Trapdoors for hard lattices and new cryptographic constructions

@article{Gentry2007TrapdoorsFH,
  title={Trapdoors for hard lattices and new cryptographic constructions},
  author={Craig Gentry and Chris Peikert and Vinod Vaikuntanathan},
  journal={Proceedings of the fortieth annual ACM symposium on Theory of computing},
  year={2007}
}
We show how to construct a variety of "trapdoor" cryptographic tools assuming the worst-case hardness of standard lattice problems (such as approximating the length of the shortest nonzero vector to within certain polynomial factors). Our contributions include a new notion of trapdoor function with preimage sampling, simple and efficient "hash-and-sign" digital signature schemes, and identity-based encryption. A core technical component of our constructions is an efficient algorithm that, given… 

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