A key-exchange system based on imaginary quadratic fields
Journal of Cryptology
One-way accumulators: a decentralized alternative to digital signatures
EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
Accountable certificate management using undeniable attestations
Proceedings of the 7th ACM conference on Computer and communications security
Eliminating counterevidence with applications to accountable certificate management
Journal of Computer Security
Efficient Accumulators without Trapdoor Extended Abstracts
ICICS '99 Proceedings of the Second International Conference on Information and Communication Security
Dynamic Accumulators and Application to Efficient Revocation of Anonymous Credentials
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
How to Time-Stamp a Digital Document
CRYPTO '90 Proceedings of the 10th Annual International Cryptology Conference on Advances in Cryptology
Time-Stamping with Binary Linking Schemes
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Generic Lower Bounds for Root Extraction and Signature Schemes in General Groups
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
Reducing Logarithms in Totally Non-maximal Imaginary Quadratic Orders to Logarithms in Finite Fields
ASIACRYPT '99 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Security of Cryptosystems Based on Class Groups of Imaginary Quadratic Orders
ASIACRYPT '00 Proceedings of the 6th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
A Statistically-Hiding Integer Commitment Scheme Based on Groups with Hidden Order
ASIACRYPT '02 Proceedings of the 8th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Blind, Auditable Membership Proofs
FC '00 Proceedings of the 4th International Conference on Financial Cryptography
Optimally Efficient Accountable Time-Stamping
PKC '00 Proceedings of the Third International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
Asymptotically Fast Discrete Logarithms in Quadratic Number Fields
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
Universal Accumulators with Efficient Nonmembership Proofs
ACNS '07 Proceedings of the 5th international conference on Applied Cryptography and Network Security
Strong Accumulators from Collision-Resistant Hashing
ISC '08 Proceedings of the 11th international conference on Information Security
An Accumulator Based on Bilinear Maps and Efficient Revocation for Anonymous Credentials
Irvine Proceedings of the 12th International Conference on Practice and Theory in Public Key Cryptography: PKC '09
Collision-free accumulators and fail-stop signature schemes without trees
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
Secure hash-and-sign signatures without the random oracle
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Efficient non-interactive proof systems for bilinear groups
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
A Course in Computational Algebraic Number Theory
A Course in Computational Algebraic Number Theory
Accumulators from bilinear pairings and applications
CT-RSA'05 Proceedings of the 2005 international conference on Topics in Cryptology
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Cryptographic accumulators are well-known to be useful in many situations. However, the most efficient accumulator (the RSA accumulator) it is not secure against a certificate authority who has herself selected the RSA modulus n. We generalize previous work and define the root accumulator in modules over Euclidean rings. We prove that the root accumulator is secure under two different pairs of assumptions on the module family and on the used hash function. Finally, we propose a new instantiation of the root accumulator, based on class groups of imaginary quadratic order, that combines the best properties of previous solutions. It has short (non)membership proofs like the RSA accumulator, and at the same time it is secure against a malicious certificate authority. Up to this point, this seems to be the only unique application of class groups of imaginary quadratic orders, and we hope that this paper will motivate more research on cryptography in the said groups.