Signature schemes based on the strong RSA assumption
CCS '99 Proceedings of the 6th ACM conference on Computer and communications security
On the generation of cryptographically strong pseudorandom sequences
ACM Transactions on Computer Systems (TOCS)
Foundations of Cryptography: Basic Tools
Foundations of Cryptography: Basic Tools
SIAM Journal on Computing
Efficient and Non-interactive Non-malleable Commitment
EUROCRYPT '01 Proceedings of the International Conference on the Theory and Application of Cryptographic Techniques: Advances in Cryptology
Non-Malleable Non-Interactive Zero Knowledge and Adaptive Chosen-Ciphertext Security
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Zero-knowledge proofs of knowledge without interaction
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
Zero-knowledge sets with short proofs
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
Algebraic construction for zero-knowledge sets
Journal of Computer Science and Technology
Independent zero-knowledge sets
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
Updatable zero-knowledge databases
ASIACRYPT'05 Proceedings of the 11th international conference on Theory and Application of Cryptology and Information Security
Mercurial commitments with applications to zero-knowledge sets
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
Mercurial commitments: minimal assumptions and efficient constructions
TCC'06 Proceedings of the Third conference on Theory of Cryptography
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The idea of Zero-Knowledge Sets (ZKS) was firstly proposed by Micali, Rabin and Kilian. It allows the prover to commit to a secret set and then prove either "x ∈ S" or "x ∉ S " without revealing any more knowledge of the set S. Afterwards, R.Gennaro defined the concept of independence for ZKS and gave two tree-based constructions. In this paper, we define the independence property for ZKS in a more flexible way than the definition of Gennaro's and prove that for ZKS, our independence implies non-malleability and vice versa. Then an independent ZKS scheme is constructed in an algebraic way by mapping values to unique primes, accumulating the set members and hiding the set. Comparing with the tree-based constructions: our scheme is more efficient while proving a value belongs (resp. not belongs) to the committed set; furthermore, the committed set is easier to update.