Science
- 2008

It is proved that all the known problems admitting perfect zero-knowledge (PZK) proofs can be characterized as non-interactive instance-dependent commitment schemes, and this result is used to generalize and strengthen previous results, as well as to prove new results about PZK problems.

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