The complexity of perfect zero-knowledge
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Does co-NP have short interactive proofs?
Information Processing Letters
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
SIAM Journal on Computing
An explication of secret sharing schemes
Designs, Codes and Cryptography
Communications of the ACM
Non-Interactive Zero-Knowledge Proof Systems
CRYPTO '87 A Conference on the Theory and Applications of Cryptographic Techniques on Advances in Cryptology
Direct Minimum-Knowledge Computations
CRYPTO '87 A Conference on the Theory and Applications of Cryptographic Techniques 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
A Perfect Zero-Knowledge Proof for a Problem Equivalent to Discrete Logarithm
CRYPTO '88 Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology
Certifying Cryptographic Tools: The Case of Trapdoor Permutations
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
Proofs that yield nothing but their validity and a methodology of cryptographic protocol design
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
Random self-reducibility and zero knowledge interactive proofs of possession of information
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Multiple non-interactive zero knowledge proofs based on a single random string
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
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In this work we study relations between secret sharing and perfect zero knowledge in the non-interactive model. Both secret sharing schemes and non-interactive zero knowledge are important cryptographic primitives with several applications in the management of cryptographic keys, in multi-party secure protocols, and many other areas. Secret sharing schemes are very well-studied objects while non-interactive perfect zero-knowledge proofs seem to be very elusive. In fact, since the introduction of the non-interactive model for zero knowledge, the only perfect zero-knowledge proof known was for quadratic non residues.In this work, we show that a large class of languages related to quadratic residuosity admits non-interactive perfect zero-knowledge proofs. More precisely, we give a protocol for proving non-interactively and in perfect zero knowledge the veridicity of any "threshold" statement where atoms are statements about the quadratic character of input elements. We show that our technique is very general and extend this result to any secret sharing scheme (of which threshold schemes are just an example).