General public key residue cryptosystems and mental poker protocols
EUROCRYPT '90 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
Random oracles are practical: a paradigm for designing efficient protocols
CCS '93 Proceedings of the 1st ACM conference on Computer and communications security
A new public key cryptosystem based on higher residues
CCS '98 Proceedings of the 5th ACM conference on Computer and communications security
Signature schemes based on the strong RSA assumption
ACM Transactions on Information and System Security (TISSEC)
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
CT-RSA '02 Proceedings of the The Cryptographer's Track at the RSA Conference on Topics 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
Statistical Zero Knowledge Protocols to Prove Modular Polynomial Relations
CRYPTO '97 Proceedings of the 17th 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
Efficient Public-Key Cryptosystems Provably Secure Against Active Adversaries
ASIACRYPT '99 Proceedings of the International Conference on the Theory and Applications 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
PKC '01 Proceedings of the 4th International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
The Cramer-Shoup Strong-RSASignature Scheme Revisited
PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: Public Key Cryptography
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
DIGITALIZED SIGNATURES AND PUBLIC-KEY FUNCTIONS AS INTRACTABLE AS FACTORIZATION
DIGITALIZED SIGNATURES AND PUBLIC-KEY FUNCTIONS AS INTRACTABLE AS FACTORIZATION
A robust and verifiable cryptographically secure election scheme
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
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
Public-key cryptosystems based on composite degree residuosity classes
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
A signature scheme with efficient protocols
SCN'02 Proceedings of the 3rd international conference on Security in communication networks
Group signatures: better efficiency and new theoretical aspects
SCN'04 Proceedings of the 4th international conference on Security in Communication Networks
Proceedings of the 2006 international conference on Wireless communications and mobile computing
Homomorphic encryption and secure comparison
International Journal of Applied Cryptography
An Efficient On-Line/Off-Line Signature Scheme without Random Oracles
CANS '08 Proceedings of the 7th International Conference on Cryptology and Network Security
A correction to 'efficient and secure comparison for on-line auctions'
International Journal of Applied Cryptography
Verifiable shuffle of large size ciphertexts
PKC'07 Proceedings of the 10th international conference on Practice and theory in public-key cryptography
Efficient and secure comparison for on-line auctions
ACISP'07 Proceedings of the 12th Australasian conference on Information security and privacy
Online/offline signature schemes for devices with limited computing capabilities
CT-RSA'08 Proceedings of the 2008 The Cryptopgraphers' Track at the RSA conference on Topics in cryptology
A short signature scheme from the RSA family
ISC'10 Proceedings of the 13th international conference on Information security
Cryptanalysis of the RSA subgroup assumption from TCC 2005
PKC'11 Proceedings of the 14th international conference on Practice and theory in public key cryptography conference on Public key cryptography
Chosen ciphertext secure encryption under factoring assumption revisited
PKC'11 Proceedings of the 14th international conference on Practice and theory in public key cryptography conference on Public key cryptography
Efficient fail-stop signatures from the factoring assumption
ISC'11 Proceedings of the 14th international conference on Information security
Non-interactive zero-knowledge arguments for voting
ACNS'05 Proceedings of the Third international conference on Applied Cryptography and Network Security
Perfect non-interactive zero knowledge for NP
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
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We demonstrate the cryptographic usefulness of a small subgroup of $\mathbb{Z}_{n}^{*}$ of hidden order. Cryptographic schemes for integer commitment and digital signatures have been suggested over large subgroups of $\mathbb{Z}_{n}^{*}$, by reducing the order of the groups we obtain quite similar but more efficient schemes. The underlying cryptographic assumption resembles the strong RSA assumption. We analyze a signature scheme known to be secure against known message attack and prove that it is secure against adaptive chosen message attack. This result does not necessarily rely on the use of a small subgroup, but the small subgroup can make the security reduction tighter. We also investigate the case where $\mathbb{Z}_{n}^{*}$ has semi-smooth order. Using a new decisional assumption, related to high residuosity assumptions, we suggest a homomorphic public-key cryptosystem.