Private coins versus public coins in interactive proof systems
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Trading group theory for randomness
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
The complexity of perfect zero-knowledge
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
A hierarchy of polynomial time lattice basis reduction algorithms
Theoretical Computer Science
Non-interactive zero-knowledge and its applications
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
The knowledge complexity of interactive proof systems
SIAM Journal on Computing
Statistical zero-knowledge languages can be recognized in two rounds
Journal of Computer and System Sciences
Journal of the ACM (JACM)
SIAM Journal on Computing
The knowledge complexity of quadratic residuosity languages
Theoretical Computer Science
Generating hard instances of lattice problems (extended abstract)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
The shortest vector problem in L2 is NP-hard for randomized reductions (extended abstract)
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Honest-verifier statistical zero-knowledge equals general statistical zero-knowledge
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
An efficient non-interactive statistical zero-knowledge proof system for quasi-safe prime products
CCS '98 Proceedings of the 5th ACM conference on Computer and communications security
On the complexity of computing short linearly independent vectors and short bases in a lattice
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Multiple NonInteractive Zero Knowledge Proofs Under General Assumptions
SIAM Journal on Computing
On relationships between statistical zero-knowledge proofs
Journal of Computer and System Sciences
On the limits of nonapproximability of lattice problems
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
A sieve algorithm for the shortest lattice vector problem
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Complexity of Lattice Problems
Complexity of Lattice Problems
A complete problem for statistical zero knowledge
Journal of the ACM (JACM)
Randomness-Efficient Non-Interactive Zero-Knowledge (Extended Abstract)
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Image Density is Complete for Non-Interactive-SZK (Extended Abstract)
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Can Statistical Zero Knowledge Be Made Non-interactive? or On the Relationship of SZK and NISZK
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
Everything Provable is Provable in Zero-Knowledge
CRYPTO '88 Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology
On Defining Proofs of Knowledge
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
Comparing Entropies in Statistical Zero Knowledge with Applications to the Structure of SZK
COCO '99 Proceedings of the Fourteenth Annual IEEE Conference on Computational Complexity
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Sampling Short Lattice Vectors and the Closest Lattice Vector Problem
CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
New lattice-based cryptographic constructions
Journal of the ACM (JACM)
On lattices, learning with errors, random linear codes, and cryptography
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
Zero knowledge with efficient provers
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Worst-Case to Average-Case Reductions Based on Gaussian Measures
SIAM Journal on Computing
Trapdoors for hard lattices and new cryptographic constructions
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Limits on the Hardness of Lattice Problems in lp Norms
Computational Complexity
The complexity of the covering radius problem
Computational Complexity
Perfect non-interactive zero knowledge for NP
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
Sampling methods for shortest vectors, closest vectors and successive minima
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Zero-Knowledge Protocols for NTRU: Application to Identification and Proof of Plaintext Knowledge
ProvSec '09 Proceedings of the 3rd International Conference on Provable Security
An efficient and parallel Gaussian sampler for lattices
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
The geometry of lattice cryptography
Foundations of security analysis and design VI
Trapdoors for lattices: simpler, tighter, faster, smaller
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Lossy Trapdoor Functions and Their Applications
SIAM Journal on Computing
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We construct noninteractive statistical zero-knowledge(NISZK) proof systems for a variety of standard approximation problems on lattices, such as the shortest independent vectors problem and the complement of the shortest vector problem. Prior proof systems for lattice problems were either interactive or leaked knowledge (or both).Our systems are the first known NISZKproofs for any cryptographically useful problems that are not related to integer factorization. In addition, they are proofs of knowledge, have reasonable complexity, and generally admit efficient prover algorithms (given appropriate auxiliary input). In some cases, they even imply the first known interactivestatistical zero-knowledge proofs for certain cryptographically important lattice problems.We also construct an NISZKproof for a special kind of disjunction (i.e., OR gate) related to the shortest vector problem. This may serve as a useful tool in potential constructions of noninteractive (computational) zero knowledge proofs for NPbased on lattice assumptions.