How to prove all NP-statements in zero-knowledge, and a methodology of cryptographic protocol design
Proceedings on Advances in cryptology---CRYPTO '86
How to prove yourself: practical solutions to identification and signature problems
Proceedings on Advances in cryptology---CRYPTO '86
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Threshold Ring Signatures and Applications to Ad-hoc Groups
CRYPTO '02 Proceedings of the 22nd 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
ID-Based Blind Signature and Ring Signature from Pairings
ASIACRYPT '02 Proceedings of the 8th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
1-out-of-n Signatures from a Variety of Keys
ASIACRYPT '02 Proceedings of the 8th 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 and generalized group signatures
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
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Abe et al. proposed the methodology of ring signature (RS) design in 2002 and showed how to construct RS with a mixture of public keys based on factorization and/or discrete logarithms. Their methodology cannot be applied to knowledge signatures (KS) using the Fiat-Shamir heuristic and cut-and-choose techniques, for instance, the Goldreich KS. This paper presents a more general construction of RS from various public keys if there exists a secure signature using such a public key and an efficient algorithm to forge the relation to be checked if the challenges in such a signature are known in advance. The paper shows how to construct RS based on the graph isomorphism problem (GIP). Although it is unknown whether or not GIP is NP-Complete, there are no known arguments that it can be solved even in the quantum computation model. Hence, the scheme has a better security basis and it is plausibly secure against quantum adversaries.