Name
Abstract | ||
|---|---|---|
In 2010, van Dijk, Gentry, Halevi, and Vaikuntanathan described the first fully homomorphic encryption over the integers, called DGHV. The scheme is based on a set of m public integers ci = pqi + ri, i = 1, · · · ,m, where the integers p, qi and ri are secret. In this paper, we describe two lattice-based attacks on DGHV. The first attack is applicable when r1 = 0 and the public integers ci satisfy a linear equation a2c2 + . . .+amcm = a1q1 for suitably small integers ai, i = 2, . . . ,m. The second attack works when the positive integers qi satisfy a linear equation a1q1 + . . . + amqm = 0 for suitably small integers ai, i = 1, . . . ,m. We further apply our methods for the DGHV recommended parameters as specified in the original work of van Dijk, Gentry, Halevi, and Vaikuntanathan. |
Year | Venue | Field |
|---|---|---|
2015 | IACR Cryptology ePrint Archive | Integer,Linear equation,Discrete mathematics,Homomorphic encryption,Lattice (order),Mathematics |
DocType | Volume | Citations |
Journal | 2015 | 0 |
PageRank | References | Authors |
0.34 | 5 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Abderrahmane Nitaj | 1 | 72 | 15.00 |
| tajjeeddine rachidi | 2 | 13 | 4.70 |