The knowledge complexity of interactive proof systems
SIAM Journal on Computing
A note on efficient zero-knowledge proofs and arguments (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
On the Composition of Zero-Knowledge Proof Systems
SIAM Journal on Computing
Probabilistic checking of proofs: a new characterization of NP
Journal of the ACM (JACM)
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
Non-Interactive and Information-Theoretic Secure Verifiable Secret Sharing
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
Proofs of Partial Knowledge and Simplified Design of Witness Hiding Protocols
CRYPTO '94 Proceedings of the 14th Annual International Cryptology Conference on Advances in Cryptology
PKC '01 Proceedings of the 4th International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
Short PCPs Verifiable in Polylogarithmic Time
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
Strengthening Zero-Knowledge Protocols Using Signatures
Journal of Cryptology
The PCP theorem by gap amplification
Journal of the ACM (JACM)
Delegating computation: interactive proofs for muggles
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
Discrete Applied Mathematics
Efficient Protocols for Set Membership and Range Proofs
ASIACRYPT '08 Proceedings of the 14th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Fully homomorphic encryption using ideal lattices
Proceedings of the forty-first annual ACM symposium on Theory of computing
Linear Algebra with Sub-linear Zero-Knowledge Arguments
CRYPTO '09 Proceedings of the 29th Annual International Cryptology Conference on Advances in Cryptology
Zero-Knowledge Proofs from Secure Multiparty Computation
SIAM Journal on Computing
Efficient concurrent zero-knowledge in the auxiliary string model
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Efficient proofs that a committed number lies in an interval
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Secure Vickrey auctions without threshold trust
FC'02 Proceedings of the 6th international conference on Financial cryptography
Sub-linear zero-knowledge argument for correctness of a shuffle
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
A fully homomorphic encryption scheme
A fully homomorphic encryption scheme
Structure-preserving signatures and commitments to group elements
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
Additive combinatorics and discrete logarithm based range protocols
ACISP'10 Proceedings of the 15th Australasian conference on Information security and privacy
Non-interactive zero-knowledge arguments for voting
ACNS'05 Proceedings of the Third international conference on Applied Cryptography and Network Security
Group to group commitments do not shrink
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
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We construct practical and efficient zero-knowledge arguments with sublinear communication complexity. The arguments have perfect completeness, perfect special honest verifier zero-knowledge and computational soundness. Our zero-knowledge arguments rely on two-tiered homomorphic commitments for which pairing-based constructions already exist. As a concrete application of our new zero-knowledge techniques, we look at the case of range proofs. To demonstrate a committed value belongs to a specific N-bit integer interval we only need to communicate $O(N^{\frac{1}{3}})$ group elements.