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A New Algorithm for Solving the General Approximate Common Divisors Problem and Cryptanalysis of the FHE Based on the GACD problem
General approximate common divisors problems Fully homomorphic encryption Lattice
2016/1/26
In this paper, we propose a new algorithm for solving the general approximate common divisors (GACD) problems, which is based on lattice reduction algorithms on certain special lattices and linear equ...
Approximate common divisors via lattices
foundations / Coppersmith's algorithm lattice basis reduction approximate common divisors
2012/3/26
We analyze the multivariate generalization of Howgrave-Graham's algorithm for the approximate common divisor problem. In the $m$-variable case with modulus $N$ and approximate common divisor of size $...
Faster Algorithms for Approximate Common Divisors: Breaking Fully-Homomorphic-Encryption Challenges over the Integers
public-key cryptography / fully-homomorphic encryption cryptanalysis
2012/3/26
At EUROCRYPT '10, van Dijk, Gentry, Halevi and Vaikuntanathan presented simple fully-homomorphic encryption (FHE) schemes based on the hardness of approximate integer common divisors problems, which w...