A discrete logarithm implementation of perfect zero-knowledge blobs
Journal of Cryptology
A new public key cryptosystem based on higher residues
CCS '98 Proceedings of the 5th ACM conference on Computer and communications security
Paillier's cryptosystem revisited
CCS '01 Proceedings of the 8th ACM conference on Computer and Communications Security
The Representation Problem Based on Factoring
CT-RSA '02 Proceedings of the The Cryptographer's Track at the RSA Conference on Topics in Cryptology
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
Improved Online/Offline Signature Schemes
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
Fast RSA-Type Cryptosystem Modulo pkq
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
On the Security of Joint Signature and Encryption
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
Open problems in number theoretic complexity, II
ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
A robust and verifiable cryptographically secure election scheme
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
ESIGN: an efficient digital signature implementation for smart cards
EUROCRYPT'91 Proceedings of the 10th annual international conference on Theory and application of cryptographic techniques
Public-key cryptosystems based on composite degree residuosity classes
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Public-Key Cryptosystems with Primitive Power Roots of Unity
ACISP '08 Proceedings of the 13th Australasian conference on Information Security and Privacy
Divisible On-Line/Off-Line Signatures
CT-RSA '09 Proceedings of the The Cryptographers' Track at the RSA Conference 2009 on Topics in Cryptology
A New Rabin-type Trapdoor Permutation Equivalent to Factoring
Electronic Notes in Theoretical Computer Science (ENTCS)
New online/offline signature schemes without random oracles
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
Efficient multiple-collision trapdoor hash family
Security and Communication Networks
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In 1998/99, T. Okamoto and S. Uchiyama on the one hand and P. Paillier on the other hand introduced homomorphic encryption schemes semantically secure against passive adversaries (IND-CPA). Both schemes follow in the footsteps of Goldwasser-Micali, Benaloh-Fischer and Naccache-Stern cryptosystems, and yield their improvements above the latter by changing the group structure. Paillier’s scheme works in the group ${\mathbb Z}^{\times}_{n^{2}}$where n is an RSA modulus, whilst Okamoto-Uchiyama is located in the group ${\mathbb Z}^{\times}_{n}$for n of p2q type. The new schemes attracted much attention because of their rich mathematical structure. It is notable that Okamoto-Uchiyama is one-way under the p2q factoring assumption, whilst there is no reduction known from the one-wayness of Paillier’s scheme to a standard computational assumption. In this paper we point out that the combination of both techniques yields a new scheme that inherits all the nice properties of Paillier’s scheme and that is one-way under the p2q factoring assumption. The one-wayness is based on a new trapdoor one-way function which might be of independent interest. In addition, we show how to construct trapdoor commitment schemes with practical applications based on our new scheme and on the trapdoor function. Among other things, we propose a trapdoor commitment scheme that perfectly meets the requirements to construct Shamir-Tauman on-line/off-line signatures.