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

  title={Statistical Zero-Knowledge Proofs with Efficient Provers: Lattice Problems and More},
  author={Daniele Micciancio and Salil P. Vadhan},
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. 

Zero knowledge with efficient provers

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

  • S. Vadhan
  • Mathematics, Computer Science
  • 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

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

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

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

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

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

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

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

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.



Practical zero-knowledge proofs: Giving hints and using deficiencies

New zero-knowledge proofs are given for some number-theoretic problems that are much more efficient than the previously known proofs and do not require the prover to be superpolynomial in power.

A complete problem for statistical zero knowledge

We present the first complete problem for SZK, the class of promise problems possessing statistical zero-knowledge proofs (against an honest verifier). The problem, called Statistical Difference, i...

The complexity of perfect zero-knowledge

  • L. Fortnow
  • Computer Science, Mathematics
    Adv. Comput. Res.
  • 1989
It is shown that knowledge complexity can be used to show that a language is easy to prove and that there are not any perfect zero-knowledge protocols for NP-complete languages unless the polynomial time hierarchy collapses.

An efficient non-interactive statistical zero-knowledge proof system for quasi-safe prime products

The first simple and efficient zer~knowledge proof that an deged RSA modtius is of the correct form is presented, i.e. the product of two primes, which proves that the primes composing the RSA moddus are quasi-safe.

Random self-reducibility and zero knowledge interactive proofs of possession of information

  • M. TompaH. Woll
  • Mathematics, Computer Science
    28th Annual Symposium on Foundations of Computer Science (sfcs 1987)
  • 1987
It is shown that any "random self-reducible" problem has a zero knowledge interactive proof of this sort, and new zeroknowledge interactive proofs are exhibited for "knowledge" of the factorization of an integer, nonmembership in cyclic subgroups of Zp*, and determining whether an element generates Zp*.

Making zero-knowledge provers efficient

Zero-Knowledge Provers Efficient

Collision-Free Hashing from Lattice Problems

It is shown that essentially the same construction of one-way functions whose security is equivalent to the difficulty of some well known approximation problems in lattices can be used to obtain collision-free hashing.

Statistical Zero-Knowledge Languages can be Recognized in Two Rounds

On relationships between statistical zero-knowledge proofs

  • T. Okamoto
  • Computer Science, Mathematics
    STOC '96
  • 1996
This paper solves several fundamental open problems about statistical zero-knowledge interactive proofs (SZKIPs) and proves that the complement of L has a statisticalzero-knowledge constant (one) round interactive proof against an honest verifier.

Honest-verifier statistical zero-knowledge equals general statistical zero-knowledge

We show how to transform any interactive proof system which is statistical zero-knowledge with respect to the honest-verifier, into a proof system which is statistical zero-knowledgewith respect to