A public key cryptosystem and a signature scheme based on discrete logarithms
Proceedings of CRYPTO 84 on Advances in cryptology
Secret sharing homomorphisms: keeping shares of a secret secret
Proceedings on Advances in cryptology---CRYPTO '86
Receipt-free secret-ballot elections (extended abstract)
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
A new public key cryptosystem based on higher residues
CCS '98 Proceedings of the 5th ACM conference on Computer and communications security
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Key Distribution Protocol for Digital Mobile Communication Systems
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
Secure Voting Using Partially Compatible Homomorphisms
CRYPTO '94 Proceedings of the 14th Annual International Cryptology Conference on Advances in Cryptology
Multiparty Computation from Threshold Homomorphic Encryption
EUROCRYPT '01 Proceedings of the International Conference on the Theory and Application of Cryptographic Techniques: Advances in Cryptology
PKC '01 Proceedings of the 4th International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
M+1-st Price Auction Using Homomorphic Encryption
PKC '02 Proceedings of the 5th International Workshop on Practice and Theory in Public Key Cryptosystems: Public Key Cryptography
Non-Interactive CryptoComputing For NC1
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Probabilistic encryption & how to play mental poker keeping secret all partial information
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Verifiable secret-ballot elections
Verifiable secret-ballot elections
ITCC '05 Proceedings of the International Conference on Information Technology: Coding and Computing (ITCC'05) - Volume I - Volume 01
A survey of homomorphic encryption for nonspecialists
EURASIP Journal on Information Security
A robust and verifiable cryptographically secure election scheme
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Fully homomorphic encryption using ideal lattices
Proceedings of the forty-first annual ACM symposium on Theory of computing
Multi-authority secret-ballot elections with linear work
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
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
Public-key cryptosystems based on composite degree residuosity classes
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Efficient receipt-free voting based on homomorphic encryption
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Proceedings of the 2010 ACM Symposium on Applied Computing
A Verifiable Secret Shuffle of Homomorphic Encryptions
Journal of Cryptology
Toward basing fully homomorphic encryption on worst-case hardness
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
i-hop homomorphic encryption and rerandomizable Yao circuits
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
A generalization of Paillier’s public-key system with applications to electronic voting
International Journal of Information Security - Special Issue on Special Purpose Protocols;Guest Editor:Moti Yung
Homomorphic cryptosystems based on subgroup membership problems
Mycrypt'05 Proceedings of the 1st international conference on Progress in Cryptology in Malaysia
Evaluating 2-DNF formulas on ciphertexts
TCC'05 Proceedings of the Second international conference on Theory of Cryptography
ESORICS'05 Proceedings of the 10th European conference on Research in Computer Security
Fully homomorphic encryption with relatively small key and ciphertext sizes
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
Fully homomorphic encryption over the integers
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
Non-interactive zero-knowledge from homomorphic encryption
TCC'06 Proceedings of the Third conference on Theory of Cryptography
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In 1994, Josh Benaloh proposed a probabilistic homomorphic encryption scheme, enhancing the poor expansion factor provided by Goldwasser and Micali's scheme. Since then, numerous papers have taken advantage of Benaloh's homomorphic encryption function, including voting schemes, private multi-party trust computation, non-interactive verifiable secret sharing, online poker. In this paper we show that the original description of the scheme is incorrect, because it can result in ambiguous decryption of ciphertexts. Then we show on several applications that a bad choice in the key generation phase of Benaloh's scheme has a real impact on the behaviour of the application. For instance in an e-voting protocol, it can inverse the result of an election. Our main contribution is a corrected description of the scheme (we provide a complete proof of correctness). Moreover we also compute the probability of failure of the original scheme. Finally we show how to formulate the security of the corrected scheme in a generic setting suitable for several homomorphic encryptions.