A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Protocols for secure computations
SFCS '82 Proceedings of the 23rd 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
Public-key cryptosystems based on composite degree residuosity classes
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Implementing Gentry's fully-homomorphic encryption scheme
EUROCRYPT'11 Proceedings of the 30th Annual international conference on Theory and applications of cryptographic techniques: advances in cryptology
Efficient Fully Homomorphic Encryption from (Standard) LWE
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
(Leveled) fully homomorphic encryption without bootstrapping
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
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
Fully homomorphic encryption with polylog overhead
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
New directions in cryptography
IEEE Transactions on Information Theory
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Recently, Brenner et al. proposed a symmetric somewhat homomorphic encryption scheme and applied it to solve some practical problems, such as the Millionaires' problem, which only need to evaluate circuits of limited depth. It is claimed that the security of their scheme is built on the hardness of integer factorization. In this paper, we use the Euclidean Greatest Common Divisor (GCD) algorithm to perform cryptanalysis on Brenner et al.'s scheme. We present several algorithms to find the secret key of their scheme. Our experiments have shown that our cryptanalysis is feasible and efficient.