An efficient non-interactive statistical zero-knowledge proof system for quasi-safe prime products
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
REACT: Rapid Enhanced-Security Asymmetric Cryptosystem Transform
CT-RSA 2001 Proceedings of the 2001 Conference on Topics in Cryptology: The Cryptographer's Track at RSA
Improvement of Probabilistic Public Key Cryptosystems Using Discrete Logarithm
ICISC '01 Proceedings of the 4th International Conference Seoul on Information Security and Cryptology
Relations Among Notions of Security for Public-Key Encryption Schemes
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Secure Integration of Asymmetric and Symmetric Encryption Schemes
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
The Bit Security of Paillier's Encryption Scheme and Its Applications
EUROCRYPT '01 Proceedings of the International Conference on the Theory and Application 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
How to Enhance the Security of Public-Key Encryption at Minimum Cost
PKC '99 Proceedings of the Second International Workshop on Practice and Theory in Public Key Cryptography
Chosen-Ciphertext Security for Any One-Way Cryptosystem
PKC '00 Proceedings of the Third International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
PKC '01 Proceedings of the 4th International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
The Gap-Problems: A New Class of Problems for the Security of Cryptographic Schemes
PKC '01 Proceedings of the 4th International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
New Semantically Secure Public-Key Cryptosystems from the RSA-Primitive
PKC '02 Proceedings of the 5th International Workshop on Practice and Theory in Public Key Cryptosystems: Public Key Cryptography
DIGITALIZED SIGNATURES AND PUBLIC-KEY FUNCTIONS AS INTRACTABLE AS FACTORIZATION
DIGITALIZED SIGNATURES AND PUBLIC-KEY FUNCTIONS AS INTRACTABLE AS FACTORIZATION
Proving in zero-knowledge that a number is the product of two safe primes
EUROCRYPT'99 Proceedings of the 17th 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
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Choi et al. proposed the modified Paillier cryptosystem (M-Paillier cryptosystem). They use a special public-key g 驴 ZZ/nZZ such that g驴(n) = 1+n mod n2, where n is the RSA modulus. The distribution of the public key g is different from that of the original one. In this paper, we study the security of the usage of the public key. Firstly, we prove that the one-wayness of the M-Paillier cryptosystem is as intractable as factoring the modulus n, if the public key g can be generated only by the public modulus n. Secondly, we prove that the oracle that can generate the public-key factors the modulus n. Thus the public keys cannot be generated without knowing the factoring of n. The Paillier cryptosystem can use the public key g = 1+n, which is generated only from the public modulus n. Thirdly, we propose a chosen ciphertext attack against the M-Paillier cryptosystem. Our attack can factor the modulus n by only one query to the decryption oracle. This type of total breaking attack has not been reported for the original Paillier cryptosystem. Finally, we discuss the relationship between the M-Paillier cryptosystem and the Okamoto-Uchiyama scheme.