How to prove yourself: practical solutions to identification and signature problems
Proceedings on Advances in cryptology---CRYPTO '86
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
Efficient Group Signature Schemes for Large Groups (Extended Abstract)
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
Efficient Zero-Knowledge Proofs of Knowledge Without Intractability Assumptions
PKC '00 Proceedings of the Third International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
PKC '01 Proceedings of the 4th International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
On Defining Proofs of Knowledge
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
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
A secure and optimally efficient multi-authority election scheme
EUROCRYPT'97 Proceedings of the 16th annual 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
A verifiable random function with short proofs and keys
PKC'05 Proceedings of the 8th international conference on Theory and Practice in Public Key Cryptography
Security analysis of the strong diffie-hellman problem
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
Secure authenticated comparisons
ACNS'11 Proceedings of the 9th international conference on Applied cryptography and network security
Efficient zero-knowledge arguments from two-tiered homomorphic commitments
ASIACRYPT'11 Proceedings of the 17th international conference on The Theory and Application of Cryptology and Information Security
A secure and efficient proof of integer in an interval range
IMACC'11 Proceedings of the 13th IMA international conference on Cryptography and Coding
Progression-free sets and sublinear pairing-based non-interactive zero-knowledge arguments
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
Scaling privacy guarantees in code-verification elections
Vote-ID'13 Proceedings of the 4th international conference on E-Voting and Identity
A more efficient computationally sound non-interactive zero-knowledge shuffle argument
Journal of Computer Security - Advances in Security for Communication Networks
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We show how to express an arbitrary integer interval I = [0,H] as a sumset I =Σi=1l Gi * [0, u - 1] + [0, H′] of smaller integer intervals for some small values l, u, and H′ u - 1, where b*A = {ba: a ∈ A} and A+B = {a+b: a ∈ A ∧ b ∈ B}. We show how to derive such expression of I as a sumset for any value of 1 u H, and in particular, how the coefficients Gi can be found by using a nontrivial but efficient algorithm. This result may be interesting by itself in the context of additive combinatorics. Given the sumset-representation of I, we show how to decrease both the communication complexity and the computational complexity of the recent pairing-based range proof of Camenisch, Chaabouni and shelat from ASIACRYPT 2008 by a factor of 2. Our results are important in applications like e-voting where a voting server has to verify thousands of proofs of e-vote correctness per hour. Therefore, our new result in additive combinatorics has direct relevance in practice.